Fuzzy Semigroups - Mordeson, John N.;Malik, Davender S.;Kuroki, Nobuaki
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Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy…mehr

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Produktbeschreibung
Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. We concentrate mainly on theoretical aspects, but we do include applications. The applications are in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. An extensive account of fuzzy automata and fuzzy languages is given in [100]. Consequently, we only consider results in these areas that have not appeared in [100] andthat pertain to semigroups. In Chapter 1, we review some basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages. The purpose of this chapter is to present basic results that are needed in the remainder of the book. In Chapter 2, we introduce certain fuzzy ideals of a semigroup, namely, fuzzy two-sided ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy quasi ideals, and fuzzy generalized bi-ideals.
Autorenporträt
Dr. John N. Mordeson is Professor Emeritus of Mathematics at Creighton University. He received his B.S., M.S., and Ph.D. from Iowa State University. He is a member of Phi Kappa Phi. He has published 19 books and over 200 journal articles, and is on the editorial board of numerous journals. He has served as an external examiner for Ph.D. candidates from India, South Africa, Bulgaria and Pakistan, and has also served as a referee for numerous journals and grant agencies. He is particularly interested in applying mathematics of uncertainty to combat the problem of human träcking. Dr. Sunil Mathew is a faculty member at the Department of Mathematics, NIT Calicut, India. He has holds a master's degree from St. Josephs College, Calicut, and a Ph.D. in Fuzzy Graph Theory from the National Institute of Technology Calicut. He has 20 years of teaching and research experience, and his current research focuses on fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos. He has published more than 100 research papers and written ¿ve books, and is an editor and reviewer for several international journals. He is a member of numerous academic bodies and associations.