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Discusses major theories and applications of fuzzy soft multisets.
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.
Fuzzy sets are useful mathematical tools for simulating various kinds of uncertainty. Zadeh proposed the fuzzy set concept in 1965 as an extension of the classical notion of an ordinary (crisp) set. The membership of items in a set is evaluated in binary terms in classical set theory according to a bivalent condition, an element either belongs to or does not belong to a set. Fuzzy set theory, on the other hand, allows for a gradual assessment of the membership of elements in a set described by a membership function with a value in the real unit interval. This idea has been intensively investigated by both mathematicians and computer scientists since its inception. Fuzzy logic, fuzzy neural networks, fuzzy automata, fuzzy control systems and other applications of fuzzy set theory have emerged over time.
Soft set theory research has accelerated because it may be easily applied to a variety of fields, including Artificial Intelligence, Computer Science, medical science, Machine Learning, Information Technology, economics, the environment and engineering. The practical application of soft computing techniques, particularly soft computing techniques for handling decision-making problems, has become increasingly important.
1 Introduction to Fuzzy Sets, Soft Sets, Multisets and Their Generalizations
2 Fuzzy Soft Multiset Theory
3 Relation on Fuzzy Soft Multisets
4 Topology on Fuzzy Soft Multisets
5 Fuzzy Soft Multi Points and Their Sequences
6 Fuzzy Soft Multi Compactness and Separation Axioms
7 Fuzzy Soft Multiset Based Applications
8 Generalization of Fuzzy Soft Multisets
9 Algebraic and Topological Structures on Intuitionistic Fuzzy Soft Multisets
10 Application of Intuitionistic Fuzzy Soft Multisets