Abstract
Hesitant fuzzy linguistic decision making is a focus point in linguistic decision making, in which the main method is based on preference ordering. This paper develops a new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making; the method is inspired by the TOPSIS method and the preference degree between two hesitant fuzzy linguistic term sets (HFLTSs). To this end, we first use the preference degree to define a pseudo-distance between two HFLTSs and analyze its properties. Then we present the positive (optimistic) and negative (pessimistic) information of each criterion provided by each decision maker and aggregate these by using weights of decision makers to obtain the hesitant fuzzy linguistic positive and negative ideal solutions. On the basis of the proposed pseudo-distance, we finally obtain the positive (negative) ideal separation matrix and a new relative closeness degree to rank alternatives. We also design an algorithm based on the provided method to carry out hesitant fuzzy linguistic decision making. An illustrative example shows the elaboration of the proposed method and comparison with the symbolic aggregation-based method, the hesitant fuzzy linguistic TOPSIS method and the hesitant fuzzy linguistic VIKOR method; it seems that the proposed method is a useful and alternative decision-making method.
Highlights
In real-world practices, we always face tasks and activities in which it is necessary to use decision-making processes
In [63], Beg and Rashid firstly proposed the TOPSIS method for hesitant fuzzy linguistic term sets (HFLTSs), in which, the one decision matrix X is calculated by aggregating the opinions of decision makers; the HFLTS positiveand negative-ideal solutions are obtained by the minimization of the minimal and maximal assessments of cost criteria and the maximization of the minimal and maximal assessments of benefit criteria; the positive-ideal separation matrix is constructed by distances between X and the positive-ideal solution, which can be used to obtain the relative closeness of each alternative and rank all the alternatives
We develop a new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making, in which, we use the preference degree to define a pseudo-distance between two HFLTSs, and we present the positive and negative information of each criterion provided by each decision maker
Summary
In real-world practices, we always face tasks and activities in which it is necessary to use decision-making processes. Ashtiani et al [57] extended the TOPSIS method to solve a multiple-attribute decision-making problem with interval-valued fuzzy sets. In [63], Beg and Rashid firstly proposed the TOPSIS method for HFLTSs, in which, the one decision matrix X is calculated by aggregating the opinions of decision makers; the HFLTS positiveand negative-ideal solutions are obtained by the minimization of the minimal and maximal assessments of cost criteria and the maximization of the minimal and maximal assessments of benefit criteria; the positive-ideal separation matrix (negative-ideal separation matrix) is constructed by distances between X and the positive-ideal (negative-ideal) solution, which can be used to obtain the relative closeness of each alternative and rank all the alternatives. Fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making, in which, we use the preference degree to define a pseudo-distance between two HFLTSs, and we present the positive and negative information of each criterion provided by each decision maker.
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