Abstract
In this study, a new parametric method is proposed to rank intuitionistic fuzzy numbers in a general form. One of the advantages of the proposed method is that the decision maker’s idea is taken into account by selecting appropriate amounts of decision level and hesitation degree parameters. In some illustrative examples, the superiority of the proposed method over some other approaches is demonstrated. Furthermore, to show the ability of the method to solve intuitionistic fuzzy optimization problems, the proposed method is applied to solve intuitionistic fuzzy network data envelopment analysis (IFNDEA) problems. Also, in three appropriate examples, the validity of the suggested method and its capacity to solve real-world problems are illustrated.
Highlights
Intuitionistic fuzzy sets (IFSs), first proposed by Atanassov [1, 2], are a generalization of Zadeh’s fuzzy sets [3, 4] to model noncrisp and uncertain sets
In the work of Li [26], value and ambiguity are used to rank nonnormal triangular intuitionistic fuzzy numbers (TriIFNs), and the proposed method is applied to a personnel selection problem
By proper selection of the decision level and the hesitation degree, the decision maker’s idea is accounted for in the decision-making process, and less information is lost in IFNs. is parametric index can be applied to compare and rank IFNs
Summary
Intuitionistic fuzzy sets (IFSs), first proposed by Atanassov [1, 2], are a generalization of Zadeh’s fuzzy sets [3, 4] to model noncrisp and uncertain sets. Ye [15] calculated the expected value of a TraIFN that was introduced by Grzegorzewski [13] and applied it to a trapezoidal intuitionistic fuzzy multicriteria decision-making problem. In the work of Li [26], value and ambiguity are used to rank nonnormal triangular intuitionistic fuzzy numbers (TriIFNs), and the proposed method is applied to a personnel selection problem. Nayagam et al [28] proposed a parametric score function using improved value and ambiguity indexes to rank TraIFNs and applied it to solve a multicriteria decision-making problem. Puri and Yadav [42], by applying the expected interval and expected value (Grzegorzewski [13]), proposed an index to estimate triangular intuitionistic fuzzy input and output data in an IFDEA model. Two important limitations of the abovementioned approaches in IFDEA are that, almost all of them work for a
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