Hesitant Fuzzy Information Aggregation Research Articles

Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

In real life, incomplete information, inaccurate data, and the preferences of decision-makers during qualitative judgment would impact the process of decision-making. As a technical instrument that can successfully handle uncertain information, Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making (MADM) problems. This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership, non-membership, and priority are considered simultaneously. Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators, this paper proposes the Fermatean hesitant fuzzy Heronian mean (FHFHM) operator and the Fermatean hesitant fuzzy weighted Heronian mean (FHFWHM) operator. Then, considering the priority relationship between attributes is often easier to obtain than the weight of attributes, this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator (FHFPHM), and discusses its elegant properties such as idempotency, boundedness and monotonicity in detail. Later, for problems with unknown weights and the Fermatean hesitant fuzzy information, a MADM approach based on prioritized attributes is proposed, which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results. Finally, a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.

Probabilistic Interval-Valued Hesitant Fuzzy Information Aggregation Operators and Their Application to Multi-Attribute Decision Making

Based on the probabilistic interval-valued hesitant fuzzy information aggregation operators, this paper investigates a novel multi-attribute group decision making (MAGDM) model to address the serious loss of information in a hesitant fuzzy information environment. Firstly, the definition of probabilistic interval-valued hesitant fuzzy set will be introduced, and then, using Archimedean norm, some new probabilistic interval-valued hesitant fuzzy operations are defined. Secondly, based on these operations, the generalized probabilistic interval-valued hesitant fuzzy ordered weighted averaging (GPIVHFOWA) operator, and the generalized probabilistic interval-valued hesitant fuzzy ordered weighted geometric (GPIVHFOWG) operator are proposed, and their desirable properties are discussed. We further study their common forms and analyze the relationship among these proposed operators. Finally, a new probabilistic interval-valued hesitant fuzzy MAGDM model is constructed, and the feasibility and effectiveness of the proposed model are verified by using an example of supplier selection.

Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators

Hesitant fuzzy set is an extension of the traditional fuzzy set, and it has the membership function which was expressed by several possible numbers. Since it was introduced, it has been received wide attention from scholars due to its powerful ability in describing the uncertainty. In this paper, we first introduce some new operations on hesitant fuzzy elements (HFEs) based on Dombi t-conorm and t-norm and then proposed some new aggregation operators for HFEs, such as hesitant fuzzy Dombi weighted averaging, hesitant fuzzy Dombi ordered weighted averaging, hesitant fuzzy Dombi weighted geometric, hesitant fuzzy Dombi ordered weighted geometric, hesitant fuzzy Dombi hybrid averaging and hesitant fuzzy Dombi hybrid geometric operator. Finally, a multiple attribute group decision-making approach under hesitant fuzzy environment is presented based on these proposed operators. A real example about typhoon disaster assessment is presented to show the advantages of the proposed method.

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.

Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making

Interval-valued hesitant fuzzy information aggregation plays an important role in interval-valued hesitant fuzzy set theory, which has received more and more attention in recent years. In this paper, we investigate interval-valued hesitant fuzzy multi-attribute group decision-making problems in which there exists a prioritization relationship among the attributes. Firstly, we introduce some Einstein operational laws on interval-valued hesitant fuzzy sets, and discuss some relations of these operations. Then, we develop two interval-valued hesitant fuzzy prioritized aggregation operators with the help of Einstein operations, such as the interval-valued hesitant fuzzy Einstein prioritized weighted average (IVHFEPWA) operator and the interval-valued hesitant fuzzy Einstein prioritized weighted geometric (IVHFEPWG) operator, whose desirable properties are investigated in detail. We further analyze the relationship between these proposed operators and the existing interval-valued hesitant fuzzy prioritized aggregation operators. Moreover, an approach to interval-valued hesitant fuzzy multi-attribute group decision making is given on the basis of the proposed operators. Finally, a numerical example is provided to demonstrate their effectiveness.

Dual hesitant fuzzy group decision making method and its application to supplier selection

The concept of dual hesitant fuzzy set arising from hesitant fuzzy set is generalized by including a function reflecting the decision maker’s fuzziness about the non-membership degree of the information provided. This paper studies some dual hesitant fuzzy information aggregation operators for aggregating dual hesitant fuzzy elements, such as dual hesitant fuzzy Heronian mean operator and dual hesitant fuzzy geometric Heronian mean operator. The research resulting dual hesitant fuzzy information aggregation operators finds an important role in group decision making (GDM) applications. It can fusion the experts’ opinion to the comprehensive ones and based on which an optimal decision making scheme can be determined. The properties of the proposed operators are studied and the application on GDM are investigated. The effectiveness of the GDM method is demonstrated on the case study about supplier selection.

Time-Based Hesitant Fuzzy Information Aggregation Approach for Decision-Making Problems

Hesitant fuzzy sets have been proposed as an extension of fuzzy sets to address situations in which decision makers exhibit variations in their alternatives' assessment values. However, in real-world problems, the decision-making process has to be accomplished under situations where these assessment values may also drastically change over time. In this paper, we propose a prioritized aggregation operator to combine a time sequence of hesitant fuzzy information, where the time-based hesitancy due to changing environment is mitigated. The proposed method is applied to the service selection problem in service-based systems, where software architects must select as a group the service that has the best combination of features based on their historical assessments. We claim that the time-based hesitant fuzzy information aggregation method addresses the hesitancy at intra- and interexpert levels obtaining more robust decisions.

On Hesitant Fuzzy Reducible Weighted Bonferroni Mean and Its Generalized Form for Multicriteria Aggregation

Due to convenience and powerfulness in dealing with vagueness and uncertainty of real situation, hesitant fuzzy set has received more and more attention and has been a hot research topic recently. To differently process and effectively aggregate hesitant fuzzy information and capture their interrelationship, in this paper, we propose the hesitant fuzzy reducible weighted Bonferroni mean (HFRWBM) and present its four prominent characteristics, namely, reductibility, monotonicity, boundedness, and idempotency. Then, we further investigate its generalized form, that is, the generalized hesitant fuzzy reducible weighted Bonferroni mean (GHFRWBM). Based on the discussion of model parameters, some special cases of the HFRWBM and GHFRWBM are studied in detail. In addition, to deal with the situation that multicriteria have connections in hesitant fuzzy information aggregation, a three-step aggregation approach has been proposed on the basis of the HFRWBM and GHFRWBM. In the end, we apply the proposed aggregation operators to multicriteria aggregation and give an example to illustrate our results.

Hesitant fuzzy information aggregation in decision making

As a generalization of fuzzy set, hesitant fuzzy set is a very useful tool in situations where there are some difficulties in determining the membership of an element to a set caused by a doubt between a few different values. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy information. We first discuss the relationship between intutionistic fuzzy set and hesitant fuzzy set, based on which we develop some operations and aggregation operators for hesitant fuzzy elements. The correlations among the aggregation operators are further discussed. Finally, we give their application in solving decision making problems.