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.
Author(s): Anjan Mukherjee, Ajoy Kanti Das
Publisher: Springer
Year: 2023
Language: English
Pages: 153
City: Singapore
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Contents
About the Authors
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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
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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
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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
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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
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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
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6 Fuzzy Soft Multi Compactness and Separation Axioms
6.1 Fuzzy Soft Multi Compact Spaces
6.2 Fuzzy Soft Multi Separation Axioms
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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
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8 Generalization of Fuzzy Soft Multisets
8.1 Intuitionistic Fuzzy Soft Multi Set
8.2 Results on IFSMSs
8.3 A Study on IFSMSs
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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
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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
