Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

Shahbaz Ali; Muneeba Kousar; Qin Xin; Dragan Pamučar; Muhammad Shazib Hameed; Rabia Fayyaz

doi:10.3390/e23111498

Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

Entropy (Basel). 2021 Nov 13;23(11):1498. doi: 10.3390/e23111498.

Authors

Shahbaz Ali¹, Muneeba Kousar¹, Qin Xin², Dragan Pamučar³, Muhammad Shazib Hameed¹, Rabia Fayyaz⁴

Affiliations

¹ Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan.
² Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark.
³ Department of Logistics, Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia.
⁴ Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan.

Abstract

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.

Keywords: algorithms and applications for decision-making; belief interval-valued N-soft set; belief interval-valued soft set; possibility belief interval-valued N-soft set.