GE-Algebras Advanced by Intuitionistic Fuzzy Points

Abstract

In this paper, we introduce the notion of intuitionistic fuzzy GE-algebra by combining the concepts of GE-algebras and intuitionistic fuzzy sets. We provide a necessary and sufficient condition for an intuitionistic fuzzy set to form an intuitionistic fuzzy GE-algebra. This study examines various properties and characterizations of intuitionistic fuzzy GE-algebra. In particular, we explore the roles of (gimel A,t)is an element of,(& eth;A,s)is an element of,(gimel A,t)q,(& eth;A,s)q,(gimel A,t)is an element of boolean OR q, and (& eth;A,s)is an element of boolean OR q sets in determining the subalgebra structures within GE-algebras. Examples illustrate the results, and counterexamples clarify the necessity of the conditions. These results not only enhance the theory of GE-algebras, but also contribute to the algebraic treatment of uncertainty using intuitionistic fuzzy logic.