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New Distance And Similarity Measures Of Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we proposed a new distance and several similarity measures between interval neutrosophic sets.

Interval Neutrosophic Rough Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper combines interval-valued neutrosophic sets and rough sets. It studies rougheness in interval-valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower an upper approximations of interval neutrosophic sets.

Neutrosophic Crisp Open Set And Neutrosophic Crisp Continuity Via Neutrosophic Crisp Ideals, A. A. Salama, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp L- continuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notions and the other relevant classes are investigated. Finally, we define and study two different types of neutrosophic crisp functions.

New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

For the first time authors have ventured to study, analyse and investigate the properties of the fuzzy models, the experts opinion and so on. Here the concept of merged Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps are carried out, which are based on merged graphs and merged matrices. This concept is better than the usual combined Fuzzy Cognitive Maps. Further by this new technique we are able to give equal importance to all the experts who work with the problem. Here the new concept of New Average Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps is defined and described. This new …

Neutrosophic Parametrized Soft Set Theory And Its Decision Making, Said Broumi, Irfan Deli, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, we present definition of neutrosophic parameterized (NP) soft set and its operations. Then we define NP-aggregation operator to form NP-soft decision making method which allows constructing more efficient decision processes. We also dive an example which shows that they can be successfully applied to problem that contain indeterminacy.

Neutrosophic Ideal Theory Neutrosophic Local Function And Generated Neutrosophic Topology, A. A. Salama, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new nutrosophic topology from the original one in [8]. The basic structure, especially a basis for such generated neutrosophic topologies and several relations between different neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules …

Intuitionistic Neutrosophic Soft Set Over Rings, Florentin Smarandache, Said Broumi, Pabitra Kumar Maji

Branch Mathematics and Statistics Faculty and Staff Publications

S.Broumi and F.Smarandache introduced the concept of intuitionistic neutrosophic soft set as an extension of the soft set theory. In this paper we have applied the concept of intuitionistic neutrosophic soft set to rings theory .The notion of intuitionistic neutrosophic soft set over ring (INSSOR for short ) is introduced and their basic properties have been investigated.The definitions of intersection, union, AND, and OR operations over ring (INSSOR) have also been defined. Finally, we have defined the product of two intuitionistic neutrosophic soft set over ring.

Law Of Included Multiple-Middle & Principle Of Dynamic Neutrosophic Opposition, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the author pledges for the generalization of the Lupasco-Nicolescu’s Law of Included Middle [A, nonA, and a third value T which resolves their contradiction at another level of reality] to the Law of Included Multiple-Middle [A, antiA, and neutA, which is split into a multitude of neutralities between A and antiA, such as neutA1, neutA2, etc.]. The value (i.e. neutrality or indeterminacy related to A) actually comprises the included middle value.

Further, similarly to the extension from dialectics to neutrosophy, the author extends the Principle of Dynamic Opposition [opposition between A and antiA] …

Neutrosophic Theory And Its Applications : Collected Papers - Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every entity tends to be …

Distance In Matrices And Their Applications To Fuzzy Models And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of distance between any two m  n matrices. If the distance is 0 or m  n there is nothing interesting. When the distance happens to be a value t; 0 < t < m  n the study is both innovating and interesting. The three cases of study which is carried out in this book are 1. If the difference between two square matrices is large, will it imply the eigen values and eigen vectors of those matrices are distinct? Several open conjectures in this direction are given. 2. The difference between parity check matrix and the generator matrix for the same C(n, k) code is studied. This will help in detecting errors in storage systems as well as in cryptography.

New Results Of Intuitionistic Fuzzy Soft Set, Florentin Smarandache, Said Broumi, Mamoni Dhar, Pinaki Majumdar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, three new operations are introduced on intuitionistic fuzzy soft sets .They are based on concentration, dilatation and normalization of intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

New Operations Over Interval Valued Intuitionistic Hesitant Fuzzy Set, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the hesitant fuzzy sets. In this paper, four new operations are introduced on interval-valued intuitionistic hesitant fuzzy sets and several important properties are also studied.

New Operations On Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

An interval neutrosophic set is an instance of a neutrosophic set, which can be used in real scientific and engineering applications. In this paper, three new operations based on the arithmetic mean, geometrical mean, and respectively harmonic mean are defined on interval neutrosophic sets.

Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces, A. A. Salama, Florentin Smarandache, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the crisp topological space to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.

Single Valued Neutrosophic Information Systems Based On Rough Set Theory, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The theory of rough sets was firstly proposed by Pawlak. Later on, Smarandache introduced the concept of neutrosophic (NS) sets in 1998. In this paper based on the concept of rough neutrosohic set, we define the concept of single valued neutrosophic information systems. In addition, we will discuss the knowledge reduction and extension of the single valued neutrosophic information systems.

Interval Neutrosophic Logic, Haibin Wang, Florentin Smarandache, Yan-Qing Zhang, Rajshekhar Sunderraman

Branch Mathematics and Statistics Faculty and Staff Publications

Interval Neutrosophic Logic

More On Intuitionistic Neutrosophic Soft Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Intuitionistic Neutrosophic Soft Set theory proposed by S. Broumi and F. Samarandache [28], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper new operations on intuitionistic neutrosophic soft sets have been introduced . Some results relating to the properties of these operations have been established. Moreover ,we illustrate their interconnections between each other.

Filters Via Neutrosophic Crisp Sets, A. A. Salama, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.

N-Valued Refined Neutrosophic Logic And Its Applications To Physics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, …

Fuzzy Neutrosophic Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors give the notion of different neutrosophic models like, neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NEMs), neutrosophic relational equations (NREs), neutrosophic bidirectional associative memories (NBAMs) and neutrosophic associative memories (NAMs) for socio scientists. This book has six chapters. The first chapter introduces the basic concepts of neutrosophic numbers and notions about neutrosophic graphs which are essential to construct these neutrosophic models. In chapter two we describe the concept of neutrosophic matrices and the essential operations related with them which are used in the study and working of these neutrosophic models. However the reader must be familiar …

Correlation Coefficient Of Interval Neutrosophic Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.

Intuitionistic Neutrosophic Soft Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study the concept of intuitionistic neutrosophic set of Bhowmik and Pal. We have introduced this concept in soft sets and defined intuitionistic neutrosophic soft set. Some definitions and operations have been introduced on intuitionistic neutrosophic soft set. Some properties of this concept have been established.

Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b …

Neutrosophic Masses & Indeterminate Models Applications To Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses. The best approach for dealing with such models is the neutrosophic logic.

A New Approach To Algebraic Coding Theory Through The Applications Of Soft Sets, Florentin Smarandache, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

Algebraic codes play a signifcant role in the minimisation of data corruption which caused by defects such as inference, noise channel, crosstalk, and packet loss. In this paper, we introduce soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes. We also discuss several types of soft codes such as type-1 soft codes, complete soft codes etc. Further, we construct the soft generator matrix and soft parity check matrix for the soft linear codes. Moreover, we develop two techniques for the decoding of soft codes.

Evidence Supporting Measure Of Similarity For Reducing The Complexity In Information Fusion, Xinde Li, Jean Dezert, Florentin Smarandache, Xinhan Huang

Branch Mathematics and Statistics Faculty and Staff Publications

This paper proposes a new solution for reducing the number of sources of evidence to be combined in order to diminish the complexity of the fusion process required in some applications where the real-time constraint and strong computing resource limitation are of prime importance. The basic idea consists in selecting, among the whole set of sources of evidence, only the biggest subset of sources which are not too contradicting based on a criterion of Evidence Supporting Measure of Similarity (ESMS) in order to process solely the coherent information received. The ESMS criterion serves actually as a generic tool for outlier …

Generalized Interval Neutrosophic Soft Set And Its Decision Making Problem, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, we introduce the concept of generalized interval neutrosophic soft set and study their operations. Finally, we present an application of generalized interval neutrosophic soft set in decision making problem.

Super Special Codes Using Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes. This book has four chapters. In chapter one basic properties of codes and super matrices are given. A new type of super special vector space is constructed in chapter two of this book. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced in chapter three. Applications of these …

Neutrosophic Logic, Wave Mechanics, And Other Stories: Selected Works 2005-2008, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

There is beginning for anything; we used to hear that phrase. The same wisdom word applies to us too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere. It is often recognized that when a mathematician meets a physics-inclined mind then the result is either a series of endless debates or publication. In our story, we prefer to publish rather than perish. Therefore, our purpose with this …

Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.