Hesitant Fuzzy Aggregation Research Articles

A wind power plant site selection algorithm based on q-rung orthopair hesitant fuzzy rough Einstein aggregation information

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method’s capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects.

Improved VIKOR methodology based on $ q $-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making

<abstract><p>The main objective of this article is to introduce the idea of a q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of the q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a novel approach to uncertainty modelling in multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are proposed. Based on the q-ROHFRS operational laws, novel q-rung orthopair hesitant fuzzy rough weighted averaging operators have been developed. Some interesting properties of the proposed operators are also demonstrated. Furthermore, by using the proposed aggregation operator, we develop a modified VIKOR method in the context of q-ROHFRS. The outcome of this research is to rank and select the best alternative with the help of the modified VIKOR method based on aggregation operators for q-ROHFRS. A decision-making algorithm based on aggregation operators and extended VIKOR methodology has been developed to deal with the uncertainty and incompleteness of real-world decision-making. Finally, a numerical illustration of agriculture farming is considered to demonstrate the applicability of the proposed methodology. Also, a comparative study is presented to demonstrate the validity and effectiveness of the proposed approach. The results show that the proposed decision-making methodology is feasible, applicable, and effective to address uncertainty in decision making problems.</p></abstract>

Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making

Abstract In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant trapezoid fuzzy information. Firstly, inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers, the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed. Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed, such as the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator, the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator, the hesitant trapezoid fuzzy Hamacher Choquet average (HTrFHCA), the hesitant trapezoid fuzzy Hamacher Choquet geometric (HTrFHCG), etc. Furthermore, an approach based on the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator and the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator is proposed for MADM problems under hesitant trapezoid fuzzy environment. Finally, a numerical example for supplier selection is given to illustrate the application of the proposed approach.

Generalized Shapley probability neutrosophic hesitant fuzzy Choquet aggregation operators and their applications

Generalized Shapley probability neutrosophic hesitant fuzzy Choquet aggregation operators and their applications

Note on the aggregation operators and ranking of hesitant interval-valued fuzzy elements

Hesitant interval-valued fuzzy set, which allows decision makers to use several interval numbers to assess a variable, is a useful tool to deal with situations in which people are hesitant in providing their interval-valued assessments. In this paper, we investigate the properties of hesitant interval-valued fuzzy aggregation operators and the approach for ranking a set of hesitant interval-valued fuzzy elements. Some flaws about the properties presented by Wei et al. (Knowl Based Syst 46:43–53, 2013) are pointed out and analyzed by counterexamples, and some modifications on the properties are given. Simultaneously, two flaws about the approach for ranking hesitant interval-valued fuzzy elements provided by Wei et al. (2013) are analyzed by counterexamples. A new algorithm for ranking a set of hesitant interval-valued fuzzy elements is provided. The rationality of the modified ranking approach is investigated.

Some Hesitant Fuzzy Linguistic Muirhead Means with Their Application to Multiattribute Group Decision-Making

The proposed hesitant fuzzy linguistic set (HFLS) is a powerful tool for expressing fuzziness and uncertainty in multiattribute group decision-making (MAGDM). This paper aims to propose novel aggregation operators to fuse hesitant fuzzy linguistic information. First, we briefly recall the notion of HFLS and propose new operations for hesitant fuzzy linguistic elements (HFLEs). Second, considering the Muirhead mean (MM) is a useful aggregation technology that can consider the interrelationship among all aggregated arguments, we extend it to hesitant fuzzy linguistic environment and propose new hesitant fuzzy linguistic aggregation operators, such as the hesitant fuzzy linguistic Muirhead mean (HFLMM) operator, the hesitant fuzzy linguistic dual Muirhead mean (HFLDMM) operator, the hesitant fuzzy linguistic weighted Muirhead mean (HFLMM) operator, and the hesitant fuzzy linguistic weighted dual Muirhead mean (HFLWDMM) operator. These operators can reflect the correlations among all HFLEs. Several desirable properties and special cases of the proposed operators are also studied. Furthermore, we propose a novel approach to MAGDM in a hesitant fuzzy linguistic context based on the proposed operators. Finally, we conduct a numerical experiment to demonstrate the validity of our method. Additionally, we compare our method with others to illustrate its merits and superiorities.

Hesitant Neutrosophic Linguistic Sets and Their Application in Multiple Attribute Decision Making

In this paper, the hesitant neutrosophic linguistic set is first defined by extending a hesitant fuzzy set to accommodate linguistic terms and neutrosophic fuzzy values. Some operational laws are defined for hesitant neutrosophic linguistic fuzzy information. Several distance measures have been defined including generalized hesitant neutrosophic linguistic distance, generalized hesitant neutrosophic linguistic Hausdorff distance, and generalized hesitant neutrosophic linguistic hybrid distance. Some hesitant neutrosophic fuzzy linguistic aggregation operators based on the Choquet integral have been defined. A new multiple attribute decision making method for hesitant neutrosophic fuzzy linguistic information has been developed based on TOPSIS. In order to illustrate the feasibility and practical advantages of the new algorithm, we use it to select a company to invest. The new method is then compared with other methods.

Multiple-attribute decision-making method based on hesitant fuzzy linguistic Muirhead mean aggregation operators

The hesitant fuzzy linguistic (HFL) variable can handle the uncertainty very well, and Muirhead mean (MM) operator can consider correlations among any amount of inputs by an alterable parameter, which is a generalization of some existing operators by changing the parameter values. However, the traditional MM is only suitable for crisp numbers. In this article, we enlarge the scope of the MM operator to the HFL circumstance, and two new aggregation operators are proposed, including the HFL Muirhead mean operator and the weighted HFL Muirhead mean (WHFLMM) operator. Simultaneously, we discuss some worthy characters and some special cases concerning diverse parameter values of these operators. Moreover, a multiple-attribute decision-making method under the HFL environment is developed based on the WHFLMM operator. Lastly, a numerical example is applied to explain the feasibility of the proposed method.

Dual hesitant bipolar fuzzy aggregation operators in multiple attribute decision making

Dual hesitant bipolar fuzzy aggregation operators in multiple attribute decision making

Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamachert-norm andt-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.

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.

Hesitant triangular multiplicative aggregation operators and their application to multiple attribute group decision making

The hesitant triangular fuzzy set (HTFS) is a generalization of the hesitant fuzzy set, and it permits the membership degree of an element to a set to be represented as several possible triangular fuzzy numbers. However, we find that the HTFS uses the symmetrical 0.1---0.9 scale to express the membership degree information and the results derived by using the traditional hesitant triangular fuzzy aggregation operators based on hesitant triangular fuzzy sets are inconsistent with our intuition in some situations. To overcome this issue, we use the unsymmetrical 1---9 scale to express the membership degree information instead of the symmetrical 0.1---0.9 scale in the HTFS, and then a new concept is introduced, which we call the hesitant triangular multiplicative set reflecting our intuition more objectively. Then, we discuss their operational laws and some desirable properties. Based on these operational laws, we develop a series of hesitant triangular multiplicative aggregation operators for aggregating hesitant triangular multiplicative information and then apply them to present an approach to multiple attribute group decision making under hesitant triangular multiplicative environments. Finally, several practical examples are provided to demonstrate the validity and effectiveness of the developed aggregation operators and decision making approach.

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...

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...

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 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.

Hesitant fuzzy linguistic information aggregation in decision making

As a generalisation of fuzzy linguistic set (FLS), a hesitant fuzzy linguistic term set (HFLTS) is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. And the HFLTS is a very useful tool to deal with fuzzy linguistic uncertainty, which can be accurately and perfectly described in terms of the opinions of experts. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy linguistic information. We first discuss the relationship between FLS and HFLTS, based on which we develop some operations for hesitant fuzzy linguistic elements. The correlations among the aggregation operators are further discussed. Based on the developed operators, we introduce a method for decision making with hesitant fuzzy linguistic information. Finally, we give their application in decision making problems.