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.

Hesitant fuzzy partitioned Maclaurin symmetric mean aggregation operators in multi-criteria decision-making

A hesitant fuzzy set, enabling the membership of an element to be a set of various possible values, is highly helpful in describing people’s uncertainty in everyday life. Hesitant fuzzy aggregation operators are the standard mathematical tools for combining many inputs according to predefined criteria into a single result. The classic hesitant fuzzy aggregation operator-based approaches have been criticized because of the ignorance of criteria classification. In this work, we develop the conception of the hesitant fuzzy partitioned Maclaurin symmetric mean and hesitant fuzzy weighted partitioned Maclaurin symmetric mean operators spurred by the partitioned Maclaurin symmetric mean. Afterward, we analyze several features and peculiar instances of the formulated operators. A novel multiple criteria decision-making (MCDM) technique is propounded on the documented hesitant fuzzy weighted partitioned Maclaurin symmetric mean operator; the MCDM method chooses the optimal alternative from several alternatives. A case study of the best location selection for hospital construction is addressed to showcase the practicability of the presented technique. Eventually, we illustrate the devised approach is more widespread and efficacious than prevailing approaches via comparative and sensitive analyses.

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.

Novel Aczel–Alsina operations-based hesitant fuzzy aggregation operators and their applications in cyclone disaster assessment

As a fuzzy set (FS) expansion, the hesitant fuzzy set (HFS) is successfully employed to demonstrate circumstances where it is admissible to ascertain a few potential membership degrees (MDs) of a component in a set because of the uncertainty between various values. Considering that there is still no research on Aczel–Alsina triangular norms and conorms in a hesitant fuzzy (HF) environment, in this article we introduce for the first time, Aczel–Alsina operations on HFSs. Then, based on these operations, we originate a few new aggregation operators for aggregating HF information namely HF Aczel–Alsina weighted averaging (HFAAWA) operator, HF Aczel–Alsina ordered weighted averaging (HFAAOWA) operator, HF Aczel–Alsina hybrid averaging (HFAAHA) operator, HF Aczel–Alsina weighted geometric (HFAAWG) operator, HF Aczel–Alsina ordered weighted geometric (HFAAOWG) operator, HF Aczel–Alsina hybrid geometric (HFAAHG) operator and HF Aczel–Alsina weighted Bonferroni mean (HFAAWBM) operator. Some essential characteristics of those suggested operators are shown, and the interrelatedness between them is displayed exhaustively. Then, we take advantage of those operators to produce a methodology to interpret the HF multiple attribute decision making (MADM) difficulties. We present a functional model for cyclone disaster assessment to certify the produced approaches and to establish their effectiveness and practicality. Further, we conduct comparison analysis for the legitimacy of our produced methodologies.

A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration. The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints. Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy. This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose, we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives. Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.

Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

PurposeThis is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approachPyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.FindingsIn addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/valuePaper is original and not submitted elsewhere.

Dynamic aggregation operators and Einstein operations based on interval-valued picture hesitant fuzzy information and their applications in multi-period decision making

The traditional picture hesitant fuzzy aggregation operators are generally suitable for aggregating information acquired in the form of picture hesitant fuzzy numbers, but they will fail in dealing with interval-valued picture hesitant fuzzy information. In this paper, we describe the notion of interval-valued picture hesitant fuzzy set and the operational laws of interval-valued picture hesitant fuzzy variables. Moreover, we derive some dynamic interval-valued picture hesitant fuzzy aggregation operators (based on Einstein operators) to aggregate the interval-valued picture hesitant fuzzy information collected at different periods. Some desirable properties of these aggregation operators are discussed in detail. In addition, we develop the approaches to tackle the multi-period decision-making problems, where all decision information takes the form of interval-valued picture hesitant fuzzy information collected at different periods. In an attempt to illustrate the applications of the proposed approaches, two numerical examples are given to measure the impact of Coronavirus Disease 2019 (COVID-19) in daily life and to identify the optimal investment opportunity. Finally, a comparative analysis of the proposed and existing studies are conducted to demonstrate the effectiveness of the proposed approaches. The presented interval-valued picture hesitant fuzzy operations, aggregation operators, and decision-making approaches can widely apply to dynamic decision analysis and multi-stage decision analysis in real life.

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.

Frank Aggregation Operators and Their Application to Probabilistic Hesitant Fuzzy Multiple Attribute Decision-Making

The fuzzy aggregation information plays an important role in the group decision support system under the interval-valued hesitant fuzzy information and interval-valued probabilistic hesitant fuzzy information. Therefore, in this paper, we develop a new approach of the interval-valued hesitant fuzzy Frank aggregation (IVHFFA) and interval-valued probabilistic hesitant fuzzy aggregation (IVPHFFA) operators. First, we define some operational laws of IVHEs and IVPHFEs by using Frank t-norm and t-conorm. Furthermore, we develop a series of IVHFFA and IVPHFFA operators based on these operational laws under the IVHF and IVPHF information. Also, discuss some fundamental properties and relations of the proposed aggregation operators for IVHF and IVPHF information. In order to implement the proposed aggregation operators of IVHF and IVPHF information in group decision-making problem, we construct general algorithms for multi-attribute group decision-making problem based on the proposed IVHFFA and IVPHFFA. Finally, from the comparative and sensitivity analysis, the proposed fuzzy decision-making model is more effective and reliable as compared with existing method.

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

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

Method of MAGDM based on pythagorean trapezoidal uncertain linguistic hesitant fuzzy aggregation operator with Einstein operations

Method of MAGDM based on pythagorean trapezoidal uncertain linguistic hesitant fuzzy aggregation operator with Einstein operations

Negations and aggregation operators based on a new hesitant fuzzy partial ordering

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negations $N_n$ on ${H}$ and $mu_n$ on $bar{{B}}$ are proposed. Particularly, their De Morgan's laws are investigated with respect to binary operations ${C}$ and ${D}$ on ${H}$, as well as ${T}$ and {S} on $bar{{B}}$ respectively, where ${C}$ is a commutative fuzzy conjunction on $({H},leq_H)$ and ${T}$ is a t-norm on $(bar{{B}},leq_B)$. Finally, the new hesitant fuzzy aggregation operators are presented on ${H}$ and $bar{{B}}$ and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making.

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.

New approach of triangular neutrosophic cubic linguistic hesitant fuzzy aggregation operators

In this paper, we define the new concepts of a triangular neutrosophic cubic linguistic hesitant fuzzy number (TNCLHFN), the basic operational relations of TNCHLFNs, and the score function of TNCLHFNs. Then, we develop a triangular neutrosophic cubic linguistic hesitant fuzzy weighted arithmetic averaging (TNCLHFWAA) operator and a triangular neutrosophic cubic linguistic hesitant fuzzy weighted geometric averaging (TNCLHFWGA) operator to aggregate TNCLHFN information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the TNCLHFWAA and TNCLHFWGA operators, and the score function of TNCLHFN is established under a TNCLHFN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach. Triangular neutrosophic cubic linguistic hesitant fuzzy number with a wider scope of applications, and hence, the motivation for investigating into its applicability in different diseases in medical patients.

Trapezoidal cubic hesitant fuzzy aggregation operators and their application in group decision-making

Trapezoidal cubic hesitant fuzzy aggregation operators and their application in group decision-making

An overview on the applications of the hesitant fuzzy sets in group decision-making: Theory, support and methods

Due to the characteristics of hesitant fuzzy sets (HFSs), one hesitant fuzzy element (HFE), which is the basic component of HFSs, can express the evaluation values of multiple decision makers (DMs) on the same alternative under a certain attribute. Thus, the HFS has its unique advantages in group decision making (GDM). Based on which, many scholars have conducted in-depth research on the applications of HFSs in GDM. We have viewed lots of relevant literature and divided the existing studies into three categories: theory, support and methods. In this paper, we elaborate on hesitant fuzzy GDM from these three aspects. The first aspect is mainly about the introduction of HFSs, HFPRs and some hesitant fuzzy aggregation operators. The second aspect describes the consensus process under hesitant fuzzy environment, which is an important support for a complete decisionmaking process. In the third aspect, we introduce seven hesitant fuzzy GDM approaches, which can be applied in GDM under different decision-making conditions. Finally, we summarize the research status of hesitant fuzzy GDM and put forward some directions of future research.

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.

Hesitant fuzzy set based computational method for financial time series forecasting

Non-stochastic hesitation in fuzzy time series forecasting methods occurs due to availability of more than one fuzzification methods of time series data. Recently hesitant fuzzy set has gained attention of the researchers to address issue of aforesaid non-stochastic hesitation. In this research paper, we propose and develop a computational algorithm-based method for financial time series forecasting using hesitant fuzzy set. The proposed method uses hesitant fuzzy logical relations that are constructed using triangular fuzzy sets with equal and unequal intervals. In the proposed forecasting method, hesitant fuzzy logical relations are aggregated using a hesitant fuzzy aggregation operator. Advantages of developed hesitant fuzzy set based forecasting method are that it is easy to implement, can cope with huge time series database and enhances the accuracy in financial time series forecast. To see the performance of proposed method in financial time series forecasting, it is implemented on two financial experimental dataset of TAIFEX and SBI share price at BSE. Rigorous comparison analysis of the proposed forecasting method is done by comparing it with other conventional and computational fuzzy time series forecasting methods in terms of RMSE, AFER. Significance of accuracy enhancement in forecasted outputs is also verified using two-tailed t test.

Multiple Attribute Decision-Making with Dual Hesitant Pythagorean Fuzzy Information

Due to the uncertainty and complexity of socioeconomic environments and cognitive diversity of decision makers, the cognitive information over alternatives provided by decision makers is usually uncertain and fuzzy. Dual hesitant Pythagorean fuzzy sets (DHPFSs) provide a useful tool to depict the uncertain and fuzzy cognitions of the decision makers over attributes. To effectively handle such common cases, in this paper, some Bonferroni mean (BM) operators under DHPFS environment are proposed and some methods for multiple attribute decision-making (MADM) problems based on the BM operators with dual Pythagorean hesitant fuzzy numbers (DHPFNs) are investigated. Firstly, some new BM operators to aggregate dual Pythagorean hesitant fuzzy cognitive information are developed, which consider the interrelationship of DHPFNs, and can generate more accurate results than the existing dual Pythagorean hesitant fuzzy aggregation operators. Then, the developed aggregation operator is applied to MADM with DHPFNs and two MADM methods are designed, which can be applied to different decision-making situations. Based on the proposed operators and built models, two methods are developed to solve the MADM problems with DHPFNs and the validity and advantages of the proposed method are analyzed by comparison with some existing approaches. The methods proposed in this paper can effectively handle the MADM problems in which the attribute information is expressed by DHPFNs, the attributes’ weights are completely known, and the attributes are interactive.