Affiliations: [a] College of Information Science and Technology, Beijing Normal University, Beijing, PR China | [b] School of Computer and Artificial Intelligence, Xiamen Institute of Technology, Xiamen, PR China
Correspondence:
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Corresponding author. Wenyi Zeng, College of Information Science and Technology, Beijing Normal University, Beijing 100875, PR China
Abstract: Hesitant fuzzy linguistic term set(HFLTS), which permits decision makers to use several linguistic terms to assess a variable, is a useful tool to deal with situations in which people are hesitant in providing their assessment. In this paper, we introduce the concept of weighted hesitant fuzzy linguistic term set(WHFLTS), in which different weights are designed to these possible linguistic terms, and the weights indicate that the decision maker has different confidence in giving every possible assessment. After that, we introduce some operations such as union, intersection, complement, multiplication of weighted hesitant fuzzy linguistic elements, discuss their operation properties, and propose the score function of the weighted hesitant fuzzy linguistic element(WHFLE) to compare weighted hesitant fuzzy linguistic elements(WHFLEs). Furthermore, we introduce the concept of hesitance degree of weighted hesitant fuzzy linguistic element, present four aggregation operators such as the weighted hesitant fuzzy linguistic weighted averaging(WHFLWA) operator, the weighted hesitant fuzzy linguistic weighted geometric(WHFLWG) operator, the generalized weighted hesitant fuzzy linguistic weighted averaging(GWHFLWA) operator and the generalized weighted hesitant fuzzy linguistic weighted geometric(GWHFLWG) operator to aggregate weighted hesitant fuzzy linguistic information, and build the mathematical model of multi-criteria group decision making based on weighted hesitant fuzzy linguistic environment. Finally, two numerical examples are used to illustrate the effectiveness and applicability of our proposed method.
Keywords: Hesitant fuzzy sets, Hesitant fuzzy linguistic term sets, Weighted hesitant fuzzy
linguistic term sets, Aggregation operator, Group decision making
