(<img src=image/13426382_01.gif>)-Anti-Intuitionistic Fuzzy Soft b-Ideals in BCK/BCI-Algebras

Abstract

Among many algebraic structures, algebras of logic form an essential class of algebras. BCK and BCI-algebras are two classes of logical algebras. They were introduced by Imai and Iséki [6, 7] in 1966 and have been extensively investigated by many researchers. The concept of fuzzy soft sets is introduced in [17] to generalize standard soft sets [21]. The concept of intuitionistic fuzzy soft sets is introduced by Maji et al. [18], which is based on a combination of the intuitionistic fuzzy set [2] and soft set models. The first section will discuss the origins and importance of studies in this article. Section 2 will review the definitions of a BCK/BCI-algebra, a soft set, a fuzzy soft set, and an intuitionistic fuzzy soft set and show the essential properties of BCK/BCI-algebras to be applied in the next section. In Section 3, the concept of an anti-intuitionistic fuzzy soft b-ideal (AIFSBI) is discussed in BCK/BCI-algebras, and essential properties are provided. A set of conditions is provided for an AIFSBI to be an anti-intuitionistic fuzzy soft ideal (AIFSI). The definition of quasi-coincidence of an intuitionistic fuzzy soft point with an intuitionistic fuzzy soft set (IFSS) is considered in a more general form. In Section 4, the concepts of an (<img src=image/13426382_01.gif>)-AFSBI and an (<img src=image/13426382_01.gif>)-AIFSBI of <img src=image/13426382_02.gif> are introduced, and some characterizations of (<img src=image/13426382_01.gif>)-AIFSBI are discussed using the concept of an AIFSBI with thresholds. Finally, conditions are given for a (<img src=image/13426382_01.gif>)-AIFSBI to be a (∈,∈)-AIFSBI.