SMARANDACHE FUZZY ALGEBRA




Author: W. B. Vasantha Kandasamy
Type: eBook
Date Released: 2003
Format: pdf
Language: English
Page Count: 455
Isbn10 Code: 1931233748
Isbn13 Code: 9781931233743


The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white. In any human field, a Smarandache n-structure on a set S means a weak structure {w0} on S such that there exists a chain of proper subsets Pn–1 included in Pn–2 included in … included in P2 included in P1 included in S whose corresponding structures verify the chain {wn–1} > {wn–2} > … > {w2} > {w1} > {w0}, where ‘>’ signifies ‘strictly stronger’ (i.e. structure satisfying more axioms). This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w0} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w1}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-rings, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also applications of Smarandache groupoids, near-rings, and semi-rings in automaton theory, in error-correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter. About the Author Dr. W. B. Vasantha is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai, where she lives with her husband Dr. K. Kandasamy and daughters Meena and Kama. Her current interests include Smarandache algebraic structures, fuzzy theory, coding/ communication theory. In the past decade she has completed guidance of seven Ph.D. scholars in the different fields of non-associative algebras, algebraic coding theory, transportation theory, fuzzy groups, and applications of fuzzy theory to the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars are working under her guidance. She has to her credit 241 research papers of which 200 are individually authored. Apart from this she and her students have presented around 262 papers in national and international conferences. She teaches both undergraduate and postgraduate students at IIT and has guided 41 M.Sc. and M.Tech projects. She has worked in collaboration projects with the Indian Space Research Organization and with the Tamil Nadu State AIDS Control Society. She is currently authoring a ten book series on Smarandache Algebraic Structures in collaboration with the American Research Press.

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