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The dual hesitant fuzzy set(DHFS) is a useful tool to deal with situations in which people are hesitant about providing their satisfaction degree and dissatisfaction degree. In this paper, we introduce the concepts of weighted dual hesitant fuzzy set(WDHFS) and weighted dual hesitant fuzzy element(WDHFE). Furthermore, we introduce some basic operations such as union, intersection, complement, multiplication and power operation of weighted dual hesitant fuzzy elements, investigate their operation properties, propose the score function and the accuracy function of WDHFE to compare two weighted dual hesitant fuzzy elements, and present two kinds of aggregation operators such as WDHFWA operator and WDHFWG operator to fuse weighted dual hesitant fuzzy information. Besides, we introduce the concept of hesitance degree of WDHFE, and propose a distance measure between weighted dual hesitant fuzzy elements based on the feature vector of WDHFE, which satisfies the four properties including triangle inequality. In addition, we develop an approach to group decision making based on the weighted dual hesitant fuzzy environment. Finally, two numerical examples are used to illustrate the effectiveness and practicality of our proposed approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The main feature of Pythagorean fuzzy sets is that it is characterized by five parameters, namely membership degree, nonmembership degree, hesitancy degree, strength of commitment about membership, and direction of commitment. In this paper, we first investigate four existing comparison methods for ranking Pythagorean fuzzy sets and point out by examples that the method proposed by Yager, which considers the influence fully of the five parameters, is more efficient than the other ones. Later, we propose a variety of distance measures for Pythagorean fuzzy sets and Pythagorean fuzzy numbers, which take into account the five parameters of Pythagorean fuzzy sets. Based on the proposed distance measures, we present some similarity measures of Pythagorean fuzzy sets. Furthermore, a multiple criteria Pythagorean fuzzy group decision‐making approach is proposed. Finally, a numerical example is provided to illustrate the validity and applicability of the presented group decision‐making method. [ABSTRACT FROM AUTHOR]