Possibility Fuzzy Soft Set

Abstract

We introduce the concept of possibility fuzzy soft set and its operation and study some of its properties. We give applications of this theory in solving a decision-making problem. We also introduce a similarity measure of two possibility fuzzy soft sets and discuss their application in a medical diagnosis problem.

Fuzzy Soft Expert Set and Its Application

“…Also Maji et al [5] have introduced the concept of fuzzy soft set, a more general concept, which is a combination of fuzzy set and soft set and studied its properties and also Roy and Maji [6] used this theory to solve some decision making problems. Alkhazaleh et al [7] introduced the concept of soft multisets as a generalization of soft set. They also defined the concepts of fuzzy parameterized interval-valued fuzzy soft set [8] and possibility fuzzy soft set [9] and gave their applications in decision making and medical diagnosis.…”

“…Alkhazaleh et al [7] introduced the concept of soft multisets as a generalization of soft set. They also defined the concepts of fuzzy parameterized interval-valued fuzzy soft set [8] and possibility fuzzy soft set [9] and gave their applications in decision making and medical diagnosis. Alkhazaleh and Salleh [10] introduced the concept of a soft expert set, where the user can know the opinion of all experts in one model without any operations.…”

Mapping on Generalized Vague Soft Expert Set

“…One of the most important new mathematical tools is soft set theory defined by Molodtsov [2]. This is extended to fuzzy soft sets [3], [4], [5], [6], [7] and then to vague soft sets [8], [9], [10], [11], [12] followed by interval valued vague soft sets [13], [14], [15]. Fuzzy sets were applied to genetic algorithms [16], [17] and into multi Q-fuzzy [18].…”

Generalized Vague Soft Expert Set

“…Vague set theory was provided by Xu et al [3]. Salleh et al [4] and Alkhazaleh et al [5], [6], [7] further extended studies on fuzzy soft sets. Alhazaymeh et al [8] introduced the concept of soft intuitionistic fuzzy sets followed by the notions of vague soft sets [9], [10] and interval-valued vague soft sets [11], [12], [13].…”