Fuzzy Group Theory

The material presented makes this book a good reference for graduate students and researchers working in fuzzy group theory. This book presents an up-to-date account of research in important topics of fuzzy group theory.

Author: John N. Mordeson

Publisher: Springer

ISBN: 9783540808275

Category: Computers

Page: 300

View: 437

This book presents an up-to-date account of research in important topics of fuzzy group theory. It concentrates on the theoretical aspects of fuzzy subgroups of a group. It includes applications to abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. Fuzzy subgroups of Hamiltonian, solvable, P-Hall, and nilpotent groups are discussed. Construction of free fuzzy subgroups is determined. Numerical invariants of fuzzy subgroups of Abelian groups are developed. The problem in group theory of obtaining conditions under which a group can be expressed as a direct product of its normal subgroups is considered. Methods for deriving fuzzy theorems from crisp ones are presented and the embedding of lattices of fuzzy subgroups into lattices of crisp groups is discussed as well as deriving membership functions from similarity relations. The material presented makes this book a good reference for graduate students and researchers working in fuzzy group theory.

Characterizations of Group Theory under Q Neutrosophic Soft Environment

Since then, the theories and approaches of fuzzy soft sets on different algebraic structures developed rapidly. Mukherjee and Bhattacharya [28] studied fuzzy groups, Sharma [29] discussed intuitionistic fuzzy groups, Aktas and Cagman ...

Author: Majdoleen Abu Qamar

Publisher: Infinite Study


Category: Mathematics

Page: 17

View: 768

Neutrosophic set theory was initiated as a method to handle indeterminate uncertain data. It is identified via three independent memberships represent truth T, indeterminate I and falsity F membership degrees of an element. As a generalization of neutrosophic set theory, Q-neutrosophic set theory was established as a new hybrid model that keeps the features of Q-fuzzy soft sets which handle two-dimensional information and the features of neutrosophic soft sets in dealing with uncertainty. Different extensions of fuzzy sets have been already implemented to several algebraic structures, such as groups, symmetric groups, rings and lie algebras. Group theory is one of the most essential algebraic structures in the field of algebra. The inspiration of the current work is to broaden the idea of Q-neutrosophic soft set to group theory. In this paper the concept of Q-neutrosophic soft groups is presented. Numerous properties and basic attributes are examined. We characterize the thought of Q-level soft sets of a Q-neutrosophic soft set, which is a bridge between Q-neutrosophic soft groups and soft groups. The concept of Q-neutrosophic soft homomorphism is defined and homomorphic image and preimage of a Q-neutrosophic soft groups are investigated. Furthermore, the cartesian product of Q-neutrosophic soft groups is proposed and some relevant properties are explored.

Algebra Geometry Analysis and their Applications

A. Rosenfeld applied the notion of fuzzy set to algebra and introduced fuzzy subgroup of a group. ... General topology and Group theory can be regarded as a special case of fuzzy topology and fuzzy group theory respectively, ...

Author: Naseem Ahmad


ISBN: 818487667X

Category: Technology & Engineering

Page: 124

View: 974

The articles appeared in this book have been contributed by well-known mathematician and scientists projecting the modern development in the subject. This book covers the following topics Geometry Algebra Functional Analysis Fuzzy Topology Complex Analysis TribologyPostgraduates and researchers working in the areas of mathematics and mathematical sciences will find this book to be of immense value.

Smarandache Fuzzy Algebra

Let ,u be a fuzzy subset of a setX [f,u (x) I 0 for every x e X then we call ,u as empty fuzzy set and denote it by ¢X. ... The underlying logic of the theory of fuzzy group is to provide a strict fuzzy algebraic structure where level ...

Author: W. B. Vasantha Kandasamy

Publisher: Infinite Study

ISBN: 1931233748

Category: Algebra, Abstract

Page: 453

View: 693

The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w(0)} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w(1)}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-ring, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also, applications of Smarandache groupoids, near-rings, and semirings in automaton theory, in error correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures

For future studies, more notions in group theory could be established in fuzzy multigroup setting by redefining the notions in the light of fuzzy multigroups. REFERENCES Ajmal, N., & Prajapati, A. S. (1992). Fuzzy cosets and fuzzy ...

Author: Jana, Chiranjibe

Publisher: IGI Global

ISBN: 1799801926

Category: Mathematics

Page: 439

View: 100

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.

Fuzzy Mathematics

Conclusions By the notion of a g-nilpotent fuzzy subgroup we can investigate on fuzzification of nilpotent groups. Moreover, since this is similar to group theory, definition, it is much easier than before to study the properties of ...

Author: Etienne E. Kerre

Publisher: MDPI

ISBN: 303897322X


Page: 286

View: 328

This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics

Near Rings Fuzzy Ideals and Graph Theory

Example 1.7.22 Let u be a fuzzy subset of Z + ( set of positive integers ) defined by if xe { 2,4,6,8 , ... } u ( x ) = otherwise Define f : Z + → { 0 , 1 , 2 , 3 } as follows : f ( x ) = x mod 4 for all x e Z + .

Author: Bhavanari Satyanarayana

Publisher: CRC Press

ISBN: 1439873119

Category: Computers

Page: 480

View: 843

Near Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations.After introducing all of the necessary fundamentals of algebraic systems, the book presents the essentials of near rings theory,

Neutrosophic Sets and Systems Vol 47 2021

The fuzzy set theory has been extended to the intuitionistic fuzzy set(IFS) proposed by Atanassov [12], which incorporates the concept of non-membership as well as membership. Some other extensions of fuzzy sets are given in [13-16].

Author: Florentin Smarandache

Publisher: Infinite Study


Category: Antiques & Collectibles

Page: 652

View: 635

Papers on neutrosophic statistics, neutrosophic probability, plithogenic set, paradoxism, neutrosophic set, NeutroAlgebra, etc. and their applications.

Aggregation Functions in Theory and in Practice

∪μm and similarly with T-vague groups). As an interesting consequence of the results of this work, crisp equivalence relations subgroups and quotient groups can be aggregated obtaining fuzzy objects. Example 5.1.

Author: Vicenç Torra

Publisher: Springer

ISBN: 3319593064

Category: Technology & Engineering

Page: 264

View: 891

This book collects the abstracts of the contributions presented at AGOP 2017, the 9th International Summer School on Aggregation Operators. The conference took place in Skövde (Sweden) in June 2017. Contributions include works from theory and fundamentals of aggregation functions to their use in applications. Aggregation functions are usually defined as those functions that are monotonic and that satisfy the unanimity condition. In particular settings these conditions are relaxed. Aggregation functions are used for data fusion and decision making. Examples of these functions include means, t-norms and t-conorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals).

Fuzzy Algebraic Hyperstructures

After the introduction of fuzzy sets by Zadeh, reconsideration of the concept of classical mathematics began. On the other hand, because of the importance of group theory in mathematics, as well as its many areas of application, ...

Author: Bijan Davvaz

Publisher: Springer

ISBN: 3319147625

Category: Technology & Engineering

Page: 242

View: 764

This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors’ past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.