# Neutrosophic Set Approach to Algebraic Structures

Book

2016

## Abstract

Real world is featured with complex phenomenons. As uncertainty is inevitably involved in problems arise in various elds of life and classical methods failed to handle these type of problems. Dealing with imprecise, uncertain or imperfect information was a big task for many years. Many modelswerepresentedinordertoproperlyincorporateuncertaintyintosystem description, LotA.Zadeh in 1965 introduced the idea of a fuzzy set. Zadeh replaced conventional characteristic function of classical crisp sets which takes on its values in f0;1g by membership function which takes on its values in closed interval [0;1]. Fuzzy set theory is conceptually a very powerful technique to deal with another aspect or vision of imperfect information related to vagueness and is a modelling tool for complex systems that can be controlled by human but very tough to dene exactly. It also reduces the chances of failures in modelling. Until 1960s uncertainty was considered solely in terms of probability theory and understood as randomness but Zadeh discovered the relationships of probability and fuzzy set theory which has appropriate approach to deal with uncertainties. Fuzzy set theory not only formulate imprecise information into model but it helps us in problem solving and decision making. In fact a fuzzy set approaches are suitable when it is needed to model human knowledge or evaluation. Moreover a fuzzy logic is that branch of mathematics that allows a computer to model the real world in the same way as that of people do. Many authors have applied the fuzzy set theory to generalize the basic theories of Algebra. Mordeson et al. has discovered the grand exploration of fuzzy semigroups, where theory of fuzzy semigroups is explored along with the applications of fuzzy semigroups in fuzzy coding, fuzzy nite state mechanics and fuzzy languages etc. and fuzzy approach is also applied to the problem of integrated design of high speed planar mechanism. But at a point when we talk about degree of non-membership or falsehood then fuzzy set theory does not work properly and we need something new to deal with it more properly.

## Publisher

Pons Editions, Brussels

## ISSN

978-1-59973-471-2

English

## Keywords

neutrosophic set, neutrosophic logic, algebraic structures