期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2017
卷号：6
期号：8
页码：17544
DOI：10.15680/IJIRSET.2017.0608294
出版社：S&S Publications
摘要：The theory of fuzzy sets was introduced by L. A. Zadeh in his classic paper “Fuzzy Sets” [1] in 1965. Itenables us to describe mathematically the collection of objects for which there is no precise criteria for membership.For example, collection of beautiful women. But it is a fact that such classes of ill defined objects play an importantrole in certain real situations. In patter, classification fuzziness is a rule rather than an exception. Ever since itsinception the theory of fuzzy sets has advanced in many disciplines. Theoretical advances have been made in manydirections such as fuzzy Algebra, Fuzzy Analysis, Fuzzy Topology and Fuzzy logic. Today the theory of fuzzy sets isfinding applications in a wide variety of fields such as computer science, artificial intelligence, decision analysis,Management science, and operations research and so on. Home appliances like washing machine, vacuum cleaner aremade using fuzzy logic. My dissertation surveys some of the basic concepts and theories of “Fuzzy Algebra andTopology” which is a generalization of concepts to Fuzziness. We deal with Fuzzy subgroups of a group, levelsubgroups and homomorphism. We deals with Fuzzy direct product of fuzzy subgroups of subgroups. We describe theconcepts of Fuzzy subrings and homomorphism of subrings and subfields. We describes about Fuzzy topologicalspaces, local countability, convergence, separability, product Fuzzy topology and fuzzy homeomorphism. We describethe concepts of Fuzzy subrings and homomorphism of subrings and subfields. We describes about Fuzzy topologicalspaces, local countability, convergence, separability, product Fuzzy topology and fuzzy homomorphism.
