Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making

Manivannan Balamurugan, Nazek Alessa (), Karuppusamy Loganathan () and M. Sudheer Kumar
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Manivannan Balamurugan: Department of Mathematics, School of Science & Humanities, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India
Nazek Alessa: Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Karuppusamy Loganathan: Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India
M. Sudheer Kumar: Department of Science and Humanities, MLR Institute of Technology, Hyderabad 500043, Telangana, India

Mathematics, 2023, vol. 11, issue 21, 1-18

Abstract: In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fuzzy soft ideals is a bipolar intuitionistic fuzzy soft ideal. We also demonstrate how to use a bipolar intuitionistic fuzzy soft set to solve a problem involving decision making. Finally, we provide a general approach for handling decision-making problems using a bipolar intuitionistic fuzzy soft set.

Keywords: BCK-algebras; soft set; bipolar intuitionistic fuzzy soft set; bipolar intuitionistic fuzzy soft ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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