ENGLISH

Essentials of Fuzzy Soft Multisets: Theory and Applications

By Anjan Mukherjee , Ajoy Kanti Das

Book information

Publisher
Springer
Year
2023
ISBN
9811927596, 9789811927591
Language
english
Format
PDF
Filesize
2 MB (1686264 bytes)
Pages
153\153
Time added
2023-03-05 17:41:43

Description

This book discusses major theories and applications of fuzzy soft multisets and their generalization which help researchers get all the related information at one place. The primary objective of this book is to help bridge the gap to provide a textbook on the theories in fuzzy soft multisets and their applications in real life. It is targeted to researchers and students working in the field of fuzzy set theory, multiset theory, soft set theory and their applications. Uncertainty, vagueness and the representation of imperfect knowledge have been a problem in many fields of research, including artificial intelligence, network and communication, signal processing, machine learning, computer science, information technology, as well as medical science, economics, environments and engineering. There are many mathematical tools for dealing with uncertainties. They include fuzzy set theory, multiset theory, soft set theory and soft multiset theory. 1 Contents About the Authors 978-981-19-2760-7_1 1 Introduction to Fuzzy Sets, Soft Sets, Multisets and Their Generalizations 1.1 Introduction 1.2 Fuzzy Sets and Their Generalizations 1.3 Soft Sets and Their Generalizations 1.4 Multisets and Their Generalizations 1.5 Useful Algorithms for Solving Decision-Making Problems 1.5.1 Roy-Maji Algorithm 1.5.2 Feng's Algorithm Using Choice Values 1.5.3 Jiang's Algorithm 1.5.4 Salleh-Alkhazaleh Algorithm References 978-981-19-2760-7_2 2 Fuzzy Soft Multiset Theory 2.1 A study on FSMSs 2.2 Restricted Union and Restricted Intersection 2.3 Extended Union and Extended Intersection 2.4 AND Operator and OR Operator 2.5 Absolute and Null FSMSs 978-981-19-2760-7_3 3 Relation on Fuzzy Soft Multisets 3.1 Fuzzy Soft Multi Relations 3.2 De Morgan Laws 3.3 Associative Laws 3.4 Distributive Laws 3.4.1 Inverse of Fuzzy Soft Multi Relation 3.4.2 Various Types of Fuzzy Soft Multi Relations 978-981-19-2760-7_4 4 Topology on Fuzzy Soft Multisets 4.1 Some Results on Absolute FSMS 4.2 Fuzzy Soft Multi Topological Spaces 4.3 Fuzzy Soft Multi Basis and Sub Basis 4.4 Neighbourhoods and Neighbourhood Systems 4.5 Fuzzy Soft Multi Subspace Topology 978-981-19-2760-7_5 5 Fuzzy Soft Multi Points and Their Sequences 5.1 Fuzzy Soft Multi Points and Their Properties 5.2 Sequence of Fuzzy Soft Multi Points 5.3 Convergence Sequence of Fuzzy Soft Multi Points 5.4 Cluster Fuzzy Soft Multi Point and Its Properties 978-981-19-2760-7_6 6 Fuzzy Soft Multi Compactness and Separation Axioms 6.1 Fuzzy Soft Multi Compact Spaces 6.2 Fuzzy Soft Multi Separation Axioms 978-981-19-2760-7_7 7 Fuzzy Soft Multiset Based Applications 7.1 An Adjustable Approach Based on Feng’s Algorithm 7.2 Algorithm 2 (Feng’s Algorithm) 7.3 Algorithm 5 7.4 Advantages of Our Algorithm (Algorithm 5) are as Follows 7.5 Modified Feng’s Algorithm 7.6 Algorithm 6 (Modified Feng’s Algorithm) 7.7 Algorithm 7 7.8 Application of FSMS Theory in Information Systems References 978-981-19-2760-7_8 8 Generalization of Fuzzy Soft Multisets 8.1 Intuitionistic Fuzzy Soft Multi Set 8.2 Results on IFSMSs 8.3 A Study on IFSMSs 978-981-19-2760-7_9 9 Algebraic and Topological Structures on Intuitionistic Fuzzy Soft Multisets 9.1 Intuitionistic Fuzzy Soft Multi Relations 9.2 Various Types of IFSMRs 9.3 Inverse of IFSMRs 9.4 Weakly-Reflexive and w-reflexive IFSMRs 9.5 IFSM-Topological Spaces 9.6 Parameterized Topological Space Induced by an IFSM-Topological Space 9.7 IFSM-Compact Spaces 9.8 IFSM-Points and Separation Axioms 9.9 Sequences of IFSMSs 978-981-19-2760-7_10 10 Application of Intuitionistic Fuzzy Soft Multisets 10.1 An Adjustable Approach Based on IFSMSs 10.2 Algorithm 3 (Jiang’s Algorithm) 10.3 Algorithm 8 10.4 Case I 10.5 Case II 10.5.1 Advantages 10.5.2 Application of IFSMS Theory in Information Systems Reference

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