Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making
TL;DR: Several series of aggregation operators are proposed and two methods are proposed to determine the aggregation weight vectors based on the support degrees among aggregation arguments, so that the weight vector of decision makers are obtained more objectively.
Abstract: Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a suitable means allowing several possible degrees for an element to a set. In this paper, we study the aggregation of the hesitancy fuzzy information. Several series of aggregation operators are proposed and the connections of them are discussed. To reflect the correlation of the aggregation arguments, two methods are proposed to determine the aggregation weight vectors. Based on the support degrees among aggregation arguments, the weight vector of decision makers are obtained more objectively. To deal with the correlation of criteria, we apply the Choquet integral to get the weights of criteria. A method is also proposed for group decision making under hesitant fuzzy environment.
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TL;DR: A novel approach based on TOPSIS and the maximizing deviation method for solving MADM problems, in which the evaluation information provided by the decision maker is expressed in hesitant fuzzy elements and the information about attribute weights is incomplete is developed.
Abstract: Hesitant fuzzy set (HFS), which allows the membership degree of an element to a set represented by several possible values, is considered as a powerful tool to express uncertain information in the process of multi-attribute decision making (MADM) problems. In this paper, we develop a novel approach based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and the maximizing deviation method for solving MADM problems, in which the evaluation information provided by the decision maker is expressed in hesitant fuzzy elements and the information about attribute weights is incomplete. There are two key issues being addressed in this approach. The first one is to establish an optimization model based on the maximizing deviation method, which can be used to determine the attribute weights. According to the idea of the TOPSIS of Hwang and Yoon [1], the second one is to calculate the relative closeness coefficient of each alternative to the hesitant positive-ideal solution, based on which the considered alternatives are ranked and then the most desirable one is selected. An energy policy selection problem is used to illustrate the detailed implementation process of the proposed approach, and demonstrate its validity and applicability. Finally, the extended results in interval-valued hesitant fuzzy situations are also pointed out.
553 citations
Cites background from "Some Hesitant Fuzzy Aggregation Ope..."
...In classical MADM, the assessments of alternatives are precisely known [2,3]....
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TL;DR: This paper develops some prioritized aggregation operators for aggregating hesitant fuzzy information, and applies them to develop some models for hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level.
Abstract: In this paper, we investigate the hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level. Motivated by the ideal of prioritized aggregation operators [R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263-274], we develop some prioritized aggregation operators for aggregating hesitant fuzzy information, and then apply them to develop some models for hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approaches and to demonstrate its practicality and effectiveness.
494 citations
TL;DR: An overview on hesitant fuzzy sets is presented with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.
Abstract: The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.
405 citations
TL;DR: The E-VIKOR method and TOPSIS method are developed to solve the MCDM problems with hesitant fuzzy set information, which can be accurately and perfectly described in terms of the opinions of decision makers.
326 citations
Cites background from "Some Hesitant Fuzzy Aggregation Ope..."
...[26] developed several series of aggregation operators for hesitant fuzzy information with the aid of quasi-arithmetic means....
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TL;DR: This paper develops a wide range of hesitant fuzzy power aggregation operators for hesitant fuzzy information and demonstrates several useful properties of the operators and discusses the relationships between them.
304 citations
Cites background from "Some Hesitant Fuzzy Aggregation Ope..."
...Hesitant fuzzy set theory has been applied to several practical problems, primarily in the area of decision making [33,36,40,43,44,57,70]....
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...Intuitionistic fuzzy set (Atanassov 1986) and fuzzy multiset (Yager 1986; Miyamoto 2000) are another two generalizations of fuzzy set, while the former contains three types of information (the membership, the nonmembership and the hesitancy information), the latter permits the elements repeating more than once....
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03 Jan 1988
TL;DR: A type of operator for aggregation called an ordered weighted aggregation (OWA) operator is introduced and its performance is found to be between those obtained using the AND operator and the OR operator.
Abstract: The author is primarily concerned with the problem of aggregating multicriteria to form an overall decision function. He introduces a type of operator for aggregation called an ordered weighted aggregation (OWA) operator and investigates the properties of this operator. The OWA's performance is found to be between those obtained using the AND operator, which requires all criteria to be satisfied, and the OR operator, which requires at least one criteria to be satisfied. >
6,534 citations