Some Relation Properties Of Rough Neutrosophic Multisets

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Some Relation Properties of Rough Neutrosophic Multisets

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Author : Suriana Alias
Publisher : Infinite Study
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4./5 ( download)

Book Synopsis Some Relation Properties of Rough Neutrosophic Multisets by : Suriana Alias

Download or read book Some Relation Properties of Rough Neutrosophic Multisets written by Suriana Alias and published by Infinite Study. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rough neutrosophic multisets are an improved model of generalization pf neutrosophic multisets represented within the Pawlak’s boundary set of information: lower and upper approximation. The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. This paper establishes an axiomatic definition of rough neutrosophic multisets relation of Cartesian product over a universal set.

Rough Neutrosophic Multisets Relation with Application in Marketing Strategy

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Author : Suriana Alias
Publisher : Infinite Study
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4./5 ( download)

Book Synopsis Rough Neutrosophic Multisets Relation with Application in Marketing Strategy by : Suriana Alias

Download or read book Rough Neutrosophic Multisets Relation with Application in Marketing Strategy written by Suriana Alias and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. Therefore, the objective of this paper is to define the definition of rough neutrosophic multisets relation of Cartesian product over a universal set. Some of the relation properties of rough neutrosophic multisets such as max, min, the composition of two rough neutrosophic multisets relation, inverse rough neutrosophic multisets relation, and reflexive, symmetric and transitive rough neutrosophic multisets relation over the universe are defined. Subsequently, their properties are successfully proven. Finally, the application of rough neutrosophic multisets relation for decision making in marketing strategy is presented.

Roughness And Similarity Measure Of Rough Neutrosophic Multisets Using Vectorial Model Of Information

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Author : Suriana Alias
Publisher : Infinite Study
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4./5 ( download)

Book Synopsis Roughness And Similarity Measure Of Rough Neutrosophic Multisets Using Vectorial Model Of Information by : Suriana Alias

Download or read book Roughness And Similarity Measure Of Rough Neutrosophic Multisets Using Vectorial Model Of Information written by Suriana Alias and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The roughness and similarity measure for two different information in the same universal set is useful in explaining the strength and completeness of the information given. Then, for rough neutrosophic multisets environment, the lower and upper approximation was a concerned property to study in explaining the roughness of the information needed. Meanwhile, the vectorial models of information which are cosine measure and dice measure represent the result for the similarity measure of rough neutrosophic multisets. The finding of this set theory gives a new generalization about similarity measure for multiple information involving indeterminacy information in the same environment. Besides that, the rough neutrosophic multisets theory also applicable set-in decision making for medical diagnosis. The comparison result showed that the roughness approximation of information is essential to get the best result in a close similarity measure.

About Rough Neutrosophic Soft Sets Theory and Study Their Properties

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Author : Somen Debnath
Publisher : Infinite Study
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4./5 ( download)

Book Synopsis About Rough Neutrosophic Soft Sets Theory and Study Their Properties by : Somen Debnath

Download or read book About Rough Neutrosophic Soft Sets Theory and Study Their Properties written by Somen Debnath and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Earlier fuzzy set, vague set, intuitionistic fuzzy set, L-fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.

Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 21 / 2018

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Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599735814
Total Pages : 166 pages
Book Rating : 4.5/5 (997 download)

Book Synopsis Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 21 / 2018 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 21 / 2018 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets

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Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4./5 ( download)

Book Synopsis Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets by : Florentin Smarandache

Download or read book Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In approximation theory, neutrosophic set and logic show an important role. They are generalizations of intuitionistic fuzzy set and logic respectively. Based on neutrosophy, which is a new branch of philosophy, every idea X, has an opposite denoted as anti (X) and their neutral which is denoted as neut (X). These are the main features of neutrosophic set and logic. This chapter is based on the basic concepts of neutrosophic set as well as some of their hybrid structures. In this chapter, we define and study the notion of neutrosophic set and their basic properties. Moreover, interval-valued neutrosophic set are studied with some of their properties. Finally, we define rough neutrosophic sets.

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

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Author : Ashraf Al-Quran
Publisher : Infinite Study
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4./5 ( download)

Book Synopsis A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty by : Ashraf Al-Quran

Download or read book A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty written by Ashraf Al-Quran and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data.

Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

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Author : Hu Zhao
Publisher : Infinite Study
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4./5 ( download)

Book Synopsis Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain by : Hu Zhao

Download or read book Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain written by Hu Zhao and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

ROUGH NEUTROSOPHIC RELATION ON TWO UNIVERSAL SETS

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Author : I. AROCKIARANI
Publisher : Infinite Study
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4./5 ( download)

Book Synopsis ROUGH NEUTROSOPHIC RELATION ON TWO UNIVERSAL SETS by : I. AROCKIARANI

Download or read book ROUGH NEUTROSOPHIC RELATION ON TWO UNIVERSAL SETS written by I. AROCKIARANI and published by Infinite Study. This book was released on with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the rough neutrosophic relation of two universe sets and study the algebraic properties of two rough neutrosophic relations that are interesting in the theory of rough sets. Finally, we present the similarity rough neutrosophic relation with an example.

Handbook of Research on Advances and Applications of Fuzzy Sets and Logic

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Author : Broumi, Said
Publisher : IGI Global
ISBN 13 : 179987981X
Total Pages : 944 pages
Book Rating : 4.7/5 (998 download)

Book Synopsis Handbook of Research on Advances and Applications of Fuzzy Sets and Logic by : Broumi, Said

Download or read book Handbook of Research on Advances and Applications of Fuzzy Sets and Logic written by Broumi, Said and published by IGI Global. This book was released on 2022-03-04 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy logic, which is based on the concept of fuzzy set, has enabled scientists to create models under conditions of imprecision, vagueness, or both at once. As a result, it has now found many important applications in almost all sectors of human activity, becoming a complementary feature and supporter of probability theory, which is suitable for modelling situations of uncertainty derived from randomness. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights into branches of traditional mathematics like algebra, analysis, geometry, topology, and more. With such widespread applications, fuzzy sets and logic are an important area of focus in mathematics. The Handbook of Research on Advances and Applications of Fuzzy Sets and Logic studies recent theoretical advances of fuzzy sets and numbers, fuzzy systems, fuzzy logic and their generalizations, extensions, and more. This book also explores the applications of fuzzy sets and logic applied to science, technology, and everyday life to further provide research on the subject. This book is ideal for mathematicians, physicists, computer specialists, engineers, practitioners, researchers, academicians, and students who are looking to learn more about fuzzy sets, fuzzy logic, and their applications.

Neutrosophic Sets and Systems

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Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4./5 ( download)

Book Synopsis Neutrosophic Sets and Systems by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

ROUGH NEUTROSOPHIC SOFT SETS

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Author : Somen Debnath
Publisher : Infinite Study
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4./5 ( download)

Book Synopsis ROUGH NEUTROSOPHIC SOFT SETS by : Somen Debnath

Download or read book ROUGH NEUTROSOPHIC SOFT SETS written by Somen Debnath and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soft set(SS) theory is a mathematical tool deals with parametric data which are imprecise in nature.It is a generalization of fuzzy set theory. On the other hand Rough set(RS) theory and Neutrosophic set (NS)theory both rising as powerful tool to handle uncertain, incomplete, inconsistent and imprecise information in an effective manner.Actually Neutrosophic set is a generalization of intuitionistic fuzzy set.Earlier Neutrosophic soft set(NSS) was established by combining the concept of Soft set and Neutrosophic set .In this paper , using the concept of Rough set,Neutrosophic set and soft set a hybrid structure Rough neutrosophic soft sets(RNSS) is developed.Some properties and operations on RNSS are introduced.

Single Valued Neutrosophic Soft Approach to Rough Sets, Theory and Application

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Author : Emad Marei
Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)

Book Synopsis Single Valued Neutrosophic Soft Approach to Rough Sets, Theory and Application by : Emad Marei

Download or read book Single Valued Neutrosophic Soft Approach to Rough Sets, Theory and Application written by Emad Marei and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Neutrosophic Rough Set Algebra

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Author : C. Antony Crispin Sweety
Publisher : Infinite Study
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4./5 ( download)

Book Synopsis Neutrosophic Rough Set Algebra by : C. Antony Crispin Sweety

Download or read book Neutrosophic Rough Set Algebra written by C. Antony Crispin Sweety and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

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Author : Ashraf Al-Quran
Publisher : Infinite Study
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4./5 ( download)

Book Synopsis A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty by : Ashraf Al-Quran

Download or read book A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty written by Ashraf Al-Quran and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The ideaof neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided.

Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications

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Author : Chunxin Bo
Publisher : Infinite Study
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4./5 ( download)

Book Synopsis Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications by : Chunxin Bo

Download or read book Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications written by Chunxin Bo and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is an interesting direction to study rough sets from a multi-granularity perspective. In rough set theory, the multi-particle structure was represented by a binary relation. This paper considers a new neutrosophic rough set model, multi-granulation neutrosophic rough set (MGNRS). First, the concept of MGNRS on a single domain and dual domains was proposed. Then, their properties and operators were considered. We obtained that MGNRS on dual domains will degenerate into MGNRS on a single domain when the two domains are the same. Finally, a kind of special multi-criteria group decision making (MCGDM) problem was solved based on MGNRS on dual domains, and an example was given to show its feasibility.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

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Author : Florentin Smarandache
Publisher : MDPI
ISBN 13 : 303897384X
Total Pages : 478 pages
Book Rating : 4.0/5 (389 download)

Book Synopsis Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets by : Florentin Smarandache

Download or read book Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets written by Florentin Smarandache and published by MDPI. This book was released on 2019-04-04 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set. This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.