Power Aggregation Operators Research Articles

A Novel Multi-Attribute Decision Making Method Based on The Double Hierarchy Hesitant Fuzzy Linguistic Generalized Power Aggregation Operator

A double hierarchy hesitant fuzzy linguistic term set (DHHFLT) is deemed as an effective and powerful linguistic expression which models complex linguistic decision information more accurately by using two different hierarchy linguistic term sets. The purpose of this paper is to propose a multi-attribute decision making method to tackle complex decision issues in which attribute values are represented as double hierarchy hesitant fuzzy linguistic numbers, and there are some extreme or unreasonable data in the attribute values. To do this, firstly, four double hierarchy hesitant fuzzy linguistic generalized power aggregation operators are introduced, including the double hierarchy hesitant fuzzy linguistic generalized power average (DHHFLGPA) operator, the double hierarchy hesitant fuzzy linguistic generalized power geometric (DHHFLGPG) operator, and their weighted forms. Thereafter, several favorable properties, as well as representative cases of the proposed operators, are investigated in detail. Moreover, by virtue of the proposed operators, a novel approach is developed for coping with multi-attribute decision making cases in the double hierarchy hesitant fuzzy linguistic context. Finally, an illustrated example is given to demonstrate the practical application of the presented approach, an availability verification is given to show its validity, and a comparative analysis is also conducted to highlight the advantages of the proposed approach.

Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems

Picture fuzzy sets (PFSs) generally involve the positive membership, neutral membership and negative membership, and have an advantage of accurately describing decision-makers’ preference information. In this paper, we develop a picture fuzzy multi-criteria decision-making (MCDM) approach that can consider the interrelationship among criteria and reduce the effects of abnormal preference information simultaneously. Firstly, a weighted picture fuzzy power Choquet ordered geometric (WPFPCOG) operator and a weighted picture fuzzy power Shapley Choquet ordered geometric (WPFPSCOG) operator are respectively developed based on the fuzzy measure, Shapley fuzzy measure and power aggregation operator, and the corresponding special cases and properties are discussed briefly. Secondly, based on the developed WPFPSCOG operator and the Shapley fuzzy measure, an integrated MCDM method is constructed to deal with picture fuzzy problems where the weights of criteria are incompletely known. Then, a mathematical programming model based on the Shapley fuzzy measure is established to obtain the weights of criteria, and the WPFPSCOG operator is used to aggregate the evaluation value of each alternative. Finally, an illustration example is provided to demonstrate the effectiveness and credibility of the developed method.

Approach to Multicriteria Group Decision Making with Z-Numbers Based on TOPSIS and Power Aggregation Operators

Decisions strongly rely on information, so the information must be reliable, yet most of the real-world information is imprecise and uncertain. The reliability of the information about decision analysis should be measured. Z-number, which incorporates a restraint of evaluation on investigated objects and the corresponding degree of confidence, is considered as a powerful tool to characterize this information. In this paper, we develop a novel approach based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method and the power aggregation operators for solving the multiple criteria group decision making (MCGDM) problem where the weight information for decision makers (DMs) and criteria is incomplete. In the MCGDM, the evaluation information made by DMs is represented in the form of linguistic terms and the following calculation is performed using Z-numbers. First, we establish an optimization model based on similarity measure to determine the weights of DMs and a linear programming model with partial weight information provided by DMs based on distance measure to determine the weights of criteria. Subsequently, decision matrices from all the DMs are aggregated into a comprehensive evaluation matrix utilizing the proposed ZWAPA operator or ZWGPA operator. Then, those considered alternatives are ranked in accordance with TOPSIS idea and the feature of Z-evaluation. Finally, a practical example about supplier selection is given to demonstrate the detailed implementation process of the proposed approach, and the feasibility and validity of the approach are verified by comparisons with some existing approaches.

Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

Power Geometric Aggregation Operators Based on Connection Number of Set Pair Analysis Under Intuitionistic Fuzzy Environment

The objective of the presented paper is to develop a multiattribute decision-making (MADM) method under the intuitionistic fuzzy set (IFS) environment using the set pair analysis (SPA) theory. IFS can express the uncertain information in terms of membership grades, while the connection number (CN) based on the “identity,” “discrepancy” and “contrary” degrees of the SPA theory handles the uncertainties and certainties systems. Meanwhile, capturing the relationship between the values during the aggregation is a prominent advantage of the power aggregation operator. Motivated by these primary characteristics, in this paper, we develop some power geometric aggregation operators namely for aggregating the CNs, namely, CN power geometric, CN weighted power geometric and CN ordered weighted power geometric operators. A few properties like idempotency, commutativity and boundedness are established to show the viability and legitimacy of developed operators. Afterward, we develop a decision-making (DM) approach based on the proposed operators for tackling the MADM issues under the intuitionistic fuzzy numbers environment. Finally, real-life case of MADM problem has been discussed to manifest the developed DM approach, and obtained results are compared with the results that are obtained by the existing DM methods for showing the feasibility and validity of the developed DM approach.

An uncertain Z-number multicriteria group decision-making method with cloud models

This study focuses on developing an innovative multicriteria group decision-making (MCGDM) method to handle practical problems based on information description, information fusion and information measure. Given that various uncertain data exist in the process of managing problems, uncertain Z-numbers are introduced to represent evaluation information and measure information reliability simultaneously. Processing uncertain information requires the effective support of reliable tools; then, cloud models can be used to address uncertain Z-number information. First, uncertain Z-numbers are converted, and a novel concept of Z-trapezium-normal clouds (ZTNCs) is introduced. Next, the operations, power aggregation operators, and distance and likelihood measures of ZTNCs are defined. Subsequently, the likelihood power aggregation operator and the priority vector of the likelihood matrix are proposed. Moreover, a new MCGDM method is developed by combining the two kinds of proposed power aggregation operators with the likelihood measure. Finally, an illustrative example of new energy evaluation is provided to demonstrate the developed method, and its feasibility and validity are further verified by a comparative analysis with other existing methods.

Linguistic single-valued neutrosophic power aggregation operators and their applications to group decision-making problems

Linguistic single-valued neutrosophic set &#x0028 LSVNS &#x0029 is a more reliable tool, which is designed to handle the uncertainties of the situations involving the qualitative data. In the present manuscript, we introduce some power aggregation operators &#x0028 AOs &#x0029 for the LSVNSs, whose purpose is to diminish the influence of inevitable arguments about the decision-making process. For it, first we develop some averaging power operators, namely, linguistic single-valued neutrosophic &#x0028 LSVN &#x0029 power averaging, weighted average, ordered weighted average, and hybrid averaging AOs along with their desirable properties. Further, we extend it to the geometric power AOs for LSVNSs. Based on the proposed work; an approach to solve the group decision-making problems is given along with the numerical example. Finally, a comparative study and the validity tests are present to discuss the reliability of the proposed operators.

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Cubic uncertain linguistic powered Einstein aggregation operators and their application to multi-attribute group decision making

The cubic uncertain fuzzy linguistic variable can easily express the fuzzy information, and the power average (PA) operator is a useful tool which provides more versatility in the information aggregation procedure. In this paper, we will combine the PA operator and Einstein operations to cubic uncertain linguistic environment and propose some new PA operators. Firstly, the definition and some basic operations of cubic uncertain linguistic number, power aggregation (PA) operator and Einstein operations are introduced. Then, we propose cubic uncertain linguistic fuzzy powered Einstein averaging operator, cubic uncertain linguistic fuzzy powered Einstein weighted (CULFPEWA) operator, cubic uncertain linguistic fuzzy Einstein geometric operator and cubic uncertain linguistic fuzzy Einstein weighted geometric (CULFPEWG) operator and discuss some properties of these in detail. Furthermore, we develop the decision-making methods for multi-attribute group decision-making problems with cubic uncertain linguistic information and give the detail decision steps. At last, an illustrate example is given to show the process of decision making and the effectiveness of the proposed method.

A Multi-Criteria Group Decision-Making Method with Possibility Degree and Power Aggregation Operators of Single Trapezoidal Neutrosophic Numbers

A Multi-Criteria Group Decision-Making Method with Possibility Degree and Power Aggregation Operators of Single Trapezoidal Neutrosophic Numbers

Power aggregation operators of simplified neutrosophic sets and their use in multi-attribute group decision making

The simplified neutrosophic set &#x0028 SNS &#x0029 is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging &#x0028 SNNPWA &#x0029 operator, simplified neutrosophic number power weighted geometric &#x0028 SNNPWG &#x0029 operator, simplified neutrosophic number power ordered weighted averaging &#x0028 SNNPOWA &#x0029 operator and simplified neutrosophic number power ordered weighted geometric &#x0028 SNNPOWG &#x0029 operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multi-attribute group decision making &#x0028 MAGDM &#x0029 within the framework of SNSs is developed by the above aggregation operators. Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

Model for Multiple Attribute Decision Making Based on Picture 2-Tuple Linguistic Power Aggregation Operators

In this article, the authors investigate the multiple attribute decision making problems with picture 2-tuple linguistic information. The utilized power average and power geometric operations used to develop some picture 2-tuple linguistic power aggregation operators: picture 2-tuple linguistic power weighted average (P2TLPWA) operator, picture 2-tuple linguistic power weighted geometric (P2TLPWG) operator, picture 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, picture 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, picture 2-tuple linguistic power hybrid average (P2TLPHA) operator and picture 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators is studied. This article has utilized these operators to develop some approaches to solve the picture 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Complex Fuzzy Power Aggregation Operators

A complex fuzzy set is an extension of the fuzzy set, of which membership grades take complex values in the complex unit disk. We present two complex fuzzy power aggregation operators including complex fuzzy weighted power (CFWP) and complex fuzzy ordered weighted power (CFOWP) operators. We then study two geometric properties which include rotational invariance and reflectional invariance for these complex fuzzy aggregation operators. We also apply the new proposed aggregation operators to decision making and illustrate an example to show the validity of the new approach.

A Multicriteria Group Decision-Making Method Based on the Normal Cloud Model With Zadeh's <italic>Z </italic>-Numbers

Z -number is the general representation of real-life information with reliability, and it has adequate description power from the point of view of human perception. This study develops an innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z -numbers under the condition that the weight information is completely unknown. Processing Z -numbers requires effective support of reliable tools. Then, the normal cloud model can be employed to analyze the Z -number construct. First, the potential information involved in Z -numbers is invoked, and a novel concept of normal Z +-value is proposed with the aid of the normal cloud model. The operations, distance measurement, and power aggregation operators of normal Z +-values are defined. Moreover, an MCGDM method is developed by incorporating the defined distance measurement and power aggregation operators into the MultiObjective Optimization by Ratio Analysis plus the Full Multiplicative Form. Finally, an illustrative example concerning air pollution potential evaluation is provided to demonstrate the proposed method. Its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.

A Multi-Criteria Group Decision-Making Method with Possibility Degree and Power Aggregation Operators of Single Trapezoidal Neutrosophic Numbers

Single valued trapezoidal neutrosophic numbers (SVTNNs) are very useful tools for describing complex information, because of their advantage in describing the information completely, accurately and comprehensively for decision-making problems. In the paper, a method based on SVTNNs is proposed for dealing with multi-criteria group decision-making (MCGDM) problems. Firstly, the new operations SVTNNs are developed for avoiding evaluation information aggregation loss and distortion. Then the possibility degrees and comparison of SVTNNs are proposed from the probability viewpoint for ranking and comparing the single valued trapezoidal neutrosophic information reasonably and accurately. Based on the new operations and possibility degrees of SVTNNs, the single valued trapezoidal neutrosophic power average (SVTNPA) and single valued trapezoidal neutrosophic power geometric (SVTNPG) operators are proposed to aggregate the single valued trapezoidal neutrosophic information. Furthermore, based on the developed aggregation operators, a single valued trapezoidal neutrosophic MCGDM method is developed. Finally, the proposed method is applied to solve the practical problem of the most appropriate green supplier selection and the rank results compared with the previous approach demonstrate the proposed method’s effectiveness.

Generalized intuitionistic fuzzy soft power aggregation operator based ont‐norm and their application in multicriteria decision‐making

Generalized intuitionistic fuzzy soft power aggregation operator based on<i>t</i>‐norm and their application in multicriteria decision‐making

A Linguistic Neutrosophic Multi-criteria Group Decision-Making Approach with EDAS Method

This study develops an approach that incorporates power aggregation operators with the evaluation based on distance from average solution (EDAS) method under linguistic neutrosophic situations to solve fuzzy multi-criteria group decision-making problems. Firstly, the existing operational laws and comparison methods of linguistic neutrosophic numbers (LNNs) are analysed. Secondly, the distance measurement between two LNNs is defined. Thirdly, the power-weighted averaging operator and the power-weighted geometric operator with LNNs are developed to support the decision makers’ evaluation information. The models to derive the criteria weights are also constructed based on the proposed distance measurements. Finally, the EDAS method is extended to resolve group decision-making problems in the linguistic neutrosophic environment. An illustrative example of the property management company selection is given to verify the effectiveness and practicality of the proposed approach.

Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision‐making

AbstractThe objective of this manuscript is to present some aggregation operators for aggregating the different complex intuitionistic fuzzy (CIF) sets by considering the dependency between the pairs of its membership degrees. In the existing studies of fuzzy and its extensions, the uncertainties present in the data are handled with the help of degrees of membership that are the subset of real numbers, which may lose some useful information and hence consequently affect the decision results. A modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two‐dimensional information in a single set. Thus, motivated by this, we developed some new power aggregation operators, namely, CIF power averaging, CIF weighted power averaging, CIF ordered weighted power averaging, CIF power geometric, CIF weighted power geometric, and CIF ordered weighted power geometric. Also, some of the desirable properties of these are investigated. Further, based on these operators, a multicriteria decision‐making approach is presented under the CIF set environment. An illustrative example related to the selection of the best alternative(s) is considered to demonstrate the efficiency of the proposed approach and is validated it by comparing their results with the several existing approaches results.

Some interval-valued intuitionistic fuzzy Schweizer–Sklar power aggregation operators and their application to supplier selection

ABSTRACTSupplier selection is an important multiple attribute group decision-making (MAGDM) problem. How to choose a suitable supplier is an evaluation process with different alternatives of multiple attributes, and it also relates to the expression of the evaluation value. Considering Schweizer–Sklar t-conorm and t-norm (SSTT) can make the information aggregation process more flexible than others, and the power average (PA) operator can eliminate effects of unreasonable data from biased decision-makers. So, we extend SSTT to interval-valued intuitionistic fuzzy numbers (IVIFNs) and define Schweizer–Sklar operational rules of IVIFNs. Then, we combine the PA operator with Schweizer–Sklar operations, and propose the interval-valued intuitionistic fuzzy Schweizer–Sklar power average operator, the interval-valued intuitionistic fuzzy Schweizer–Sklar power weighted average (IVIFSSPWA) operator, the interval-valued intuitionistic fuzzy Schweizer–Sklar power geometric operator and the interval-valued intuitionistic fuzzy Schweizer–Sklar power weighted geometric (IVIFSSPWG) operator, respectively. Furthermore, we study some desirable characteristics of them and develop two methods on the basis of IVIFSSPWA and IVIFSSPWG operators. At the same time, we apply the two methods to deal with the MAGDM problems based on supplier selection. Finally, an illustrative example of supplier selection problem is given to testify the availability of the presented operators.

Some single-valued neutrosophic Bonferroni power aggregation operators in multiple attribute decision making

In this paper, we utilize power aggregation operators and Bonferroni mean to develop some single-valued neutrosophic Bonferroni power aggregation operators and single-valued neutrosophic geometric Bonferroni power aggregation operators. The prominent characteristics of these proposed operators are studied. Then, we use the SVNWBPM and SVNWGBPM operators to solve the single-valued neutrosophic multiple attribute decision making problems. Finally, a practical example for strategic suppliers’ selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.