Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis

Abstract

Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. In this paper, by introducing a generalization parameter, which itself is trapezoidal fuzzy, we define generalized trapezoidal fuzzy soft sets and then study some of their properties. Finally, applications of generalized trapezoidal fuzzy soft sets in a decision making problem and medical diagnosis problem are shown.

On Interval-Valued Hesitant Fuzzy Soft Sets

“…Very recently, integrating trapezoidal fuzzy sets with soft sets, Xiao et al [19] initiated the trapezoidal fuzzy soft sets to deal with certain linguistic assessments. Further, in order to capture the vagueness of the attribute with linguistic assessments information, Zhang et al [20] generalized trapezoidal fuzzy soft sets introduced by Xiao et al [19] and defined the concept of generalized trapezoidal fuzzy soft sets.…”

Comment on “Corrigendum to ‘On Interval‐Valued Hesitant Fuzzy Soft Sets’” and “Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis”

“…For the finite set case, Zhang et al [2] defined the concept of generalized trapezoidal fuzzy soft set and showed some examples of its operations, along with an application in decision-making. In this section we first give an example to show the following Theorem 15 is incorrect.…”

“…Theorem 15 (see [2,Theorem 29,p.7]). Let {Φ, Ψ, Γ} ⊆ (J × J) with supp Φ = 1 , supp Ψ = 2 , and supp Γ = 3 .…”

“…The aim of this article is to correct assertions (3) and (4) of Theorem 17 proposed by Khalil et al [1] and assertions (3) and (4) of Theorem 29 proposed by Zhang et al [2]. We first generalize (in an unambiguous manner) the fitting or remedy of the involved preliminary notions concerning intervalvalued hesitant fuzzy soft set and generalized trapezoidal fuzzy soft sets and then use these notions to remedy the flaw in those assertions.…”

“…It is necessary to present the theory in a mathematical (at least errorless) way. So, in this paper, we will show how to remedy flows in soft set theory by correcting assertions (3) and (4) of Theorem 17 in [1] and assertions (3) and (4) of Theorem 29 in [2] (including also remedy preliminaries they involved).…”