Intra-Regular Abel Grassmann’s Groupoids Determined by $(\in _{\gamma },\in _{\gamma }\vee q_{\delta })$ Fuzzy Sets

Abstract

It is common knowledge that various models with their limited boundaries of truth and falsehood are not sufficient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and imprecisions. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not sufficient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh introduced the concept of a fuzzy set which provides a useful mathematical tool for describing the behavior of systems that are either too complex or are ill-defined to admit precise mathematical analysis by classical methods. Our aim in this paper is to use non-associate algebraic structures such as AG-groupoids and to develop the resulting properties. For the applications of this concept we introduce generalized fuzzy ideals and discuss their properties, specifically we characterize intra regular AG-groupoids using the properties of generalized fuzzy ideals.