[119] **viXra:1803.0735 [pdf]**
*submitted on 2018-03-30 15:55:52*

**Authors:** Huda E. Khalid, Ahmed K. Essa, A. A. Salama

**Comments:** 115 Pages.

ان التحليل النيوتروسوفكي يعد تعميما لتحليل المجموعة ، والتي بدورها تعد تعميما لتحليل الفترة ، ان الحسبان النيوتروسوفكي التمهيدي يشير الى قيم ثابتة للاتعيين ، بينما حسبان التفاضل والتكامل النيوتروسوفكي يمكن اعتبارها رياضيات ذات لاتعيين متغير ، مبادئ حساب التفاضل والتكامل النيوتروسوفي وحساب التفاضل والتكامل النيوتروسوفكي يمكن تطويرهما بطرق عديدة ، وذلك بالاعتماد على انواع اللاتعيين التي تملكها المسألة كذلك بالاعتماد على الطرق المستخدمة في التعامل معها . قدمنا في هذا الكتاب بعض الامثلة عن اللاتعيينات الخاصة ، لكن يوجد الكثير من اللاتعيينات في حياتنا اليومية ، يجب علينا دراستها واعادة حلها باستخدام طرق مشابهة او طرق مختلفة عن التي ذكرناها . لذلك نحن بحاجة الى مزيد من الابحاث العلمية في حقل النيوتروسوفك . يمكن مستقبلا دراسة حسبان التفاضل والتكامل النيوتروسوفكي الجزئي من خلال ابحاث متقدمة في هذا المضمار . قدم المؤلف في هذا الكتاب ولاول مرة افكار لكل من شبه الغاية النيوتروسوفية ، وشبة الاستمرارية النيوتروسوفكية بطرق مختلفة عن شبه – الاستمرارية التقليدية, وشبه المشتقة النيوتروسوفكية, وشبه التكامل النيوتروسوفكي بطرق تختلف عن حسبان التفاضل والتكامل الجزئي الاعتيادي ، بالاضافة الى التعاريف التقليدية للغاية والاستمرارية والمشتقة والتكامل تباعا.

**Category:** General Mathematics

[118] **viXra:1803.0633 [pdf]**
*replaced on 2018-03-26 06:48:03*

**Authors:** Koji KOBAYASHI

**Comments:** 12 Pages.

This paper describes about "Almost all monotone circuit family" and introduce its interesting advantages to measuring problem complexity.
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)).
This "NNF Circuit family" have good characteristic which present each accept input exclusivity and symmetry. Each input make some INPUT-gate and NOT-gate output 1 which set is different from another input, and meet these output in OR-gate and finally connect (specified) OUTPUT-gate. That is, NNF circuit start accept input that exclusive each other, and meet each input as symmetry input step by step and finally goal same output. Especially, some different variables which sandwich reject inputs correspond to unique AND-gate. That is, we can measure problem complexity by using different variables of accept inputs. For examples, such number of different variables type of negation HornSAT is at most polynomial size. This is one of reason that we can compute P problem easily.

**Category:** General Mathematics

[117] **viXra:1803.0622 [pdf]**
*submitted on 2018-03-23 07:18:35*

**Authors:** Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri, Florentin Smarandache

**Comments:** 15 Pages.

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers.

**Category:** General Mathematics

[116] **viXra:1803.0620 [pdf]**
*submitted on 2018-03-23 07:20:51*

**Authors:** Nabeela Ishfaq, Sidra Sayed, Muhammad Akram, Florentin Smarandache

**Comments:** 19 Pages.

Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information that exists in real life.

**Category:** General Mathematics

[115] **viXra:1803.0619 [pdf]**
*submitted on 2018-03-23 07:21:50*

**Authors:** Mehmet Serhat CAN, Ömerül Faruk ÖZGÜVEN

**Comments:** 12 Pages.

Bu çalışmada, giriş değişkenlerinin nötrosofik küme teorisindeki doğru (T), belirsiz (I) ve yanlış (F) üyelik fonksiyonları kullanılarak, evrensel küme üzerindeki dağılımlarının gruplandırıldığı nötrosofik üyelik değerli bulanık mantık-PID (NBMD-PID) denetleyici ile geleneksel bulanık mantık-PID denetleyicinin (BMD-PID) gerçek zamanlı karşılaştırılması yapılmıştır.

**Category:** General Mathematics

[114] **viXra:1803.0617 [pdf]**
*submitted on 2018-03-23 07:36:28*

**Authors:** Shawkat Alkhazaleh, Ayman A. Hazaymeh

**Comments:** 8 Pages.

In this work we use the concept of a ’n’-valued refined neutrosophic soft sets and its
properties to solve decision making problems, Also a similarity measure between two ’n’-
valued refined neutrosophic soft sets are proposed. A medical diagnosis (MD) method is
established for ’n’-valued refined neutrosophic soft set setting using similarity measures.
Lastly a numerical example is given to demonstrate the possible application of similarity measures in medical diagnosis (MD).

**Category:** General Mathematics

[113] **viXra:1803.0616 [pdf]**
*submitted on 2018-03-23 07:37:21*

**Authors:** J. Malarvizhi, G.Divya

**Comments:** 8 Pages.

In this paper we define Antipodal single valued neutrosophic graph and some Isomorphic properties of Antipodal single valued neutrosophic graph are discussed.

**Category:** General Mathematics

[112] **viXra:1803.0615 [pdf]**
*submitted on 2018-03-23 07:38:55*

**Authors:** Sudip Bhattacharyya, Bikas Koli Roy, Pinaki Majumdar

**Comments:** 21 Pages.

An Interval Neutrosophic set (INS) is an instance of a Neutrosophic set and also an emerging tool
for uncertain data processing in real scientific and engineering applications. In this paper, several distance and similarity measures between two Interval Neutrosophic sets have been discussed.

**Category:** General Mathematics

[111] **viXra:1803.0613 [pdf]**
*submitted on 2018-03-23 07:41:10*

**Authors:** Süleyman ŞENYURT, Gülşah KAYA

**Comments:** 10 Pages.

In this paper, we defined the neutrosophic continuous function, neutrosophic open function, neutrosophic closed function and neutrosophic homeomorphism on neutrosophic topological spaces. Then, we give some characteristics of these functions; neutrosophic closed function is a neutrosophic continuous function, neutrosophic open function is a neutrosophic continuous function.

**Category:** General Mathematics

[110] **viXra:1803.0612 [pdf]**
*submitted on 2018-03-23 07:42:46*

**Authors:** Tuhin Bera, Nirmal Kumar Mahapatra

**Comments:** 21 Pages.

In this paper, the notion of neutrosophic soft metric space (NSMS) is introduced in terms of neutrosophic soft points and several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft metric space is defined and illustrated by examples. Further, the concept of Cauchy sequence in NSMS is developed and some related theorems have been established, too.

**Category:** General Mathematics

[109] **viXra:1803.0611 [pdf]**
*submitted on 2018-03-23 07:43:45*

**Authors:** P. Thirunavukarasu, R. Suresh

**Comments:** 8 Pages.

In this paper, we introduced a new concept of complex neutrosophic graphs called regular complex neutrosophic graph with degree for complex neutrosophic graphs and studied some properties of this new concept. The concept of regular complex
neutrosophic graph is an extension of complex neutrosophic fuzzy graphs of type.

**Category:** General Mathematics

[108] **viXra:1803.0610 [pdf]**
*submitted on 2018-03-23 07:44:40*

**Authors:** Yan-Ling Bao, Hai-Long Yang

**Comments:** 14 Pages.

Neutrosophic set (NS) theory was originally established by Smarandache for handling indeterminate and inconsistent information. In this paper, we introduce single valued neutrosophic refined rough sets by combining single valued neutrosophic refined sets with rough sets and further study the hybrid model from two perspectives—constructive viewpoint and axiomatic viewpoint.

**Category:** General Mathematics

[107] **viXra:1803.0603 [pdf]**
*submitted on 2018-03-23 07:53:48*

**Authors:** Samah Ibrahim Abdel Aal, Mahmoud M. A. Abd Ellatif, Mohamed Monir Hassan

**Comments:** 14 Pages.

One of the most important reasons for information systems failure is lack of quality. Information Systems Quality (ISQ) evaluation is important to prevent the lack of quality. ISQ evaluation is one of the most important Multi-Criteria Decision Making (MCDM) problems.

**Category:** General Mathematics

[106] **viXra:1803.0601 [pdf]**
*submitted on 2018-03-23 07:55:53*

**Authors:** Abteen Ijadi Maghsoodi, Gelayol Abouhamzeh, Mohammad Khalilzadeh, Edmundas Kazimieras Zavadskas

**Comments:** 21 Pages.

The selection process of appropriate Performance Appraisal (PA) methods for organizations in today’s dynamic and agile environments along with its funding scales is a complex problem.

**Category:** General Mathematics

[105] **viXra:1803.0599 [pdf]**
*submitted on 2018-03-23 07:58:48*

**Authors:** Sindhu Saranya, V. Ellappan

**Comments:** 10 Pages.

Segmenting blood vessel from the retinal image is important for detecting many retinal vascular disorders. Diseases which are all affecting the blood vessels of the eye are known as Retinal vascular disorders.

**Category:** General Mathematics

[104] **viXra:1803.0598 [pdf]**
*submitted on 2018-03-23 07:59:39*

**Authors:** M.Kaviyarasu, K.Indhira

**Comments:** 8 Pages.

The aim of the paper is to investigate the relationship between BCK/BCIalgebras
and other algebras namely d-algebras, Q-algebras-BCH-algebras- TM-algebras-INK-algebras and we introduce some algebraic system.

**Category:** General Mathematics

[103] **viXra:1803.0597 [pdf]**
*submitted on 2018-03-23 08:00:55*

**Authors:** Sidra Sayed, Nabeela Ishfaq, Muhammad Akram, Florentin Smarandache

**Comments:** 20 Pages.

A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough
neutrosophic sets to graphs.

**Category:** General Mathematics

[102] **viXra:1803.0593 [pdf]**
*submitted on 2018-03-23 08:08:13*

**Authors:** V.Krishnaraj, R.Vikramaprasad, R.Dhavaseelan

**Comments:** 8 Pages.

In this paper, we introduce the concepts of length, distance, eccentricity, radius, diameter, status, total status, median and central vertex of a single valued neutrosophic graph. We present the concept of self-centered single valued neutrosophic graph. We investigated some properties of self-centered single valued neutrosophic graphs.

**Category:** General Mathematics

[101] **viXra:1803.0590 [pdf]**
*submitted on 2018-03-23 08:10:11*

**Authors:** Said Broumi, Mohamed Talea, Florentin Smarandache, Kishore Kumar P.K.

**Comments:** 6 Pages.

single valued neutrosophic graph is a generalized
structure of fuzzy graph, intuitionistic fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs
and intuitionistic fuzzy graphs.

**Category:** General Mathematics

[100] **viXra:1803.0584 [pdf]**
*submitted on 2018-03-23 08:16:05*

**Authors:** J.Dhivya, B.Sridevi

**Comments:** 9 Pages.

Neutrosophic set (NS) is very useful to express incomplete, uncertainty, and inconsistent information in a more general way. In the
modern medical technologies, each element can be expressed as NS having different truth – membership, indeterminacy – membership, and
falsity – membership degrees.

**Category:** General Mathematics

[99] **viXra:1803.0583 [pdf]**
*submitted on 2018-03-23 08:17:19*

**Authors:** Xin Li, Xiaohong Zhang

**Comments:** 15 Pages.

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of
possible values designed by truth, indeterminacy, and falsity membership hesitant functions.

**Category:** General Mathematics

[98] **viXra:1803.0569 [pdf]**
*submitted on 2018-03-23 08:34:24*

**Authors:** Harish Garg, Nancy

**Comments:** 18 Pages.

Neutrosophic sets (NS) contain the three ranges: truth, indeterminacy, and falsity membership degrees,and are very useful for describing and handling the uncertainties in the real life problem.

**Category:** General Mathematics

[97] **viXra:1803.0563 [pdf]**
*submitted on 2018-03-23 08:42:30*

**Authors:** E. M. Solouma

**Comments:** 16 Pages.

In Smarandache geometry, a regular non-null curve in Minkowski 3-space, whose position vector is collected by the Frenet frame vectors of other regular non-null curve, is said to be
Smarandache curve.

**Category:** General Mathematics

[96] **viXra:1803.0562 [pdf]**
*submitted on 2018-03-23 08:43:57*

**Authors:** Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Florentin Smarandache, Manjeet Singh

**Comments:** 9 Pages.

The concept of single valued neutrosophic graphs (SVNGs) generalizes the concept of fuzzy graphs and intuitionistic fuzzy graphs. The purpose of this research paper is to define different types of strong degrees in SVNGs and introduce novel concepts, such as the vertex truth-membership, vertex indeterminacy-membership and falsity-membership sequence in SVNG with proof and numerical illustrations.

**Category:** General Mathematics

[95] **viXra:1803.0561 [pdf]**
*submitted on 2018-03-23 08:45:12*

**Authors:** Florentin Smarandache, Jun Ye

**Comments:** 4 Pages.

Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to
“Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489),
located in Basel, Switzerland, was a success.

**Category:** General Mathematics

[94] **viXra:1803.0560 [pdf]**
*submitted on 2018-03-23 08:46:35*

**Authors:** Edmundas Kazimieras Zavadskas, Jurgita Antucheviciene, Tatjana Vilutiene, Hojjat Adeli

**Comments:** 21 Pages.

Sustainable decision-making in civil engineering, construction and building technology can be supported by fundamental scientific achievements and multiple-criteria decision-making (MCDM) theories.

**Category:** General Mathematics

[93] **viXra:1803.0558 [pdf]**
*submitted on 2018-03-23 08:51:29*

**Authors:** Marie Truelove, Maria Vasardani, Stephan Winter

**Comments:** 13 Pages.

This paper demonstrates a framework of processes for identifying potential witnesses of events from evidence they post to social media.

**Category:** General Mathematics

[92] **viXra:1803.0557 [pdf]**
*submitted on 2018-03-23 08:52:43*

**Authors:** Ashraf Al-Quran, Nasruddin Hassan

**Comments:** 14 Pages.

This paper presents a novel complex neutrosophic soft expert set (CNSES) concept. The range of values of CNSES is extended to the unit circle in the complex plane by adding an additional term called the phase term which describes
CNSES’s elements in terms of the time aspect.

**Category:** General Mathematics

[91] **viXra:1803.0554 [pdf]**
*submitted on 2018-03-23 08:56:25*

**Authors:** Dragisa STANUJKIC, Edmundas Kazimieras ZAVADSKAS, Darjan KARABASEVIC, Florentin SMARANDACHE, Zenonas TURSKIS

**Comments:** 18 Pages.

The weights of evaluation criteria could have a significant impact on the results obtained by
applying multiple criteria decision-making methods.

**Category:** General Mathematics

[90] **viXra:1803.0553 [pdf]**
*submitted on 2018-03-23 08:57:29*

**Authors:** Andrei-Lucian Drăgoi

**Comments:** 32 Pages.

This article proposes a synthesized classification of some Goldbach-like conjectures, including those which are “stronger” than the Binary Goldbach’s Conjecture (BGC) and launches a new generalization of BGC briefly called “the Vertical Binary Goldbach’s Conjecture” (VBGC), which is essentially a metaconjecture, as VBGC states an infinite number of conjectures stronger than BGC, which all apply on
“iterative” primes with recursive prime indexes (i-primeths).

**Category:** General Mathematics

[89] **viXra:1803.0551 [pdf]**
*submitted on 2018-03-23 08:59:08*

**Authors:** Lavinia Corina Ciungu

**Comments:** 21 Pages.

In this paper we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute.

**Category:** General Mathematics

[88] **viXra:1803.0548 [pdf]**
*submitted on 2018-03-23 09:02:07*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 11 Pages.

In recent years, the Big Bang as described by the Lambda CDM-Standard Model Cosmology has become widely accepted by majority of physics and cosmology communities.

**Category:** General Mathematics

[87] **viXra:1803.0542 [pdf]**
*submitted on 2018-03-23 06:12:38*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 2 Pages.

Although virus is widely known to significantly affect many biological form of life, its physical model is quite rare. In this regard, experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing.

**Category:** General Mathematics

[86] **viXra:1803.0541 [pdf]**
*submitted on 2018-03-23 06:14:05*

**Authors:** JieWang, Xiyue Tang, Guiwu Wei

**Comments:** 15 Pages.

In this article, we expand the dual generalized weighted BM (DGWBM) and dual generalized weighted geometric Bonferroni mean (DGWGBM) operator with single valued neutrosophic numbers (SVNNs) to propose the dual generalized single-valued neutrosophic number WBM (DGSVNNWBM) operator and dual generalized single-valued neutrosophic numbers WGBM
(DGSVNNWGBM) operator. Then, the multiple attribute decision making (MADM) methods are
proposed with these operators. In the end, we utilize an applicable example for strategic suppliers selection to prove the proposed methods.

**Category:** General Mathematics

[85] **viXra:1803.0540 [pdf]**
*submitted on 2018-03-23 06:15:13*

**Authors:** Gehad Ismail Sayed, Aboul Ella Hassanien

**Comments:** 12 Pages.

This paper presents an automatic mitosis detection
approach of histopathology slide imaging based on
using neutrosophic sets (NS) and moth-flame optimization (MFO).

**Category:** General Mathematics

[84] **viXra:1803.0538 [pdf]**
*submitted on 2018-03-23 06:17:58*

**Authors:** Juan-juan Peng, Jian-qiang Wang, Jun-hua Hu, Chao Tian

**Comments:** 14 Pages.

Multi-valued neutrosophic sets (MVNSs) have recently become a subject of great interest for researchers, and have been applied widely to multi-criteria decision-making (MCDM) problems. In this paper, the multi-valued neutrosophic geometric weighted Choquet integral Heronian mean (MVNGWCIHM) operator, which is based on the Heronian mean and Choquet integral, is proposed, and some special cases and the corresponding properties of the operator are discussed.

**Category:** General Mathematics

[83] **viXra:1803.0535 [pdf]**
*submitted on 2018-03-23 06:21:20*

**Authors:** Jun Ye

**Comments:** 10 Pages.

The normal distribution is a usual one of various distributions in the real world. A normal
neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number,
which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information.

**Category:** General Mathematics

[82] **viXra:1803.0533 [pdf]**
*submitted on 2018-03-23 06:24:39*

**Authors:** Bao-lin Li, Juan-ru Wang, Li-hua Yang, Xue-tao Li

**Comments:** 32 Pages.

The neutrosophic set and linguistic term set are widely applied in recently years. Motivated
by the advantages of them, we combine the multi-valued neutrosophic set and linguistic set and define the concept of the mult i-valued neutrosophic linguistic set (MVNLS).

**Category:** General Mathematics

[81] **viXra:1803.0532 [pdf]**
*submitted on 2018-03-23 06:26:00*

**Authors:** Victor Vladareanu, Rozica Moga, Paul Schiopu, Luige Vladareanu

**Comments:** 6 Pages.

The work presents the studies and research in order to implement new techniques concerning
semi-active control of the magneto rheological dissipaters dynamic systems with applications to the antivibration isolating systems and the reducing of structural vibrations of the power systems.

**Category:** General Mathematics

[80] **viXra:1803.0527 [pdf]**
*submitted on 2018-03-23 06:34:50*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

În mod paradoxist, există pinguini la ecuator! Atât de mici în comparație cu cei din Antarctica...

**Category:** General Mathematics

[79] **viXra:1803.0524 [pdf]**
*submitted on 2018-03-23 06:45:35*

**Authors:** Ümit Budak, Yanhui Guo, Abdulkadir Sengür, Florentin Smarandache

**Comments:** 12 Pages.

Hough transform (HT) is a useful tool for both pattern recognition and image processing
communities. In the view of pattern recognition, it can extract unique features for description of
various shapes, such as lines, circles, ellipses, and etc.

**Category:** General Mathematics

[78] **viXra:1803.0523 [pdf]**
*submitted on 2018-03-23 06:46:34*

**Authors:** Bijan Davvaz, Samy M. Mostafa, Fatema F.Kareem

**Comments:** 10 Pages.

In this paper, the concept of a neutrosophic KU-algebra is introduced and some related
properties are investigated. Also, neutrosophic KU-ideals of a neutrosophic KU-algebra are
studied and a few properties are obtained. Furthermore, a few results of neutrosophic KU-ideals of a neutrosophic KU-algebra under homomorphism are discussed

**Category:** General Mathematics

[77] **viXra:1803.0522 [pdf]**
*submitted on 2018-03-23 06:47:35*

**Authors:** Debabrata Mandal

**Comments:** 11 Pages.

Neutrosophic ideals of a semiring are introduced
and studied in the sense of Smarandache[14], along with some operations such as intersection, composition, cartesian product etc. on them. Among the other results/characterizations, it is
shown that all the operations are structure preserving.

**Category:** General Mathematics

[76] **viXra:1803.0521 [pdf]**
*submitted on 2018-03-23 06:48:36*

**Authors:** Jun Ye

**Comments:** 10 Pages.

A neutrosophic number (NN) presented by Smarandache can express determinate and/or
indeterminate information in real life. NN (z = a + uI) consists of the determinate part a and the
indeterminate part uI for a, u 2 R (R is all real numbers) and indeterminacy I, and is very suitable for representing and handling problems with both determinate and indeterminate information.

**Category:** General Mathematics

[75] **viXra:1803.0517 [pdf]**
*submitted on 2018-03-23 06:52:20*

**Authors:** Madad Khan, Saima Anis, Florentin Smarandache, Young Bae Jun

**Comments:** 17 Pages.

The notion of neutrosophic N-structure is introduced, and applied it to semigroup. The notions of neutrosophic N-subsemigroup,
neutrosophic N-product and "-neutrosophic N-subsemigroup are introduced, and several properties are investigated.

**Category:** General Mathematics

[74] **viXra:1803.0515 [pdf]**
*submitted on 2018-03-23 06:54:24*

**Authors:** Jun Ye, Wenhua Cuim Zhikang Lu

**Comments:** 10 Pages.

The possible optimal ranges of the decision variables and NN objective function are indicated when the indeterminacy I is considered for possible interval ranges in real situations.

**Category:** General Mathematics

[73] **viXra:1803.0514 [pdf]**
*submitted on 2018-03-23 07:00:46*

**Authors:** K. Thirusangu, S. Poornavel, R. Vasuki

**Comments:** 11 Pages.

In this paper, the notion of neutrosophic Q- fuzzy left N-subgroups is introduced in a near ring and investigated some related properties. Characterization of neutrosophic Q- fuzzy left N-subgroups with respect to T-norm and S-norm are given. Few homomorphic image and its pre-image on neutrosophic Q- fuzzy are obtained.

**Category:** General Mathematics

[72] **viXra:1803.0513 [pdf]**
*submitted on 2018-03-23 07:01:30*

**Authors:** K. Thirusangu, S. Poornavel, R. Vasuki

**Comments:** 6 Pages.

Goguen [1967] introduced L-fuzzy set. Murali [1991] analyzed lattice of fuzzy algebras and closure systems. Saibaba [2008] initiated fuzzy lattice ordered groups, and studied many properties on fuzzy lattice. Swamy and Raju [1991] gave a detailed findings on algebraic fuzzy system.

**Category:** General Mathematics

[71] **viXra:1803.0512 [pdf]**
*submitted on 2018-03-23 07:02:26*

**Authors:** A.Edward Samuel, R.Narmadhagnanam

**Comments:** 7 Pages.

In this paper, a new approach (cosecant similarity measure) is proposed to construct the decision method for medical diagnosis by using neutrosophic refined set. Also, we develop a technique to diagnose which patient is suffering from what disease.

**Category:** General Mathematics

[70] **viXra:1803.0511 [pdf]**
*submitted on 2018-03-23 07:03:32*

**Authors:** C. Antony Crispin Sweety, I. Arockiarani

**Comments:** 9 Pages.

A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we defne concepts of Rough Neutrosophic algebra and investigate some of their properties.

**Category:** General Mathematics

[69] **viXra:1803.0509 [pdf]**
*submitted on 2018-03-23 07:06:01*

**Authors:** Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi, Florentin Smarandache

**Comments:** 27 Pages.

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and
intuitionistic fuzzy sets (IFs) fail to handle indeterminate information.

**Category:** General Mathematics

[68] **viXra:1803.0507 [pdf]**
*submitted on 2018-03-23 07:08:16*

**Authors:** Mehmet Şahin, Abdullah Kargın

**Comments:** 8 Pages.

In this paper; new properties for neutrosophic
triplet groups are introduced. A notion of neutrosophic triplet metric space is given and properties of neutrosophic triplet metric spaces are studied.

**Category:** General Mathematics

[67] **viXra:1803.0506 [pdf]**
*submitted on 2018-03-23 07:09:29*

**Authors:** A.Mary Margaret, M.Trinita Pricilla

**Comments:** 13 Pages.

The aim of this paper is to introduce and develop a new class of sets namely neutrosophic vague generalized pre-closed sets in neutrosophic vague topological space. Further we have analyse the properties of neutrosophic vague generalized pre-open sets.

**Category:** General Mathematics

[66] **viXra:1803.0505 [pdf]**
*submitted on 2018-03-23 07:14:54*

**Authors:** Florentin Smarandache, Mirela Teodorescu, Daniela Gîfu

**Comments:** 4 Pages.

This paper describes the importance of Neutrosophy Theory in order to find a method that could solve the uncertainties arising on discursive analysis.

**Category:** General Mathematics

[65] **viXra:1803.0501 [pdf]**
*submitted on 2018-03-22 11:48:26*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

Neutrosophic logic is defined as a five-valued logic on {-0, 0, 0<p<1, 1, 1+}.
We map this using Meth8/VL4 and find it not tautologous.
We next map the multiplication look up table of sub-indeterminacies and find it a vector space.
Neutrosophic logic is not suitable as a universal logic to map and confirm all other logic systems.

**Category:** General Mathematics

[64] **viXra:1803.0499 [pdf]**
*submitted on 2018-03-22 19:18:51*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

The Dezert-Smarandache theory arises from the following scenario with Alice and Bob as suspects.
That either Alice or Bob is not innocent or both Alice and Bob are not innocent is a tautology.
If cast with a probability, that either Alice or Bob is not innocent or both Alice and Bob are not innocent is ordinal one.
Neither scenario is tautologous in the Meth8/VL4 modal logic model checker.

**Category:** General Mathematics

[63] **viXra:1803.0490 [pdf]**
*submitted on 2018-03-22 08:44:38*

**Authors:** Zhong-xing Wang, Jian Li

**Comments:** 18 Pages.

Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making
(MCDM) processes. However, some important issues related to correlation coefficient utilization
within probabilistic hesitant fuzzy environments remain to be addressed.

**Category:** General Mathematics

[62] **viXra:1803.0486 [pdf]**
*submitted on 2018-03-22 08:48:57*

**Authors:** Gülcan Petriçli, Gül Gökay Emel

**Comments:** 30 Pages.

Supplier Selection is one of the most studied areas in management and decision sciences. However, it is still a highly problematic subject since decision-makers take an educated guess after a certain stage in real life practices.

**Category:** General Mathematics

[61] **viXra:1803.0485 [pdf]**
*submitted on 2018-03-22 08:50:04*

**Authors:** Florentin Smarandache, Dmitri Rabounski

**Comments:** 1 Page.

“Angel particle” bearing properties of both particles and anti-particles, which was recently discovered by the Stanford team of experimental physicists, is usually associated
with Majorana fermions (predicted in 1937 by Ettore Majorana). In this message we point out that particles bearing properties of both matter and anti-matter were as well predicted without any connexion with particle physics, but on the basis of pure mathematics, namely — neutrosophic logic which is a generalization of fuzzy and intuitionistic fuzzy logics in mathematics.

**Category:** General Mathematics

[60] **viXra:1803.0484 [pdf]**
*submitted on 2018-03-22 08:51:42*

**Authors:** Ion PATRASCU, Florentin SMARANDACHE

**Comments:** 3 Pages.

In acest articol rezolvam doua probleme de minim geometric.

**Category:** General Mathematics

[59] **viXra:1803.0476 [pdf]**
*submitted on 2018-03-22 09:00:22*

**Authors:** Chris Lucas

**Comments:** 7 Pages.

A deliberation upon the possibility of generating a comprehensive view of ‘mind as a whole’ by integrating biology, psychology and sociology, and considering ‘Mind’ as a dynamical interplay between values existing over many levels and
scales of complex systems.

**Category:** General Mathematics

[58] **viXra:1803.0474 [pdf]**
*submitted on 2018-03-22 09:02:25*

**Authors:** Le Wang, Hong-yu Zhang, Jian-qiang Wang

**Comments:** 16 Pages.

In this study, comprehensive multi-criteria
decision-making (MCDM) methods are investigated under bipolar neutrosophic environment. First, the operations of BNNs are redefined based on the Frank operations considering the extant operations of bipolar neutrosophic numbers (BNNs) lack flexibility and robustness.

**Category:** General Mathematics

[57] **viXra:1803.0473 [pdf]**
*submitted on 2018-03-22 09:05:45*

**Authors:** Abdolreza Rashno, Behzad Nazari, Dara D. Koozekanani, Paul M. Drayna, Saeed Sadri, Hossein Rabbani, Keshab K. Parhi

**Comments:** 26 Pages.

A fully-automated method based on graph shortest path, graph cut and neutrosophic (NS) sets is presented for fluid segmentation in OCT volumes for exudative age related macular degeneration (EAMD) subjects.

**Category:** General Mathematics

[56] **viXra:1803.0472 [pdf]**
*submitted on 2018-03-22 09:06:54*

**Authors:** P Veeresh, R Praveen Sam, C Shoba Bindu

**Comments:** 9 Pages.

In recent years, computational capability of mobile devices such as Laptops, mobile phones, PDAs, etc., are greatly improved. Implementation of SOA ("Service Oriented Architectures") in mobile ad hoc networks increases the flexibility of using mobile devices.

**Category:** General Mathematics

[55] **viXra:1803.0471 [pdf]**
*submitted on 2018-03-22 09:08:06*

**Authors:** Ashraful Alam

**Comments:** 9 Pages.

Fuzzy Cognitive Maps (FCM) have been applied in many fields successfully to show the causes and effect relationship. In this research work, the relationship between risk factors band symptoms of Diabetes has been analyzed with the help of FCM. FCM is a fuzzy-graph modeling approach based on expert’s opinion.

**Category:** General Mathematics

[54] **viXra:1803.0466 [pdf]**
*submitted on 2018-03-22 09:16:21*

**Authors:** Seon Jeong Kim, Seok-Zun Song, Young Bae Jun

**Comments:** 16 Pages.

As a more general platform which extends the notions of the classical set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set, Smarandache developed the concept of neutrosophic set which consists of three member functions, so called truth membership function, indeterminacy membership function and falsity membership function.

**Category:** General Mathematics

[53] **viXra:1803.0465 [pdf]**
*submitted on 2018-03-22 09:17:31*

**Authors:** Hai-Long Yang, Yan-Ling Bao, Zhi-Lian Guo

**Comments:** 23 Pages.

Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and
inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues.

**Category:** General Mathematics

[52] **viXra:1803.0464 [pdf]**
*submitted on 2018-03-22 09:19:06*

**Authors:** R. Dhavaseelan, S. Jafari, C. Ozel, M. A. Al-Shumrani

**Comments:** 17 Pages.

In this paper, the concepts of generalized neutrosophic contra-continuous function, gen-
eralized neutrosophic contra-irresolute function and strongly generalized neutrosophic
contra-continuous function are introduced. Some interesting properties are also studied.

**Category:** General Mathematics

[51] **viXra:1803.0460 [pdf]**
*submitted on 2018-03-22 09:25:44*

**Authors:** Muhammad Akram, Muzzamal Sitara, Florentin Smarandache

**Comments:** 20 Pages.

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures.We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

**Category:** General Mathematics

[50] **viXra:1803.0457 [pdf]**
*submitted on 2018-03-22 09:29:14*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 2 Pages.

In their classic book, the art of thinking, Robert Bramson and Allen Harrison describe five thinking styles that one tends to adopt: pragmatist, analyst, realist, synthesist, and idealist. In this paper, we tell our story on
thinking modes we often use, and sometimes we took a synthesizer mode, i.e. to combine three or four of the above thinking styles. We present some examples too. We hope this retelling may be useful for young scientists and mathematicians in developing new theories either in theoretical physics and cosmology.

**Category:** General Mathematics

[49] **viXra:1803.0456 [pdf]**
*submitted on 2018-03-22 09:30:28*

**Authors:** Mihaela Colhon, Stefan Vladutescu, Xenia Negrea

**Comments:** 14 Pages.

In the latest studies concerning the sentiment polarity of words, the authors mostly consider
the positive and negative constructions, without paying too much attention to the neutral words,
which can have, in fact, significant sentiment degrees.

**Category:** General Mathematics

[48] **viXra:1803.0455 [pdf]**
*submitted on 2018-03-22 09:31:43*

**Authors:** Yohana Yunet Bakarbessy, Henry W. M. Patty, Elvinus R. Persulessy

**Comments:** 6 Pages.

Penelitian ini membahas identifikasi struktur-struktur tersebut melalui definisi dan teorema dengan tahapan sebagai berikut : mengidentifikasi struktur ring dan perkembangannya seperti lapangan, near-ring dan near-field, mengidentifikasi struktur dasar Smarandache near-ring yang dibangun oleh near-ring dengan himpunan bagian sejatinya near-field, mengidentifikasi struktur dasar Smarandache near-ring lainnya berdasarkan perkembangan struktur dasar Smarandache near-ring.

**Category:** General Mathematics

[47] **viXra:1803.0453 [pdf]**
*submitted on 2018-03-22 09:35:20*

**Authors:** F. Naveed, B. Hu

**Comments:** 6 Pages.

The inability to detect the Emerald Ash Borer (EAB) at an early stage has led to the enumerable loss of different species of ash trees.
Due to the increasing risk being posed by the EAB, a robust and accurate method is needed for identifying Individual Tree Crowns (ITCs) that are at a risk of being infected or are already diseased.

**Category:** General Mathematics

[46] **viXra:1803.0452 [pdf]**
*submitted on 2018-03-22 09:36:53*

**Authors:** Edjard de Souza Mota, Jacob M. Howe, Artur S. d'Avila Garcez

**Comments:** 12 Pages.

The learning of rules from examples is of continuing interest to machine learning since it allows generalization from fewer training examples. Inductive Logic Programming (ILP) generates hypothetical rules (clauses) from a knowledge base augmented with (positive and negative) examples.

**Category:** General Mathematics

[45] **viXra:1803.0450 [pdf]**
*submitted on 2018-03-22 09:39:17*

**Authors:** A. Edward Samuel, R. Narmadhagnanam

**Comments:** 12 Pages.

The objective of the study was to find out the relationship between the disease and the symptoms seen within patients and diagnose
the disease that impacted the patient using n-valued interval neutrosophic sets. Neoteric methods were devised in n-valued interval
neutrosophic sets. Utilization of medical diagnosis was commenced with using prescribed procedures to identify a person suffering from
the disease for a considerable period. The result showed that the proposed methods were free from shortcomings that affect the existing
methods and found to be more accurate in diagnosing the diseases. It was concluded that the techniques adopted in this study were more
reliable and easier to handle medical diagnosis problems.

**Category:** General Mathematics

[44] **viXra:1803.0447 [pdf]**
*submitted on 2018-03-22 09:51:19*

**Authors:** Muhammad Akram, Muzzamal Sitara

**Comments:** 25 Pages.

In this research article, we introduce certain notions of interval-valued neutrosophic graph structures.

**Category:** General Mathematics

[43] **viXra:1803.0445 [pdf]**
*submitted on 2018-03-22 10:09:15*

**Authors:** J. G. Lee, P. K. Lim, J. H. Kim, K. Hur

**Comments:** 21 Pages.

First of all, we dene an intuitionistic quotient mapping and obtain its some properties. Second, we dene some types continuities, open and closed mappings. And we investigate relationships among them and give some examples. Finally, we introduce the notions of an intuitionistic subspace and the heredity, and obtain some properties of each concept.

**Category:** General Mathematics

[42] **viXra:1803.0443 [pdf]**
*submitted on 2018-03-22 10:11:35*

**Authors:** J. H. Kim, P. K. Lim, J. G. Lee, K. Hur

**Comments:** 18 Pages.

First of all, we list some concepts and results introduced by[10, 15]. Second, we give some examples related to intuitionistic topologies
and intuitionistic bases, and obtain two properties of an intuitionistic base and an intuitionistic subbase. And we dene intuitionistic intervals in R.Finally, we dene some types of intuitionistic closures and interiors, and
obtain their some properties.

**Category:** General Mathematics

[41] **viXra:1803.0440 [pdf]**
*submitted on 2018-03-22 10:15:01*

**Authors:** Zhikang Lu, Jun Ye

**Comments:** 12 Pages.

Fault diagnosis is an important task for the normal operation and maintenance of equipment.
In many real situations, the diagnosis data cannot provide deterministic values and are usually
imprecise or uncertain.

**Category:** General Mathematics

[40] **viXra:1803.0439 [pdf]**
*submitted on 2018-03-22 10:16:40*

**Authors:** Azeddine Elhassouny, Florentin Smarandache

**Comments:** 13 Pages.

The purpose of this paper is to present an e[xtension and alternative of the hybrid method based on Saaty’s Analytical Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution method (AHP-TOPSIS), that based on the AHP and its use of pairwise comparisons, to a new method called α -D MCDM-TOPSIS( α -Discounting Method for multicriteria decision making-TOPSIS).

**Category:** General Mathematics

[39] **viXra:1803.0437 [pdf]**
*submitted on 2018-03-22 10:19:12*

**Authors:** Nguyen Xuan Thao, Le Hoang Son, Bui Cong Cuong, Mumtaz Ali, Luong Hong Lan

**Comments:** 9 Pages.

In this paper, we propose the concept of fuzzy equivalence on standard neutrosophic sets and rough standard neutrosophic sets. We also provide
some formulas for fuzzy equivalence on standard neutrosophic sets and rough standard neutrosophic sets. We also apply these formulas for cluster
analysis. Numerical examples are illustrated.

**Category:** General Mathematics

[38] **viXra:1803.0435 [pdf]**
*submitted on 2018-03-22 10:22:21*

**Authors:** Jean-Claude Okaingni, Sié Ouattara, Adles Kouassi, Wognin J. Vangah, Aubin K. Koffi, Alain Clement

**Comments:** 17 Pages.

In this paper, the theory of plausible and paradoxical reasoning of Dezert-Smarandache (DSmT) is used to take into account the paradoxical character through the intersections of vegetation, aquatic and mineral surfaces. In order to do this, we developed a classification model of pixels by aggregating information
using the DSmT theory based on the PCR5 rule using the NDVI, MNDWI and NDBaI spectral indices obtained from the ASTER satellite images.

**Category:** General Mathematics

[37] **viXra:1803.0431 [pdf]**
*submitted on 2018-03-22 07:33:12*

**Authors:** S. Shanmugam, J. Preethi

**Comments:** 13 Pages.

Arthritis is the most familiar element of disability in the World. At a rate of 20 million people in the US are suffering from Arthritis. It characterizes around 200 rheumatic diseases and conditions that influence joints. The tissues surround the joint, and other connective tissue.

**Category:** General Mathematics

[36] **viXra:1803.0419 [pdf]**
*submitted on 2018-03-22 07:50:43*

**Authors:** Mumtaz Ali, Le Hoang Son, Irfan Deli, Nguyen Dang Tien

**Comments:** 11 Pages.

Neutrosophic set, proposed by Smarandache considers a truth membership function, an indeterminacy membership function and a falsity membership function. Soft set, proposed by Molodtsov is a mathematical framework which has the ability of independency of parameterizations inadequacy, syndrome of fuzzy set, rough set, probability.

**Category:** General Mathematics

[35] **viXra:1803.0418 [pdf]**
*submitted on 2018-03-22 07:51:46*

**Authors:** Ion PATRASCU, Florentin SMARANDACHE

**Comments:** 2 Pages.

In this Note, the authors present some properties of Apollonius circles of rank −1 associated to a triangle.

**Category:** General Mathematics

[34] **viXra:1803.0413 [pdf]**
*submitted on 2018-03-22 07:58:18*

**Authors:** Harmeet Kaur, Navdeep Singh

**Comments:** 8 Pages.

A group of defective cells that grow inside or around the brain referred as Barin Tumor. The number of Brain Tumor cases around the World is increasing day by day. So, it is significant to detect it at anearly stage. Segmentation of brain images holds thesignificant part for detection of Tumor brain.

**Category:** General Mathematics

[33] **viXra:1803.0412 [pdf]**
*submitted on 2018-03-22 07:59:54*

**Authors:** Fu Yuhua

**Comments:** 9 Pages.

As No.4 of comparative physics series papers, this paper mainly discusses the comparative studies of various theories (or formulae) of force, and
on this basis, presents the concepts of generalized theory of force and generalized
theories clusters of force.

**Category:** General Mathematics

[32] **viXra:1803.0411 [pdf]**
*submitted on 2018-03-22 08:01:12*

**Authors:** Linfan MAO

**Comments:** 20 Pages.

A complex system S consists of m components, maybe inconsistence with m ≥ 2 such as those of self-adaptive systems, particularly the biological systems and usually, a system with contradictions, i.e., there are no a classical mathematical subfield applicable. Then, how can we hold its global and local behaviors or true face?

**Category:** General Mathematics

[31] **viXra:1803.0407 [pdf]**
*submitted on 2018-03-22 08:15:56*

**Authors:** X), Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Rajkumar Verma

**Comments:** 5 Pages.

Interval valued bipolar neutrosophic sets is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making. In this paper, an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (UNWCG) in which the edge weights is represented by
a an interval valued bipolar neutrosophic number is presented.

**Category:** General Mathematics

[30] **viXra:1803.0406 [pdf]**
*submitted on 2018-03-22 08:17:34*

**Authors:** M. Kavitha, P. Murugadas, S. Sriram

**Comments:** 15 Pages.

Uncertainty forms have a very important part in our daily life. During the time we handle real life problems involving uncertainty like Medical elds, Engineering, Industry and Economics and so on.

**Category:** General Mathematics

[29] **viXra:1803.0405 [pdf]**
*submitted on 2018-03-22 08:18:26*

**Authors:** Xu Wu

**Comments:** 19 Pages.

Mobile cloud computing (MCC) has attracted extensive attention in recent years. With the prevalence of MCC, how to select trustworthy and high quality mobile cloud services becomes one of the most urgent problems.

**Category:** General Mathematics

[28] **viXra:1803.0403 [pdf]**
*submitted on 2018-03-22 08:21:38*

**Authors:** Rıdvan Sahin, Peide Liu

**Comments:** 9 Pages.

As a combination of the hesitant fuzzy set
(HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truthhesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS.

**Category:** General Mathematics

[27] **viXra:1803.0401 [pdf]**
*submitted on 2018-03-21 20:09:35*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

In neutrosophic logic, the designated values are ((1 or 0) or (less_than 1 and greater_than 0)) as three sets. As rendered, it is not tautologous, not bivalent, and hence refuted.
Note: This paper was uploaded to General Mathematics because of the deluge of neutrosophic papers mainly from PRC, but is more properly under the heading Set theory and logic where our other papers are regarding neutrosophic matters.

**Category:** General Mathematics

[26] **viXra:1803.0392 [pdf]**
*submitted on 2018-03-21 10:09:07*

**Authors:** Yanhui Guo, Ümit Budak, Abdulkadir Sengür, Florentin Smarandache

**Comments:** 10 Pages.

A fundus image is an effective tool for ophthalmologists studying eye diseases.
Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering.

**Category:** General Mathematics

[25] **viXra:1803.0390 [pdf]**
*submitted on 2018-03-21 10:14:29*

**Authors:** XiaoWang, Jianhu Zhao, Bangyan Zhu, Tingchen Jiang, Tiantian Qin

**Comments:** 16 Pages.

To accurately achieve side scan sonar (SSS) image target detection, a novel target detection algorithm based on a neutrosophic set (NS) and diffusion maps (DMs) is proposed in this paper. Firstly, the neutrosophic subset images were obtained by transforming the input SSS image into the NS domain. Secondly, the shadowed areas of the SSS image were detected using the single gray value threshold method before the diffusion map was calculated.

**Category:** General Mathematics

[24] **viXra:1803.0389 [pdf]**
*submitted on 2018-03-21 10:15:23*

**Authors:** Lei Cai, Dianjun Chen, Luyong Zhang

**Comments:** 6 Pages.

Decoupling characteristics of Software Defined Network(SDN) control plane and data plane provides us with a new idea to improve dynamic routing. SDN
controllers can easily obtain the global situation of the whole network. The network topology information and bandwidth data are applied to the classical Dijstra algorithm.

**Category:** General Mathematics

[23] **viXra:1803.0377 [pdf]**
*submitted on 2018-03-21 06:15:57*

**Authors:** Min Xian, Yingtao Zhang, H. D. Cheng, Fei Xu, Kuan Huang, Boyu Zhang, Jianrui Ding, Chunping Ning, Ying Wang

**Comments:** 9 Pages.

Breast ultrasound (BUS) image segmentation is challenging and critical for BUS Computer-Aided Diagnosis (CAD) systems. Many BUS segmentation approaches have been proposed in the last two decades, but the performances of most approaches
have been assessed using relatively small private datasets with different quantitative metrics, which result in discrepancy in performance comparison.

**Category:** General Mathematics

[22] **viXra:1803.0375 [pdf]**
*submitted on 2018-03-21 06:21:05*

**Authors:** Yoichi Hayashi, Kazuhiro Fukunaga

**Comments:** 13 Pages.

Although liver cancer is the second most common cause of death from cancer worldwide, because of the limited accuracy and interpretability of extracted classification rules, the diagnosis of liver disease remains difficult. In addition, hepatitis, which is inflammation of the liver, can progress to fibrosis, cirrhosis, or even liver cancer.

**Category:** General Mathematics

[21] **viXra:1803.0373 [pdf]**
*submitted on 2018-03-21 07:02:01*

**Authors:** Yilin Dong, Xinde Li, Yihai Liu

**Comments:** 25 Pages.

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs)
to subjective probabilities (called Bayesian BBAs).

**Category:** General Mathematics

[20] **viXra:1803.0368 [pdf]**
*submitted on 2018-03-21 07:46:04*

**Authors:** Prem Kumar Singh

**Comments:** 26 Pages.

The precise measurement of uncertainty exists in the complex fuzzy attributes and their graphical analytics is a mathematically expensive tasks for knowledge processing researchers. To deal with this problem recently, the calculus of complex neutrosophic sets are introduced to characterize the uncertainty in data based on its truth, indeterminacy, and falsity membership– value, independently.

**Category:** General Mathematics

[19] **viXra:1803.0367 [pdf]**
*submitted on 2018-03-21 07:47:15*

**Authors:** Xindong Peng, Jingguo Dai

**Comments:** 27 Pages.

In this paper, we define a new axiomatic definition of interval neutrosophic similarity measure, which is presented by interval neutrosophic number (INN). Later, the objective weights of various attributes are determined via Shannon entropy theory; meanwhile, we develop the combined weights, which can show both subjective information and objective information.

**Category:** General Mathematics

[18] **viXra:1803.0366 [pdf]**
*submitted on 2018-03-21 07:48:30*

**Authors:** Xindong Peng, Chong Liu

**Comments:** 14 Pages.

This paper presents three novel single-valued neutrosophic soft set (SVNSS) methods. First, we initiate a new axiomatic definition of single-valued neutrosophic similarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory.

**Category:** General Mathematics

[17] **viXra:1803.0365 [pdf]**
*submitted on 2018-03-21 07:49:51*

**Authors:** Run-yu Zhang, Mingyang Yu, Yan Gao

**Comments:** 6 Pages.

By co mbin ing neutrosophic sets and hesitant fuzzy sets, the definition of hesitant neutrosophic sets is presented. Based on the Euclidean distance and the cosine similarity formu la, the similarity formu la of neutrosophic sets is constructed. Then its similarity formu la is also provided. According to the similarity formu la of hesitant neutrosophic sets, a new mu lti-attribute VIKOR decision-making method for hesitant neutrosophic information is develop. At last an illustrative example is given to verify its practicality and effectiveness.

**Category:** General Mathematics

[16] **viXra:1803.0361 [pdf]**
*submitted on 2018-03-21 07:56:24*

**Authors:** Serpil Altinirmak, Basil Okoth, Mustafa Ergun, Caglar Karamasa

**Comments:** 14 Pages.

Mobile banking, also known as m-banking, provides low cost, innovative and easily accessible services to customers with technological developments as compared to retail banking. In this context, m-banking quality factors of the banks are considered to be important issues for customers. The aim of this study is to analyze the m-banking quality factors and to rank banks offering this service in Turkey under incomplete, inconsistent and indeterminate information.

**Category:** General Mathematics

[15] **viXra:1803.0360 [pdf]**
*submitted on 2018-03-21 07:58:11*

**Authors:** Süleyman ŞENYURT, Selin SİVAS

**Comments:** 15 Pages.

In this paper, Firstly we define NC-Smarandache curve, then we calculate the curvature and
torsion of NB and TNB- Smarandache curves together with NC-Smarandache curve. Here T, N and B are Frenet vectors of a curve α and vector C is unit Darboux vector.

**Category:** General Mathematics

[14] **viXra:1803.0359 [pdf]**
*submitted on 2018-03-21 08:00:34*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

In this note we recall some formulas for pi. they express pi in terms of the Golden Ratio.

**Category:** General Mathematics

[13] **viXra:1803.0358 [pdf]**
*submitted on 2018-03-21 07:59:46*

**Authors:** Mostafa El-Baz, Ibrahim El-Henawy

**Comments:** 5 Pages.

Cloud Computing has already changed the way that people think about and use the information technology services. Cloud data storage is one of such services in which data is stored, managed, remotely backed up and accessed by users over the Internet. when the organization need to depend on cloud computing solution as intelligent solution ,the first problem facing the organization is to choosing the appropriate provider between different providers available especially in the cases of confused portfolios which contain complex pricing models and different criteria's. for addressing this problem the thesis providing a multi-criteria algorithm which based on neutrosophic to help the organization to choose the best appropriate providers achieving high degree of security and privacy according their requirements map .

**Category:** General Mathematics

[12] **viXra:1803.0349 [pdf]**
*submitted on 2018-03-21 08:27:50*

**Authors:** Z. Hajighasemi, S. M. Mousavi

**Comments:** 23 Pages.

Failure modes and effects analysis (FMEA) is a well-known risk analysis approach that has been conducted to distinguish, analyze and mitigate serious failure modes.

**Category:** General Mathematics

[11] **viXra:1803.0347 [pdf]**
*submitted on 2018-03-21 08:33:31*

**Authors:** Fangling Ren, Mingming Kong, Zheng Pei

**Comments:** 19 Pages.

Hesitant fuzzy linguistic decision making is a focus point in linguistic decision making,
in which the main method is based on preference ordering.

**Category:** General Mathematics

[10] **viXra:1803.0342 [pdf]**
*submitted on 2018-03-21 08:50:57*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 4 Pages.

Some years ago, Matt Visser asked the following interesting questions: How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?)

**Category:** General Mathematics

[9] **viXra:1803.0336 [pdf]**
*submitted on 2018-03-21 09:43:35*

**Authors:** Nadeem Akhtar, Mohammad Naved Qureshi, Mohd Vasim Ahamad

**Comments:** 13 Pages.

As a technique of Information Retrieval, we can consider clustering as an unsupervised learning problem in which we provide a structure to unlabeled and unknown data.

**Category:** General Mathematics

[8] **viXra:1803.0329 [pdf]**
*submitted on 2018-03-21 09:54:30*

**Authors:** Baolin Li, Juanru Wang, Lihua Yang, Xuetao Li

**Comments:** 6 Pages.

In order to handle the indeterminate information and inconsistent information in some complex decision-making environment, some novel aggregation operators are firstly proposed based on Einstein operational
laws and generalized aggregation operators under simplified neutrosophic environment, where the truth-membership degree, indeterminacy-membership degree and
falsity-membership degree of each element are singleton subsets in [0,1] .

**Category:** General Mathematics

[7] **viXra:1803.0320 [pdf]**
*submitted on 2018-03-21 10:06:35*

**Authors:** Harish Garg, Sukhveer Singh

**Comments:** 25 Pages.

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic
fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws.

**Category:** General Mathematics

[6] **viXra:1803.0308 [pdf]**
*submitted on 2018-03-20 11:01:02*

**Authors:** Ling Shuwei

**Comments:** 11 Pages.

The Color Dimension Theorem is divided into two parts: The first part gives a constructive proof of the four-color theorem, and points out that the existence of the "one-dimensional-two-color, two-dimensional-four-color" relationship is not accidental; The second part discusses the upper limit of the dimensionality of the space. The method is: suppose the space above the N dimension exists, there must be a geometry. Considering the projection of this geometry on the plane, we will find that this projection image produces a paradox, which means N The space above the dimension does not exist

**Category:** General Mathematics

[5] **viXra:1803.0294 [pdf]**
*submitted on 2018-03-20 23:22:34*

**Authors:** D Williams

**Comments:** 14 Pages.

A Mathematical Museum is described for INSPIRING students and the general public and provide an alternative to the soul-destroying 19th century institutionalised rote-learning (with subsequent near-instantaneous forgetting) of barely understood material in assembly-line schools/factories of "learning" by people who are thereby taught to HATE mathematics.

**Category:** General Mathematics

[4] **viXra:1803.0158 [pdf]**
*submitted on 2018-03-11 07:58:47*

**Authors:** Yuly Shipilevsky

**Comments:** 4 Pages.

A class of converted target functions
preserving the set of minimizers

**Category:** General Mathematics

[3] **viXra:1803.0130 [pdf]**
*submitted on 2018-03-09 05:41:53*

**Authors:** Suraj deshmukh

**Comments:** 1 Page.

It was just found luckily. It is a new method to get primes easily.
Just a rearrangement of numbers.

**Category:** General Mathematics

[2] **viXra:1803.0111 [pdf]**
*submitted on 2018-03-08 06:41:04*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents eight series for pi.

**Category:** General Mathematics

[1] **viXra:1803.0085 [pdf]**
*replaced on 2018-03-27 08:31:42*

**Authors:** Koji KOBAYASHI

**Comments:** 18 Pages.

This paper describes about complexity of PH problems by using "Almost all monotone circuit family" and "Accept input pair that sandwich reject inputs".
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF Circuit family".
To clarify NNF circuit family limitation, we pay attention to AND-gate and OR-gate relation. If two accept "Neighbor input" pair that sandwich reject "Boundary input" in Hamming distance, NNF circuit have to meet these different variables of neighbor inputs in AND-gate to differentiate boundary inputs. NNF circuit have to use unique AND-gate to identify such neighbor input.
The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" in PH. NTD is subset of tautology DNF that do not become tautology if proper subset of one variable permutate positive / negative. NTD include many different variables which number is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size of length, and NTD that include PH is not in P.

**Category:** General Mathematics