[36] **viXra:1608.0364 [pdf]**
*submitted on 2016-08-27 03:19:35*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 1 Page.

TRL Lustre Is The Light’s Cumulative Consecutive Higher Orders Orthogonal Primality Overgrowth (All Inclusive) Of It’s Own Primality.

**Category:** General Mathematics

[35] **viXra:1608.0348 [pdf]**
*submitted on 2016-08-25 08:09:08*

**Authors:** Edgar Valdebenito

**Comments:** 14 Pages.

In this note we give some formulas for Catalan's constant G=0.915965594177...

**Category:** General Mathematics

[34] **viXra:1608.0347 [pdf]**
*submitted on 2016-08-25 08:14:20*

**Authors:** Edgar Valdebenito

**Comments:** 13 Pages.

In this note we give some formulas related with: pi constant pi=3.1415...,Catalan's constant G=0.9159...,Euler's constant gamma=0.5772...

**Category:** General Mathematics

[33] **viXra:1608.0296 [pdf]**
*submitted on 2016-08-24 01:36:28*

**Authors:** Florentin Smarandache

**Comments:** 33 Pages.

This chapter may look like a glossary of the fusion rules and we also introduce new ones presenting their formulas and examples: Conjunc
tive, Disjunctive, Exclusive Disjunctive, Mixed Conjunctive-Disjunctive rules, Conditional rule, Dempster’s, Yager’s, Smets’ TBM rule, Dubois-Prade’s, Dezert-Smarandache classical and hybrid rules, Murphy’s average rule, Inagaki-Lefevre-Colot-Vannoorenberghe Unified Combination rules [and, as particular cases:
Iganaki’s parameterized rule, Weighted Average Operator, minC (M. Daniel), and newly Proportional Conflict Redistribution rules (Smarandache-Dezert) among which PCR5 is the most exact way of redistribution of the conflicting mass to non-empty sets following the path of the conjunctive rule], Zhang’s Center Combination rule, Consensus Operator (Jøsang), Cautious Rule (Smets), -junctions rules (Smets), etc. and three new T -norm & T -conorm rules adjusted from fuzzy and neutrosophic sets to information fusion (Tchamova-Smarandache). Introducing the degree of union and degree of inclusion with respect
to the cardinal of sets not with the fuzzy set point of view, besides that of intersection,
many fusion rules can be improved.

**Category:** General Mathematics

[32] **viXra:1608.0294 [pdf]**
*submitted on 2016-08-24 01:38:48*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 18 Pages.

This chapter introduces the notion of qualitative belief assignment to model beliefs of human experts expressed in natural language (with linguistic labels).We show how qualitative beliefs can be efficiently combined using an extension of Dezert-Smarandache Theory (DSmT) of plausible and paradoxical quantitative reasoning to qualitative reasoning. We propose a new arithmetic on linguistic labels which allows a direct extension of classical or hybrid DSm fusion rules. An approximate qualitative PCR5 rule is also proposed jointly with a Qualitative Average Operator. We also show how crisp or interval mappings can be used to deal indirectly with linguistic labels. A very simple example is provided to illustrate our qualitative fusion rules.

**Category:** General Mathematics

[31] **viXra:1608.0292 [pdf]**
*submitted on 2016-08-24 01:45:02*

**Authors:** J. Dezert, A. Tchamova, P. Konstantinova, Florentin Smarandache

**Comments:** 21 Pages.

We analyze the behavior of several combinational rules for temporal/sequential attribute data fusion for target type estimation. Our comparative analysis is based on: Dempster’s fusion rule, Proportional Conflict Redistribution rule no.
5 (PCR5), Symmetric Adaptive Combination (SAC) rule and a new fusion rule, based on fuzzy T-conorm and T-norm operators (TCN).

**Category:** General Mathematics

[30] **viXra:1608.0290 [pdf]**
*submitted on 2016-08-24 01:49:56*

**Authors:** Xinhan Huang, Xinde Li, Min Wang

**Comments:** 22 Pages.

Characteristics of uncertainty and imprecision, even imperfection is presented from knowledge acquisition in map reconstruction of autonomous mobile robots. Especially in the course of building grid map using sonar, this characteristic
of uncertainty is especially servere.

**Category:** General Mathematics

[29] **viXra:1608.0289 [pdf]**
*submitted on 2016-08-24 01:51:11*

**Authors:** Arnaud Martin, Christophe Osswald

**Comments:** 21 Pages.

In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the Dempster- Shafer theory has relaunched the studies on the combination rules especially for the management of the conflict. Many combination rules have been proposed in the last few years. We study here different combination rules and compare them in terms
of decision on didactic example and on generated data. Indeed, in real applications,
we need a reliable decision and it is the final results that matter. This chapter shows that a fine proportional conflict redistribution rule must be preferred for the combination in the belief function theory.

**Category:** General Mathematics

[28] **viXra:1608.0288 [pdf]**
*submitted on 2016-08-24 01:55:36*

**Authors:** A. A. K. Majumdar

**Comments:** 3 Pages.

This paper gives an alternative approach to ¯nd the determinant of the right circular matrix with geometric sequence, using the known results of the circulant matrix.Keywords circulant matrix, right circulant matrix with geometric sequence.

**Category:** General Mathematics

[27] **viXra:1608.0287 [pdf]**
*submitted on 2016-08-24 01:57:02*

**Authors:** Samuel Corgne, Laurence Hubert-Moy, Gregoire Mercier, Jean Dezert

**Comments:** 13 Pages.

This chapter presents an environmental application of DSmT for the land cover prediction. The spatial prediction of land cover at the field scale in winter is useful to reduce the bare soils in agricultural intensive regions.

**Category:** General Mathematics

[26] **viXra:1608.0286 [pdf]**
*submitted on 2016-08-24 01:58:54*

**Authors:** Milan Daniel

**Comments:** 25 Pages.

Dempster’s rule, non-normalized conjunctive rule, Yager’s rule and Dubois-Prade’s rule for belief functions combination are generalized to be applicable to hyper-power sets according to the DSm theory. A comparison of the rules with
DSm rule of combination is presented. A series of examples is included.

**Category:** General Mathematics

[25] **viXra:1608.0283 [pdf]**
*submitted on 2016-08-24 02:02:21*

**Authors:** Andrew Schumann

**Comments:** 23 Pages.

The Dezert-Smarandache theory of plausible and paradoxical reasoning is based on the premise that some elements i of a frame have a non-empty
intersection.

**Category:** General Mathematics

[24] **viXra:1608.0282 [pdf]**
*submitted on 2016-08-24 02:03:23*

**Authors:** Albena Tchamova, Tzvetan Semerdjiev, Jean Dezert

**Comments:** 12 Pages.

This chapter presents an approach for target behavior tendency estimation (Receding, Approaching). It is developed on the principles of Dezert-Smarandache theory (DSmT) of plausible and paradoxical reasoning applied to conventional
sonar amplitude measurements, which serve as an evidence for corresponding decision-making procedures.

**Category:** General Mathematics

[23] **viXra:1608.0280 [pdf]**
*submitted on 2016-08-24 02:06:16*

**Authors:** Denis de Brucq

**Comments:** 20 Pages.

This chapter presents new important links between the most important theories developed in literature for managing uncertainties (i.e. probability, fuzzy sets and evidence theories).

**Category:** General Mathematics

[22] **viXra:1608.0277 [pdf]**
*submitted on 2016-08-24 02:10:34*

**Authors:** J. Dezert, A. Tchamova, T. Semerdjiev, P. Konstantinova

**Comments:** 18 Pages.

The objective of this chapter is to present and compare different fusion rules which can be used for Generalized Data Association (GDA) for multitarget tracking (MTT) in clutter.

**Category:** General Mathematics

[21] **viXra:1608.0274 [pdf]**
*submitted on 2016-08-24 02:14:26*

**Authors:** A. A. K. Majumdar

**Comments:** 8 Pages.

Two types of the Smarandache LCM ratio functions have been introduced by Murthy. Recently, the second type of the Smarandache LCM ratio function has been considered by Khainar, Vyawahare and Salunke. This paper establishes the relationships
between these two forms of the Smarandache LCM ratio functions, and derives some reduction
formulas and interesting properties in connection with these functions.

**Category:** General Mathematics

[20] **viXra:1608.0265 [pdf]**
*submitted on 2016-08-23 04:07:10*

**Authors:** Jean Dezert, Florentin Smarandache, Mohammad Khoshnevisan

**Comments:** 18 Pages.

This chapter presents several classes of fusion problems which cannot be directly approached by the classical mathematical theory of evidence, also known as Dempster-Shafer Theory (DST), either because Shafer’s model for the frame of
discernment is impossible to obtain, or just because Dempster’s rule of combination fails to provide coherent results (or no result at all). We present and discuss the potentiality of the DSmT combined with its classical (or hybrid) rule of combination to attack these infinite classes of fusion problems.

**Category:** General Mathematics

[19] **viXra:1608.0264 [pdf]**
*submitted on 2016-08-23 04:08:39*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 20 Pages.

In this chapter one studies, within the DSmT framework, the case when the sources of information provide imprecise belief functions/masses, and we generalize
the DSm rules of combination (classic or hybrid rules) from scalar fusion to sub-unitary interval fusion and, more generally, to any set of sub-unitary interval fusion. This work generalizes previous works available in literature which appear limited to IBS (Interval-valued Belief Structures) in the Transferable Belief Model framework. Numerical didactic examples of these new DSm fusion rules for dealing with imprecise information are also presented.

**Category:** General Mathematics

[18] **viXra:1608.0263 [pdf]**
*submitted on 2016-08-23 04:09:58*

**Authors:** Ion P ATRASCU, Florentin SMARANDACHE

**Comments:** 4 Pages.

In this paper, the notion of Apollonius circle of rank k is introduced and a number of results related to the classical Apollonius circles are generalized.

**Category:** General Mathematics

[17] **viXra:1608.0262 [pdf]**
*submitted on 2016-08-23 04:12:13*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

This short paper presents mathematical rebuses.

**Category:** General Mathematics

[16] **viXra:1608.0261 [pdf]**
*submitted on 2016-08-23 04:14:00*

**Authors:** Jean Dezert, Florentin Smarandache, Albena Tchamova

**Comments:** 13 Pages.

Modern multitarget-multisensor tracking systems involve the development of reliable methods for the data association and the fusion of multiple sensor information, and more specifically the partitioning of observations into tracks. This
chapter discusses and compares the application of Dempster-Shafer Theory (DST) and the Dezert-Smarandache Theory (DSmT) methods to the fusion of multiple sensor attributes for target identification purpose. We focus our attention on the paradoxical Blackman’s association problem and propose several approaches to outperform Blackman’s solution. We clarify some preconceived ideas about the use of degree of
conflict between sources as potential criterion for partitioning evidences.

**Category:** General Mathematics

[15] **viXra:1608.0259 [pdf]**
*submitted on 2016-08-23 04:17:08*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 13 Pages.

In this chapter, we examine several issues for ordering or partially ordering elements of hyper-power sets involved in the DSmT. We will show the benefit of some of these issues to obtain a nice and interesting structure of matrix representation
of belief functions.

**Category:** General Mathematics

[14] **viXra:1608.0258 [pdf]**
*submitted on 2016-08-23 04:18:43*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 34 Pages.

This chapter presents a general overview and foundations of the DSmT, i.e. the recent theory of plausible and paradoxical reasoning developed by the authors, specially for the static or dynamic fusion of information arising from several independent but potentially highly conflicting, uncertain and imprecise sources of
evidence. We introduce and justify here the basis of the DSmT framework with respect to the Dempster-Shafer Theory (DST), a mathematical theory of evidence developed in 1976 by Glenn Shafer. We present the DSm combination rules and provide some simple illustrative examples and comparisons with other main rules of
combination available in the literature for the combination of information for simple
fusion problems. Detailed presentations on recent advances and applications of DSmT are presented in the next chapters of this book.

**Category:** General Mathematics

[13] **viXra:1608.0257 [pdf]**
*submitted on 2016-08-23 04:19:57*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 13 Pages.

The development of DSmT is based on the notion of Dedekind’s lattice, called also hyper-power set in the DSmT framework, on which is defined the general basic belief assignments to be combined. In this chapter, we explain the structure of the hyper-power set, give some examples of hyper-power sets and show how they can be generated from isotone Boolean functions. We also show the interest to work with the hyper-power set rather than the power set of the refined frame of discernment in
terms of complexity.

**Category:** General Mathematics

[12] **viXra:1608.0249 [pdf]**
*submitted on 2016-08-23 04:03:04*

**Authors:** Jean Dezert, Florentin Smarandache, Milan Daniel

**Comments:** 12 Pages.

This chapter introduces a generalized pignistic transformation (GPT)developed in the DSmT framework as a tool for decision-making at the pignistic level. The GPT allows to construct quite easily a subjective probability measure
from any generalized basic belief assignment provided by any corpus of evidence. We focus our presentation on the 3D case and we provide the full result obtained by the proposed GPT and its validation drawn from the probability theory.

**Category:** General Mathematics

[11] **viXra:1608.0248 [pdf]**
*submitted on 2016-08-23 04:05:22*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 44 Pages.

This chapter presents a general method for combining uncertain and paradoxical (i.e. highly conflicting) sources of evidence for a wide class of fusion problems. From the foundations of the DSmT we show how the DSm rule of combination can be extended to take into account all possible integrity constraints (if any) of the problem under consideration due to the true nature of elements/concepts
involved into it. We show how Shafer’s model can be considered as a specific hybrid DSm model and can be easily handled by the DSmT and one presents here a new efficient alternative to Dempster’s rule of combination, following steps of previous researchers towards this quest. Several simple didactic examples are also provided to show the efficiency and the generality of the approach proposed in this work.

**Category:** General Mathematics

[10] **viXra:1608.0196 [pdf]**
*submitted on 2016-08-19 04:32:18*

**Authors:** Victor VLADAREANU, Ovidiu-Ilie SANDRU, Mihnea Alexandru MOISESCU, Florentin SMARANDACHE, Hongnian YU

**Comments:** 6 Pages.

The paper presents an application of Extenics Engineering principles to a two-dimensional robotic workspace. This provides the mathematical basis and considerations for obtaining the trajectory tracking reference in robotic applications. A brief history and overview of the relevant theoretical concepts is provided.

**Category:** General Mathematics

[9] **viXra:1608.0194 [pdf]**
*submitted on 2016-08-19 04:42:48*

**Authors:** Mumtaz Ali, Florentin Smarandache, Jian-qiang Wang

**Comments:** 8 Pages.

Fuzzy sets and intuitionistic fuzzy sets can’t
handle imprecise, indeterminate, inconsistent, and incomplete information. Neutrosophic sets play an important role to overcome this difficulty. A neutrosophic set has a truth membership function, indeterminate membership function, and a falsehood membership functions that can handle all types of ambiguous information. New type of union and intersection has been proposed in this paper.

**Category:** General Mathematics

[8] **viXra:1608.0193 [pdf]**
*submitted on 2016-08-19 04:45:46*

**Authors:** Young Bae Jun, Florentin Smarandache, Chang Su Kim

**Comments:** 3 Pages.

R-unions and R-intersections of T-external (Iexternal,F-external) neutrosophic cubic sets are considered.Examples to show that the R-intersection and R-union of Texternal
(I-external, F-external) neutrosophic cubic sets may not be a T-external (I-external, F-external) neutrosophic cubic setare provided. Conditions for the R-union and R-intersection of T-external (I-external, F-external) neutrosophic cubic sets to be a T-external (I-external, F-external) neutrosophic cubic set are discussed.

**Category:** General Mathematics

[7] **viXra:1608.0192 [pdf]**
*submitted on 2016-08-19 04:47:23*

**Authors:** Said Broumi, Mohamed Talea, Florentin Smarandache, Assia Bakali

**Comments:** 8 Pages.

The single valued neutrosophic graph is a new
version of graph theory presented recently as a generalization of fuzzy graph and intuitionistic fuzzy graph. The single valued
neutrosophic graph (SVN-graph) is used when the relation between nodes (or vertices) in problems are indeterminate. In this paper, we examine the properties of various types of degrees, order and size of single valued neutrosophic graphs and a new definition for regular single valued neutrosophic graph is given.

**Category:** General Mathematics

[6] **viXra:1608.0191 [pdf]**
*submitted on 2016-08-19 04:48:59*

**Authors:** Irfan Deli, Yusuf Subas, Florentin Smarandache, Mumtaz Ali

**Comments:** 8 Pages.

Interval valued bipolar fuzzy weighted
neutrosophic set(IVBFWN-set) 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.

**Category:** General Mathematics

[5] **viXra:1608.0190 [pdf]**
*submitted on 2016-08-19 04:50:30*

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

**Comments:** 8 Pages.

This study introduces the concept of uncertainty analysis of Neutrosophic Theory in the sphere of Maintenance Operating System
(MOS). The aim of this study is to underline the importance of uncertainties solving in Maintenance Operating System. In maintenance
process appear ambiguous states that can’t be assimilated neither true, nor false, meaning that the threshold state is a neutral one, being defined as fault in most of cases. In this regard, this uncertaintymaking decision
process can be associated as functioning according to rules of Neutrosophy, and can be evaluated using elements of Neutrosophic
Structures, Pareto Charts, maintenance metrics. Identification of uncertainties and study of their impact on maintenance, making the right
decision, is the main focus of this paper.

**Category:** General Mathematics

[4] **viXra:1608.0189 [pdf]**
*submitted on 2016-08-19 04:52:32*

**Authors:** Azeddine Elhassouny, Florentin Smarandache

**Comments:** 7 Pages.

In this paper, (1) one simplified the standard
TOPSIS to new Multi-Criteria Decision-Making (MCDM) called Simplified-TOPSIS. Simplified-TOPSIS gives the same results and simplifies the calculation of the classical TOPSIS. An
example is presented distinctions between Simplified-TOPSIS and classical TOPSIS are underlined. (2) extend the new Simplified-TOPSIS method to Neutrosophic-simplified-TOPSIS
using single valued Neutrosophic information. An example showing the interest of Neutrosophic-simplified-TOPSIS to manipulate the uncertainty linked to information presented in Multi-Criteria Decision-Making.

**Category:** General Mathematics

[3] **viXra:1608.0042 [pdf]**
*submitted on 2016-08-04 10:59:34*

**Authors:** Mohsen Soori, Behrooz Arezoo, Mohsen Habibi

**Comments:** 11 pages, Journal of Manufacturing Science and Engineering, 138(8), 081005, 2016

Virtual manufacturing systems carry out the simulation of manufacturing processes in digital environment in order to increase accuracy as well as productivity in part production. There are different error sources in machine tools, such as tool deflection, geometrical deviations of moving axis, and thermal distortions of machine tool structures. The errors due to tool deflection are caused by cutting forces and have direct effects on dimensional accuracy, surface roughness of the parts, and efficient life of the cutting tool, holder, and spindle. This paper presents an application of virtual machining systems in order to improve the accuracy and productivity of part manufacturing by monitoring and minimizing the tool deflection error. The tool deflection error along machining paths is monitored to present a useful methodology in controlling the produced parts with regard to desired tolerances. Suitable tool and spindle can also be selected due to the ability of error monitoring. In order to minimize the error, optimization technique based on genetic algorithms is used to determine optimized machining parameters. Free-form profile of virtual and real machined parts with tool deflection error is compared in order to validate reliability as well as accuracy of the software.

**Category:** General Mathematics

[2] **viXra:1608.0010 [pdf]**
*submitted on 2016-08-02 08:58:48*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

In this note we give some formulas for Catalan's constant: G=0.915965594177...

**Category:** General Mathematics

[1] **viXra:1608.0009 [pdf]**
*submitted on 2016-08-02 09:02:04*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

In this note we show some identities with hyperbolic functions

**Category:** General Mathematics