Fuzzy semigroups.
type: Item
instance of: scholarly article
title: Fuzzy semigroups.
zbMATH Open document ID: 1036.20058
author: John N. Mordeson
author: D. S. Malik
author: Nobuaki Kuroki
published in: Studies in Fuzziness and Soft Computing
publication date: 2003-09-15T00:00:00Z
review text: When the concept of fuzzy set was introduced by \textit{L. A. Zadeh} in his seminal paper ``Fuzzy sets'' [Inf. Control 8, 338-353 (1965; Zbl 0139.24606)], it attracted the attention of some influential scientists and mathematicians. Theoreticians recognized that the concept has opened a new direction in pure mathematics. A. Rosenfeld is the first one to use the notion of a fuzzy subset in several areas of mathematics, especially in abstract algebras. After Kuroki's works on fuzzy ideal theory of semigroups, many authors have worked in the region of fuzzy semigroup theory. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup, it is an aspect of algebraic semigroup theory. Some applications in fuzzy coding theory, fuzzy finite state machines, and fuzzy languages are also included in this book. The book consists of 10 Chapters. After some basic results on fuzzy subsets, semigroups, codes, finite state machines and languages, in Chapter 2, certain fuzzy ideals of a semigroup are discussed. In Chapter 3, Some fuzzy regular semigroups, for example, left (right) regular semigroups, complete regular semigroups, quasi-regular semigroups, are characterized in terms of fuzzy ideals of a semigroup. In Chapter 4, the semilattices of groups are considered mainly in terms of fuzzy ideals. In Chapter 5, the relationship of fuzzy congruences on a group and fuzzy normal subgroups is established. In Chapters 6, 7 \(T^*\)-pure semigroups, fuzzy congruences on a \(T^*\)-pure semigroup and different types of fuzzy prime ideals are considered. Applications are given in Chapters 8, 9, 10 including fuzzy coding on a free monoid, fuzzy finite machines and regular fuzzy languages which did not appear in another book written by \textit{J. N. Mordeson} and \textit{D. S. Malik} [Fuzzy automata and languages. Theory and applications (2002; Zbl 1046.68068)]. The book represents a major contribution to the literature on fuzzy semigroups…
reviewed by: Xie Xiang-Yun
Mathematics Subject Classification ID: 20M99
Mathematics Subject Classification ID: 20N25
Mathematics Subject Classification ID: 20M12
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 20-02
zbMATH DE Number: 1980895
zbMATH Keywords: fuzzy semigroups
zbMATH Keywords: fuzzy subsets
zbMATH Keywords: fuzzy ideals
zbMATH Keywords: fuzzy congruences
zbMATH Keywords: prime fuzzy ideals
zbMATH Keywords: fuzzy codes
zbMATH Keywords: finite state machines
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1980895