Hesitant Fuzzy Aggregation Operators Research Articles

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...

Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making

As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. We first introduce some new operational rules of hesitant fuzzy sets based on the Hamacher t-norm and t-conorm, in which a family of hesitant fuzzy Hamacher operators is proposed for aggregating hesitant fuzzy information. Some basic properties of these proposed operators are given, and the relationships between them are shown in detail. We further discuss the interrelations between the proposed aggregation operators and the existing hesitant fuzzy aggregation operators. Applying the proposed hesitant fuzzy operators, we develop a new technique for hesitant fuzzy multicriteria decision making problems. Finally, the effectiveness of the proposed technique is illustrated by mean of a practical example.

Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making

Hesitant fuzzy sets, originally proposed by Torra, can be used as an efficient tool for dealing with situations in which experts hesitate between several numerical values to define the membership o...

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...

Hesitant intuitionistic fuzzy linguistic aggregation operators and their applications to multiple attribute decision making

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs). Firstly, mo...

Dynamic hesitant fuzzy aggregation operators in multi-period decision making

Purpose – The purpose of this paper is to present some dynamic hesitant fuzzy aggregation operators to tackle with the multi-period decision-making problems where all decision information is provided by decision makers in hesitant fuzzy information from different periods. Design/methodology/approach – First, the notions and operational laws of the hesitant fuzzy variable are defined. Then, some dynamic hesitant fuzzy aggregation operators involve the dynamic hesitant fuzzy weighted averaging (DHFWA) operator, the dynamic hesitant fuzzy weighted geometric (DHFWG) operator, and their generalized versions are presented. Some desirable properties of these proposed operators are established. Furthermore, two linguistic quantifier-based methods are introduced to determine the weights of periods. Next, the paper extends the results to the interval-valued hesitant fuzzy situation. Furthermore, the authors develop an approach to solve the multi-period multiple criteria decision making (MPMCDM) problems. Finally, an illustrative example is given. Findings – The presented hesitant fuzzy aggregation operators are very suitable for aggregating the hesitant fuzzy information collected at different periods. The developed approach can solve the MPMCDM problems where all decision information takes the form of hesitant fuzzy information collected at different periods. Practical implications – The presented hesitant fuzzy aggregation operators and decision-making approach can widely apply to dynamic decision analysis, multi-stage decision analysis in real life. Originality/value – The paper presents the useful way to aggregate the hesitant fuzzy information collected at different periods in MPMCDM situations.

An Accurate Method for Determining Hesitant Fuzzy Aggregation Operator Weights and Its Application to Project Investment

As a generalization of fuzzy sets, hesitant fuzzy set is a very useful technique to represent decision makers' hesitancy in decision making. Various hesitant fuzzy weighted operators have been developed to aggregate hesitant fuzzy information, but it seems that there is no investigation on the weighted approach of obtaining their weights, which is decisive for the calculation and comparison of hesitant fuzzy elements HFEs in multicriteria group decision making. In this paper, we propose an accurate weighted method AWM of monotonicity and proportionality, based on nothing but the score function and the new deviation function. Because of the above properties, AWM may be an accurate and objective technique to calculate the weights of HFEs and aggregation operator. Then, based on this weighted approach, we develop two new hesitant fuzzy ordered weighted aggregation operators, that is, hesitant fuzzy ordered accurate weighted averaging and hesitant fuzzy ordered accurate weighted geometric operators, and study their relationships and properties. In the end, an illustrative project investment problem is used to demonstrate how to apply the proposed weighted approach and to observe the computational consequences resulting from new aggregation operators. This work contributes significantly to improve the hesitant fuzzy theory, and proposes two new hesitant fuzzy aggregation operators.

Hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making

Hamacher product is a t-norm and Hamacher sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some hesitant fuzzy aggregation operators. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy multiple attribute decision making problems. Finally, a practical example for evaluating the customer satisfaction of e-commerce websites is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Multiple Attribute Decision Making Based on Hesitant Fuzzy Einstein Geometric Aggregation Operators

We first define an accuracy function of hesitant fuzzy elements (HFEs) and develop a new method to compare two HFEs. Then, based on Einstein operators, we give some new operational laws on HFEs and some desirable properties of these operations. We also develop several new hesitant fuzzy aggregation operators, including the hesitant fuzzy Einstein weighted geometric (HFEWGε) operator and the hesitant fuzzy Einstein ordered weighted geometric (HFEWGε) operator, which are the extensions of the weighted geometric operator and the ordered weighted geometric (OWG) operator with hesitant fuzzy information, respectively. Furthermore, we establish the connections between the proposed and the existing hesitant fuzzy aggregation operators and discuss various properties of the proposed operators. Finally, we apply the HFEWGεoperator to solve the hesitant fuzzy decision making problems.

Hesitant triangular fuzzy information aggregation operators based on Bonferroni means and their application to multiple attribute decision making.

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

Some interval-valued hesitant fuzzy aggregation operators based on Archimedean t-norm and t-conorm with their application in multi-criteria decision making

As a generalization of hesitant fuzzy set (HFS), interval-valued hesitant fuzzy set (IVHFS) permits an element's membership degree to be a set of several possible interval values and can therefore be used as an efficient mathematical tool for modeling people's hesitancy and uncertainty in multi-criteria decision making (MCDM). The Archimedean t-conorm and t-norm provide a generalization of a variety of other t-conorms and t-norms that include the Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms as special cases. In this paper, we first present some new operational laws for interval-valued hesitant fuzzy elements (IVHFEs) based on the Archimedean t-conorm and t-norm. Then, based on these operational laws, we develop several Archimedean t-conorm-and t-norm-based interval-valued hesitant fuzzy aggregation operators, which provide a family of interval-valued hesitant fuzzy aggregation operators that include the existing interval-valued hesitant fuzzy aggregation operators based on the Algebraic and Einstein t-conorms and t-norms as special cases. Some desired properties and special cases of the developed operators are investigated in detail. Furthermore, we develop an approach to MCDM under interval-valued hesitant fuzzy environments. Finally, an illustrative example is provided to show the effectiveness and practicality of the proposed operators and approach.

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.

Models for decision making problems with hesitant fuzzy information

We investigate the decision making problems with hesitant fuzzy information. Firstly, some operational laws of hesitant fuzzy elements and score function of hesitant fuzzy elements are introduced. Then, we have developed two induced generalized hesitant fuzzy aggregation operators: induced generalized hesitant fuzzy choquet ordered averaging (IGHFCOA) operator and induced generalized hesitant fuzzy choquet ordered geometric (IGHFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have applied the IGHFCOA and IGHFCOG operators to decision making problems for five kinds of Protein's nutritional assessment with hesitant fuzzy information. Finally an illustrative example has been given to show the developed method.

Continuous hesitant fuzzy aggregation operators and their application to decision making under interval-valued hesitant fuzzy setting.

Interval-valued hesitant fuzzy set (IVHFS), which is the further generalization of hesitant fuzzy set, can overcome the barrier that the precise membership degrees are sometimes hard to be specified and permit the membership degrees of an element to a set to have a few different interval values. To efficiently and effectively aggregate the interval-valued hesitant fuzzy information, in this paper, we investigate the continuous hesitant fuzzy aggregation operators with the aid of continuous OWA operator; the C-HFOWA operator and C-HFOWG operator are presented and their essential properties are studied in detail. Then, we extend the C-HFOW operators to aggregate multiple interval-valued hesitant fuzzy elements and then develop the weighted C-HFOW (WC-HFOWA and WC-HFOWG) operators, the ordered weighted C-HFOW (OWC-HFOWA and OWC-HFOWG) operators, and the synergetic weighted C-HFOWA (SWC-HFOWA and SWC-HFOWG) operators; some properties are also discussed to support them. Furthermore, a SWC-HFOW operators-based approach for multicriteria decision making problem is developed. Finally, a practical example involving the evaluation of service quality of high-tech enterprises is carried out and some comparative analyses are performed to demonstrate the applicability and effectiveness of the developed approaches.

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.

An approach to multiple attribute decision making problems based on hesitant fuzzy set

In this paper, we investigate the multiple attribute decision making with hesitant fuzzy information. Motivated by the ideal of dependent aggregation, in this paper, we develop some dependent hesitant fuzzy aggregation operators: the dependent hesitant fuzzy ordered weighted averaging (DHFOWA) operator and the dependent hesitant fuzzy ordered weighted geometric (DHFOWG) operator, in which the associated weights only depend on the aggregated hesitant fuzzy arguments and can relieve the influence of unfair hesitant fuzzy arguments on the aggregated results by assigning low weights to those “false” and “biased” ones and then apply them to develop some approaches for multiple attribute group decision making with hesitant fuzzy information. Finally, an illustrative example for supplier selection is given to verify the developed approach and to 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.

Group decision making under hesitant fuzzy environment with application to personnel evaluation

In many personnel evaluation scenarios, decision makers are asked to provide their preferences anonymously to both ensure privacy and avoid psychic contagion. The use of hesitant fuzzy sets is a powerful technique for representing this type of information and has been well studied. This paper explores aggregation methods for prioritized hesitant fuzzy elements and their application on personnel evaluation. First, the generalized hesitant fuzzy prioritized weighted average (GHFPWA) and generalized hesitant fuzzy prioritized weighted geometric (GHFPWG) operators are presented. Some desirable properties of the methods are discussed and special cases are investigated in detail. Previous research has indicated that many existing hesitant fuzzy aggregation operators are special cases of the proposed operators. Then, a procedure and algorithm for group decision making is provided using these proposed generalized hesitant fuzzy aggregation operators. Finally, the group decision making method is applied to a representative personnel evaluation problem that involves a prioritization relationship over the evaluation index.

Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making

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.