[37] **viXra:1804.0449 [pdf]**
*submitted on 2018-04-28 09:07:14*

**Authors:** Songsong Dai

**Comments:** 5 Pages.

The single valued neutrosophic set (SVNS) is a subclass of neutrosophic set,which can describe and handle indeterminate information and inconsistent information. Since a SVNS is characterized independently by three functions: a truth-membership function, an indeterminacy-membership function, and a falsity-membership function.

**Category:** General Mathematics

[36] **viXra:1804.0448 [pdf]**
*submitted on 2018-04-28 09:09:13*

**Authors:** M. Lellis Thivagar, Saeid Jafari, V. Sutha Devi, V. Antonysamy

**Comments:** 9 Pages.

The main objective of this study is to introduce a new hybrid intelligent structure called Neutrosophic nano topology. Fuzzy nano topology and intuitionistic nano topology can also be deduced from the neutrosophic nano topology. Based on the neutrosophic nano approximations we have classiﬁed neutrosophic nano topology. Some properties like neutrosophic nano interior and neutrosophic nano closure are derived.

**Category:** General Mathematics

[35] **viXra:1804.0447 [pdf]**
*submitted on 2018-04-28 09:10:34*

**Authors:** Selçuk Topal, Ferhat Taş

**Comments:** 5 Pages.

The main goal of this paper is to construct Bézier surface modeling for neutrosophic data problems. We show how to build the surface model over a data sample from agriculture science after the theoretical structure of the modeling is introduced. As a sampler application for agriculture systems, we give a visualization of Bézier surface model of an estimation of a given yield of bean seeds grown in a field over a period.

**Category:** General Mathematics

[34] **viXra:1804.0446 [pdf]**
*submitted on 2018-04-28 09:12:12*

**Authors:** Young Bae Jun, Florentin Smarandache, Mehmat Ali Ozturk

**Comments:** 10 Pages.

The notions of a commutative (∈, ∈)-neutrosophic ideal and a commutative falling neutrosophic ideal are introduced, and several properties are investigated.

**Category:** General Mathematics

[33] **viXra:1804.0445 [pdf]**
*submitted on 2018-04-28 09:13:45*

**Authors:** Surapati Pramanik, Rama Mallick, Anindita Dasgupta

**Comments:** 22 Pages.

Multi-attribute decision making (MADM) is a mathematical tool to solve decision problems involving conflicting attributes. With the increasing complexity, uncertainty of objective things and the neutrosophic nature of human thought, more and more attention has been paid to the investigation on multi attribute decision making in neutrosophic environment, and convincing research results have been reported in the literature.

**Category:** General Mathematics

[32] **viXra:1804.0444 [pdf]**
*submitted on 2018-04-28 09:15:12*

**Authors:** Surapati Pramanik, Partha Pratim Dey, Florentin Smarandache

**Comments:** 10 Pages.

Interval bipolar neutrosophic set is a significant extension of interval neutrosophic set where every element of the set comprises of three independent positive membership functions and three independent negative membership functions.

**Category:** General Mathematics

[31] **viXra:1804.0443 [pdf]**
*submitted on 2018-04-28 09:16:49*

**Authors:** Pranab Biswas, Surapati Pramanik, Bibhas Chandra Giri

**Comments:** 7 Pages.

In this paper, we introduce interval trapezoidal neutrosophic number and define some arithmetic operations of the proposed interval trapezoidal neutrosophic numbers. Then we consider a multiple attribute decision making (MADM) problem with interval trapezoidal neutrosophic numbers.

**Category:** General Mathematics

[30] **viXra:1804.0442 [pdf]**
*submitted on 2018-04-28 09:18:09*

**Authors:** Kalyan Sinha, Pinaki Majumdar

**Comments:** 8 Pages.

This paper introduces the single valued neutrosophic (i.e. SVN) digraph. The basic terminologies and operations of SVN digraphs have been deﬁned. Later certain types of SVN digraphs are shown and some of the important properties of SVN digraphs are investigated. Finally SVN digraphs are applied in solving a multicriterion decision making problems.

**Category:** General Mathematics

[29] **viXra:1804.0441 [pdf]**
*submitted on 2018-04-28 09:19:26*

**Authors:** G. Muhiuddin, Hashem Bordbar, Florentin Smarandache, Young Bae Jun

**Comments:** 8 Pages.

Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈,∈)-neutrosophic ideal.

**Category:** General Mathematics

[28] **viXra:1804.0439 [pdf]**
*submitted on 2018-04-28 09:21:28*

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

**Comments:** 10 Pages.

Saeid and Jun introduced the notion of neutrosophic points, and studied neutrosophic subalgebras of several types in BCK/BCI-algebras by using the notion of neutrosophic points.

**Category:** General Mathematics

[27] **viXra:1804.0438 [pdf]**
*submitted on 2018-04-28 09:23:58*

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

**Comments:** 14 Pages.

Single valued neutrosophic set is an important mathematical tool for tackling uncertainty in scientific and engineering problems because it can handle situation involving indeterminacy.

**Category:** General Mathematics

[26] **viXra:1804.0437 [pdf]**
*submitted on 2018-04-28 09:24:53*

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

**Comments:** 10 Pages.

In this paper, tangent similarity measure of interval valued neutrosophic sets is proposed and its properties are examined. The concept of interval valued neutrosophic set is a powerful mathematical tool to deal with incomplete, indeterminate and inconsistent information. The concept of this tangent similarity measure is based on interval valued neutrosophic information.

**Category:** General Mathematics

[25] **viXra:1804.0436 [pdf]**
*submitted on 2018-04-28 09:27:32*

**Authors:** Surapati Pramanik, Rumi Roy, Tapan Kumar Roy, Florentin Smarandache

**Comments:** 9 Pages.

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

**Category:** General Mathematics

[24] **viXra:1804.0435 [pdf]**
*submitted on 2018-04-28 09:30:48*

**Authors:** Surapati Pramanik, Rumi Roy, Tapan Kumar Roy, Florentin Smarandache

**Comments:** 9 Pages.

In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively.

**Category:** General Mathematics

[23] **viXra:1804.0434 [pdf]**
*submitted on 2018-04-28 09:32:24*

**Authors:** Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

**Comments:** 14 Pages.

Neutrosophic cubic set consists of interval neutrosophic set and single valued neutrosophic set simultaneously. Due to its unique structure, neutrosophic cubic set can express hybrid information consisting of single valued neutrosophic information and interval neutrosophic information simultaneously.

**Category:** General Mathematics

[22] **viXra:1804.0433 [pdf]**
*submitted on 2018-04-28 09:33:42*

**Authors:** M. Mullai, R. Surya

**Comments:** 5 Pages.

Inventory control of an ideal resource is the most important one which fulﬁls various activities (functions) of an organisation. The supplier gives the discount for an item in the cost of units inorder to motivate the buyers (or) customers to purchase the large quantity of that item.

**Category:** General Mathematics

[21] **viXra:1804.0432 [pdf]**
*submitted on 2018-04-28 09:34:44*

**Authors:** Sahidul Islam, Tanmay Kundu

**Comments:** 11 Pages.

This paper describes neutrosophic goal geometric programming method, a new concept to solve multi-objective non-linear optimization problem under uncertainty.

**Category:** General Mathematics

[20] **viXra:1804.0431 [pdf]**
*submitted on 2018-04-28 09:36:12*

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

**Comments:** 22 Pages.

The motivation of the present paper is to extend the concept of neutrosophic soft prime ideal over a ring. In this paper the concept of neutrosophic soft completely prime ideals, neutrosophic soft completely semi-prime ideals and neutrosophic soft prime k - ideals have been introduced. These are illustrated with suitable examples also. Several related properties, theorems and structural characteristics of each are studied here.

**Category:** General Mathematics

[19] **viXra:1804.0430 [pdf]**
*submitted on 2018-04-28 09:37:46*

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

**Comments:** 13 Pages.

In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also.

**Category:** General Mathematics

[18] **viXra:1804.0429 [pdf]**
*submitted on 2018-04-28 09:38:51*

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

**Comments:** 9 Pages.

In this paper, we introduce new type of similarity measures for single valued neutrosophic sets based on hyperbolic sine function. The new similarity measures are namely, single valued neutrosophic hyperbolic sine similarity measure and weighted single valued neutrosophic hyperbolic sine similarity measure.

**Category:** General Mathematics

[17] **viXra:1804.0427 [pdf]**
*submitted on 2018-04-28 09:40:08*

**Authors:** Emad Marei

**Comments:** 10 Pages.

This paper aims to introduce a single valued neutrosophic soft approach to rough sets based on neutrosophic right minimal structure. Some of its properties are deduced and proved. A comparison between traditional rough model and suggested model, by using their properties is concluded to show that Pawlak’s approach to rough sets can be viewed as a special case of single valued neutrosophic soft approach to rough sets. Some of rough concepts are redefined and then some properties of these concepts are deduced, proved and illustrated by several examples. Finally, suggested model is applied in a decision making problem, supported with an algorithm.

**Category:** General Mathematics

[16] **viXra:1804.0426 [pdf]**
*submitted on 2018-04-28 09:41:19*

**Authors:** Salah Bouzina, Djamel Hamoud

**Comments:** 3 Pages.

The main objective of this research is a simple attempt to suggest three new logical connectors and establish an equation a chart of truth for each of them. Secondly, and using the logical operations of these three connectors, we seek to show how comprehensive and widespread and effective is the Neutrosophic logic (NL) compared to any other logic, taking into account the Fuzzy Logic (FL) as well as the classical logic (CL) as a comparative model.

**Category:** General Mathematics

[15] **viXra:1804.0425 [pdf]**
*submitted on 2018-04-28 09:42:37*

**Authors:** M. Lellis Thivagar, S. Jafari, V. Antonysamy, V. Sutha Devi

**Comments:** 10 Pages.

In this paper we desire to extend the neutrosophic topological spaces into N-neutrosophic topological spaces. Also we show that this theory can be deduced to N-intuitionistic and N-fuzzy topological spaces etc. Further we develop not only the concept of classical generalized closed sets into N-neutrosophic topological spaces but also obtain its basic properties. Finally we investigate its continuous function and generalized continuous function.

**Category:** General Mathematics

[14] **viXra:1804.0424 [pdf]**
*submitted on 2018-04-28 09:43:58*

**Authors:** Pranab Biswas, Surapati Pramanik, Bibhas C. Giri

**Comments:** 11 Pages.

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a popular strategy for MultiAttribute Decision Making (MADM). In this paper, we extend the TOPSIS strategy of MADM problems in trapezoidal neutrosophic number environment. The attribute values are expressed in terms of single-valued trapezoidal neutrosophic numbers.

**Category:** General Mathematics

[13] **viXra:1804.0423 [pdf]**
*submitted on 2018-04-28 09:45:16*

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

**Comments:** 10 Pages.

The concept of neutrosophic can provide a generalization of fuzzy set and intuitionistic fuzzy set that make it is the best fit in representing indeterminacy and uncertainty. Single Valued Triangular Numbers (SVTrN-numbers) is a special case of neutrosophic set that can handle ill-known quantity very difficult problems.

**Category:** General Mathematics

[12] **viXra:1804.0422 [pdf]**
*submitted on 2018-04-28 09:47:05*

**Authors:** Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

**Comments:** 13 Pages.

In this paper, we extend the VIKOR VIsekriterijumska optimizacija i KOmpromisno Resenje) strategy to multiple attribute group decision-making (MAGDM) with bipolar neutrosophic set environment. In this paper, we first define VIKOR strategy in bipolar neutrosophic set environment to handle MAGDM problems, which means we combine the VIKOR with bipolar neutrosophic number to deal with MAGDM.

**Category:** General Mathematics

[11] **viXra:1804.0336 [pdf]**
*submitted on 2018-04-24 00:07:05*

**Authors:** Walter Gress

**Comments:** 2 Pages.

The behavior of vectors whence taken upon limits to infinity.

**Category:** General Mathematics

[10] **viXra:1804.0288 [pdf]**
*submitted on 2018-04-21 00:44:20*

**Authors:** Kishan Sharma

**Comments:** 7 Pages.

In the present paper, the author derived the results based on
q-Laplace transform of the K-Function introduced by Sharma[7]. Some
special cases of interest are also discussed.

**Category:** General Mathematics

[9] **viXra:1804.0287 [pdf]**
*submitted on 2018-04-21 00:47:59*

**Authors:** N.Vithya, P.Thangavelu

**Comments:** 8 Pages.

In this paper the notion of b#D-sets is introduced. Some weak separation axioms namely
b#
−Dk, b#
−R0, b#-R1 and b#-S0 are introduced and studied. Some lower separation axioms
are characterized by using these separation axioms.

**Category:** General Mathematics

[8] **viXra:1804.0225 [pdf]**
*submitted on 2018-04-16 07:54:40*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents continued radicals and trigonometric formulas for the argument 2npi/13, n=1,2,3,4,5,6.

**Category:** General Mathematics

[7] **viXra:1804.0195 [pdf]**
*submitted on 2018-04-14 11:41:48*

**Authors:** Claude Michael Cassano

**Comments:** 10 Pages.

This linear algebra technique provides a useful method of obtaining exact solutions to homogeneous linear ordinary differential equations. The Bessel half integer solutions, being long well known, have been used here to verify with confidence the above linear independence technique for solving ordinary differential equations. The Bessel second order LHODE has been used, here, as an example application of this vector space transformation technique. Clearly, it may be used on other non-general elementary second order LHODE, such as the Legendre, Laguerre, Hermite and other second order LHODE's. Using the two linearly independent solutions of a second order linear homogeneous ordinary differential equations insures that the two functions are linearly independent. However, any two linearly independent functions may be used, and the two resulting differential equations need not be the same, as was the case for the Bessel's above. In fact, clearly, the technique may also be used for higher order LHODE's, since there are N linearly independent solutions of an N-th order LHODE there would be an equal number of transformation equations.

**Category:** General Mathematics

[6] **viXra:1804.0173 [pdf]**
*submitted on 2018-04-12 14:33:36*

**Authors:** Yeray Cachón Santana

**Comments:** 11 Pages.

As far as I know, there is no a study on fractals on non euclidean metrics.This paper proposes a first approach method about generating fractals on a non-euclidean metric. The idea is to extend the calculus of fractals on non-euclidean metrics. Using the Riemann metric, there will be defined a non-euclidean modulo of a complex number in order to check the divergence of the series generated by the Mandelbrot set. It also shown that the
fractals are not invariant versus rotations. The study will be extended to the quaternions, where is shown that the study of fractals might not be extended to quaternions with a general metric because of the high divergence of the series (a condition in order to generate a fractal is selecting bounded operators). Finally, a Java program will be found as example to show those kind of fractals, where any metric can be defined, so it will be helpful to study those properties.

**Category:** General Mathematics

[5] **viXra:1804.0171 [pdf]**
*submitted on 2018-04-12 14:59:06*

**Authors:** Allen C. Conti

**Comments:** 1 Page. (c) Allen C. Conti 2015-2018

Possible solution to the Fermat Conjecture regarding other exponents satisfying the Pythagorus relationship. Solution uses algebraic substitution, logical deduction and modulus verification.

**Category:** General Mathematics

[4] **viXra:1804.0073 [pdf]**
*submitted on 2018-04-04 08:06:18*

**Authors:** Christophe Chalons

**Comments:** 8 Pages.

Papier décrivant des procédés usant abusivement du mot science et qui met en garde

**Category:** General Mathematics

[3] **viXra:1804.0066 [pdf]**
*submitted on 2018-04-04 15:53:11*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 3 Pages.

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint
boundary value problem may be computed in a direct and straightforward fashion from the
general solution obtained by a generalized Sundman transformation for the related differential
equation, which appeared to be a special case of a more general equation. As a result, various initial
and boundary value problems may be solved explicitly and exactly.

**Category:** General Mathematics

[2] **viXra:1804.0015 [pdf]**
*submitted on 2018-04-02 07:53:08*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas of pi in terms of sum of arctangents.

**Category:** General Mathematics

[1] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-28 20:27:44*

**Authors:** Koji KOBAYASHI

**Comments:** 14 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family.
NNF circuit have symmetry of OR-gate input line, so NNF circuit cannot identify from OR-gate output line which of OR-gate input line is 1. So NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some decision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design high complexity problem with almost perfct nonlinear (APN) function.

**Category:** General Mathematics