Mathematics and Statistics Vol. 10(3), pp. 515 - 522
DOI: 10.13189/ms.2022.100306
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()-Anti-Intuitionistic Fuzzy Soft b-Ideals in BCK/BCI-Algebras

Aiyared Iampan 1,*, M. Balamurugan 2, V. Govindan 3
1 Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand
2 Department of Mathematics, Sri Vidya Mandir Arts and Science College (Autonomous), India
3 Department of Mathematics, Dmi St John The Baptist University, Malawi


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 ()-AFSBI and an ()-AIFSBI of are introduced, and some characterizations of ()-AIFSBI are discussed using the concept of an AIFSBI with thresholds. Finally, conditions are given for a ()-AIFSBI to be a (∈,∈)-AIFSBI.

BCK/BCI-algebra, Intuitionistic Fuzzy Soft Set, Anti-intuitionistic Fuzzy Soft B-ideal and ()-anti-intuitionistic Fuzzy Soft B-ideal

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Aiyared Iampan , M. Balamurugan , V. Govindan , "()-Anti-Intuitionistic Fuzzy Soft b-Ideals in BCK/BCI-Algebras," Mathematics and Statistics, Vol. 10, No. 3, pp. 515 - 522, 2022. DOI: 10.13189/ms.2022.100306.

(b). APA Format:
Aiyared Iampan , M. Balamurugan , V. Govindan (2022). ()-Anti-Intuitionistic Fuzzy Soft b-Ideals in BCK/BCI-Algebras. Mathematics and Statistics, 10(3), 515 - 522. DOI: 10.13189/ms.2022.100306.