Dual Hesitant Fuzzy Aggregation Operators Research Articles

A note on “Some dual hesitant fuzzy Hamacher aggregation operators and their applications to multiple attribute decision making”

As dual hesitant fuzzy sets can express the uncertainty of data efficiently, the aggregation of dual hesitant fuzzy information plays an important role in both theory and application. However, some existing dual hesitant fuzzy aggregation operators are not rigorous enough actually. In this note, we show that some theorems in an earlier paper by Ju et al. [1] (Journal of Intelligent & Fuzzy Systems 27 (2014) 2481–2495) are not correct, i.e., the dual hesitant fuzzy Hamacher weighted averaging operator (DHFHWA) and some other aggregation operators proposed by Ju et al. don’t satisfy idempotency and boundedness. Therefore, the purpose of this paper is to make researchers aware of that some aggregation operators in literature [1] are flawed and limited for many applications.

Development of Archimedean t‐norm and t‐conorm‐based interval‐valued dual hesitant fuzzy aggregation operators with their application in multicriteria decision making

AbstractIn this article, Archimedean t‐norm and t‐conorm (At‐N&t‐CN)‐based aggregation operators are developed for aggregating the interval‐valued dual hesitant fuzzy (IVDHF) elements (IVDHFEs), which can cover a wide variety of existing aggregation operators. After introducing the concept of IVDHF set, several related terms, viz., score function, accuracy function, and degree of hesitancy are defined. Using At‐N&t‐CN, different operations for IVDHFEs are presented. Conversion processes from the developed operators to other forms of operators in several variants of fuzzy environments are discussed. An approach to solve multicriteria decision making problem in IVDHF context is presented using the developed concepts. To demonstrate proficiency of the developed method, an illustrative example is presented. Furthermore, several numerical examples, studied previously, are also solved, and achieved solutions are compared with the existing ones to establish the robustness of the proposed operator.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

AbstractAs an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given, and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

Maclaurin symmetric means of dual hesitant fuzzy information and their use in multi-criteria decision making

This paper investigates the Maclaurin symmetric mean (MSM) within the context of dual hesitant fuzzy sets and develops the dual hesitant fuzzy Maclaurin symmetric mean (DHFMSM), which can address the issues in previous dual hesitant fuzzy aggregation operators. Moreover, we put forward the geometric Maclaurin symmetric mean considering both the MSM and the geometric mean and apply it to propose a dual hesitant fuzzy geometric Maclaurin symmetric mean (DHFGMSM), followed by its several properties and special cases. Subsequently, considering the importance of each argument, the weighted DHFMSM and the weighted DHFGMSM are presented and used to develop an algorithm for realistic multi-criteria decision-making problems. Finally, the practicality of the new results is illustrated by a case study, and the advantages of the new results are highlighted by a comparison with other existing methods.

Dual hesitant fuzzy aggregation operators based on Bonferroni means and their applications to multiple attribute decision making

Dual hesitant fuzzy aggregation operators based on Bonferroni means and their applications to multiple attribute decision making

Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm

Dual hesitant fuzzy set (DHFS) is a new generalization of fuzzy set (FS) consisting of two parts (i.e., the membership hesitancy function and the non-membership hesitancy function), which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set (FS), intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-conorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.

Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making

Multi-criteria decision making (MCDM) has been a hot topic in decision making and systems engineering. The dual hesitant fuzzy sets (DHFSs) is a useful tool to deal with vagueness and ambiguity in the MADM problems. In this paper, we propose a wide range of dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm for dual hesitant fuzzy information. We first redefine some basic operations of dual hesitant fuzzy sets, which are consistent with those of dual hesitant fuzzy sets. We introduce three kinds of distance measures for dual hesitant fuzzy sets, which the corresponding support measures can be obtained. Then we propose several power aggregation operators on dual hesitant fuzzy sets, study their properties and give some specific dual hesitant fuzzy aggregation operators. In the end, we develop two approaches for multiple attribute group decision making with dual hesitant fuzzy information, and illustrate a real world example to show the behavior of the proposed operators.

Dual hesitant fuzzy interaction operators and their application to group decision making

Considering that there may exist some interactions between membership function and non-membership function of different dual hesitant fuzzy sets (DHFSs), in this paper we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of dual hesitant fuzzy aggregation operators are developed, including dual hesitant fuzzy weighted interaction averaging operator, dual hesitant fuzzy weighted interaction geometric operator, dual hesitant fuzzy ordered weighted interaction averaging operator, dual hesitant fuzzy ordered weighted interaction geometric operator, dual hesitant fuzzy hybrid interaction averaging operator, and dual hesitant fuzzy hybrid interaction geometric operator. The properties of these aggregation operators are investigated. The key advantage of these operators is that the interactions between non-membership function and membership function of different DHFSs are considered, and much more information provided by decision makers (DMs) has been taken into account. Additionally, approaches to multiple attributes decision-making are given based on the aggregation operators under hesitant fuzzy environment and an example is given to illustrate the application of DHFSs in group forecasting.

Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making

With respect to multiple attribute decision making (MADM) problems in which the attributes are inter-dependent and take the form of dual hesitant fuzzy elements, a new MADM method with dual hesitan...

Dual hesitant fuzzy aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making MADM problem based on the aggregation operators with dual hesitant fuzzy information. Then, motivated by the ideal of arithmetic...

Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making

With respect to multiple attribute decision making (MADM) problems in which the attributes are inter-dependent and take the form of dual hesitant fuzzy elements, a new MADM method with dual hesitant fuzzy information is investigated in this paper. Firstly, by using the Choquet integral, some new aggregation operators are developed for aggregating the dual hesitant fuzzy information, such as the dual hesitant fuzzy Choquet ordered average (DHFCOA) operator, the dual hesitant fuzzy Choquet ordered geometric (DHFCOG) operator, the generalized dual hesitant fuzzy Choquet ordered average (GDHFCOA) operator and the generalized dual hesitant fuzzy Choquet ordered geometric (GDHFCOG) operator. Then, some special cases, desirable properties of these operators and the relationships between them are discussed. Furthermore, based on the DHFCOA operator, an approach to MADM is proposed under dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

Multiple Attribute Decision Making Based on Generalized Aggregation Operators under Dual Hesitant Fuzzy Environment

We investigate the multiple attribute decision making (MADM) problems with dual hesitant fuzzy information. We first introduce some basic concepts and operations on dual hesitant fuzzy sets. Then, we develop some generalized dual hesitant fuzzy aggregation operators which encompass some existing operators as their particular cases and discuss their basic properties. Next, we apply the generalized dual hesitant fuzzy Choquet ordered aggregation (GDHFCOA) operator to deal with multiple attribute decision making problems under dual hesitant fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

Dual hesitant fuzzy aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making MADM problem based on the aggregation operators with dual hesitant fuzzy information. Then, motivated by the ideal of arithmetic and geometric operation, we have developed some aggregation operators for aggregating dual hesitant fuzzy information: dual hesitant fuzzy weighted average DHFWA operator, dual hesitant fuzzy weighted geometric DHFWG operator, dual hesitant fuzzy ordered weighted average DHFOWA operator, dual hesitant fuzzy ordered weighted geometric DHFOWG operator, dual hesitant fuzzy hybrid average DHFHA operator and dual hesitant fuzzy hybrid geometric DHFHG operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the dual hesitant fuzzy multiple attribute decision making problems. Finally, a practical example for potential evaluation of emerging technology commercialization with dual hesitant fuzzy information is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Interval-valued dual hesitant fuzzy aggregation operators and their applications to multiple attribute decision making

This paper investigates multiple attribute decision making (MADM) problems in which the attribute values take the form of interval-valued dual hesitant fuzzy elements (IVDHFEs). Firstly, motivated by the concepts of dual hesitant fuzzy set (DHFS) and interval number, the concept, operational laws and comparison laws of interval-valued dual hesitant fuzzy elements are proposed. Then, based on the operational laws of IVDHFEs, some aggregation operators are developed for aggregating the interval-valued dual hesitant fuzzy information, such as the interval-valued dual hesitant fuzzy weighted aggregation operators, the interval-valued dual hesitant fuzzy ordered weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy ordered weighted aggregation operators and the interval-valued dual hesitant fuzzy hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed in detail. Based on the interval-valued dual hesitant fuzzy weighted average (IVDHFWA) operator, an approach to multiple attribute decision making is proposed under interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.