Power Aggregation Operators Research Articles

Hesitant Uncertain Linguistic Z-Numbers and Their Application in Multi-criteria Group Decision-Making Problems

This paper introduces hesitant uncertain linguistic Z-numbers (HULZNs) based on Z-numbers and linguistic models. HULZNs can serve as a reliable tool to depict complex and uncertain decision-making information and reflect the hesitancy of DMs. This paper focuses on the development of an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is incompletely known. Handling qualitative information requires the effective support of quantitative tools, after which the linguistic scale function is employed to deal with linguistic information. First, the operations and distance of HULZNs are defined. Then, two power aggregation operators for HULZNs are proposed. Subsequently, a new MCGDM approach is developed by incorporating the power aggregation operators and the VIKOR model. Finally, an illustrative example of ERP system selection is provided for demonstration, and the feasibility and validity of the proposed method are further verified by sensitivity analysis and comparison with an existing method.

Approaches to Multiple Attribute Decision Making Based on the Hesitant Fuzzy Uncertain Linguistic Power Aggregation Operators and Their Applications to Service Quality Evaluation in Higher Education

In this paper, we investigate the multiple attribute decision making problems based on the power aggregation operators with hesitant fuzzy uncertain linguistic information. Then, we have developed some power aggregation operators for aggregating hesitant fuzzy uncertain linguistic information: hesitant fuzzy uncertain linguistic power weighted average (HFULPWA) operator and hesitant fuzzy uncertain linguistic power weighted geometric (HFULPWG) operator. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for evaluating the service quality in higher education is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Linguistic hesitant fuzzy power aggregation operators and their applications in multiple attribute decision-making

As a generalization of hesitant fuzzy sets (HFSs) and hesitant fuzzy linguistic term sets (HFLTSs), linguistic hesitant fuzzy sets (LHFSs) establish a proper interpretation of the hesitancy, inconsistency and uncertainty of experts in evaluating decision alternatives. In this paper, based on the cloud model, we discuss multiple attribute decision-making problems with linguistic hesitant fuzzy information. To extend the applicability of LHFSs, we introduce the concept of a comprehensive cloud of LHFSs that is based on which form of LHFSs with different length can be unified. Utilizing the comprehensive cloud, we define the distance measure between two LHFSs, which makes the support measure of two LHFSs possible. By extending the power operators to the linguistic hesitant fuzzy environment, a series of linguistic hesitant fuzzy power aggregation operators are established. We also study the properties and applications of these aggregation operators and develop two approaches for linguistic hesitant fuzzy multiple attribute decision-making. Finally, two practical examples are given to demonstrate the applicability and effectiveness of the proposed approach.

Simplified Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development

For many companies, green product development has become a key strategic consideration due to regulatory requirements and market trends. In this paper, the life cycle assessment technique is used to develop an innovative multi-criteria group decision-making approach that incorporates power aggregation operators and a TOPSIS-based QUALIFLEX method in order to solve green product design selection problems using neutrosophic linguistic information. Differences in semantics as well as the risk preferences of decision-makers are considered in the proposed method. The practicality and effectiveness of the proposed approach are then demonstrated through an illustrative example, in which the proposed method is used to select the optimum green product design, followed by sensitivity and comparative analyses.

A Multi-Criteria Decision-Making Method Using Power Aggregation Operators for Single-valued Neutrosophic Sets

As a generalization of intuitionistic fuzzy sets, neutrosophic sets (NSs) can be better handle the incomplete, indeterminate and inconsistent information, which have attracted the widespread concerns for researchers. In this paper, some new aggregation operators are proposed under single-valued neutrosophic environment. Firstly, the definition and operational laws of single-valued neutrosophic numbers (SVNNs) are introduced. Then, the single-valued neutrosophic power average (SVNPA) operator and the single- valued neutrosophic power weighted average (SVNPWA) operator are developed, and some properties of SVNPWA operator are also analyzed. Furthermore, a method for solving multi-criteria decision-making (MCDM) problems is explored based on the power aggregation operators and cosine similarity measures. Finally, an illustrative example is shown to verify the effectiveness and practicality of the proposed method.

The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making

Neutrosophic number (NN) is a useful tool which is used to overcome the difficulty of describing indeterminate evaluation information. The purpose of the study is to propose some power aggregation operators based on neutrosophic number which is used to deal with multiple attributes group decision making problems more effectively. Firstly, the basic concepts and the operational rules and the characteristics of NNs are introduced. Then, some aggregation operators based on neutrosophic numbers are developed, included the neutrosophic number weighted power averaging (NNWPA) operator, the neutrosophic number weighted geometric power averaging (NNWGPA) operator, the generalized neutrosophic number weighted power averaging (GNNWPA) operator. At the same time, the properties of above operators are studied such as idempotency, monotonicity, boundedness and so on. Then, the generalized neutrosophic number weighted power averaging (GNNWPA) operator is applied to solve multiple attribute group decision making (MAGDM) problems. Afterwards, a numerical example is given to demonstrate the effective of the new developed method, and some comparison are conducted to verify the influence of different parameters or to reveal the difference with another method. In the end, the main conclusion of this paper is summarized.

Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment

This paper aims to investigate the type of fuzzy multiple attribute group decision making (MAGDM) where arguments being aggregated are allowed to support each other. In order to enable decision makers to express their preferences more comprehensively, we firstly put forward a hybrid tool, an interval-valued dual hesitant fuzzy linguistic set (IVDHFLS), which employs interval-valued hesitant membership and nonmembership degrees to assess linguistic terms. Basic operational laws for IVDHFLS are discussed, also a distance measure is designed to overcome irrationality in traditional methodology for hesitant fuzzy sets, i.e., artificially adding values to mismatching membership or nonmembership degrees. We next develop fundamental generalized power average aggregation operators for IVDHFLS, including power average operator, power geometric average operator, power ordered weighted average operator and power ordered weighted geometric average operator. Desirable properties and special cases of these aggregation operators are further analyzed. Furthermore, based on the generalized operators above, we construct two approaches for MAGDM with mutually supportive arguments being aggregated under interval-valued dual hesitant fuzzy linguistic environments. Finally, case studies are conducted to verify effectiveness and practicality of the developed approaches.

Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making

Multi-criteria decision making (MCDM) has been a hot topic in decision making and systems engineering. The dual hesitant fuzzy sets (DHFSs) is a useful tool to deal with vagueness and ambiguity in the MADM problems. In this paper, we propose a wide range of dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm for dual hesitant fuzzy information. We first redefine some basic operations of dual hesitant fuzzy sets, which are consistent with those of dual hesitant fuzzy sets. We introduce three kinds of distance measures for dual hesitant fuzzy sets, which the corresponding support measures can be obtained. Then we propose several power aggregation operators on dual hesitant fuzzy sets, study their properties and give some specific dual hesitant fuzzy aggregation operators. In the end, we develop two approaches for multiple attribute group decision making with dual hesitant fuzzy information, and illustrate a real world example to show the behavior of the proposed operators.

Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problem based on the arithmetic and geometric aggregation operators with interval valued hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we shall develop some aggregation operators for aggregating interval valued hesitant fuzzy uncertain linguistic information: interval valued hesitant fuzzy uncertain linguistic arithmetic aggregation operators, interval valued hesitant fuzzy uncertain linguistic geometric aggregation operators, interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, interval valued hesitant fuzzy uncertain linguistic prioritized aggregation operators, interval valued hesitant fuzzy uncertain linguistic power aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we shall utilize these operators to develop some approaches to solve the interval valued hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some 2-tuple linguistic generalized power aggregation operators and their applications to multiple attribute group decision making

Some 2-tuple linguistic generalized power aggregation operators and their applications to multiple attribute group decision making

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

Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators

On the basis of Frank operators, the operational rules of intuitionistic fuzzy numbers are redefined, then the intuitionistic fuzzy Frank power average operator (IFFPA), intuitionistic fuzzy Frank power weighted average operator (IFFPWA) and intuitionistic fuzzy Frank power ordered weighted average operator (IFFPOWA) are proposed by combining Frank operations and power aggregation operators. At the same time, some desirable properties of these operators, such as idempotency, commutativity and boundedness, are studied, and some special cases are analyzed. Furthermore, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of the intuitionistic fuzzy numbers, two group decision making methods based on IFFPWA and IFFPOWA operators are developed. Finally, an illustrative example is given to verify the proposed methods and to demonstrate their practicality and effectiveness.

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

In recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy membership and falsity-membership degree have a set of crisp values between zero and one, espectively.

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

AbstractIn recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy- membership and falsity-membership degree have a set of crisp values between zero and one, respectively. Then the operations of multi-valued neutrosophic numbers (MVNNs) based on Einstein operations are defined, and a comparison method for MVNNs is developed depending on the related research of HFSs and Atanassov's intuitionistic fuzzy sets (IFSs). Furthermore, the multi-valued neutrosophic power weighted average (MVNPWA) operator and the multi-valued neutrosophic power weighted geometric (MVNPWG) operator are proposed and the desirable properties of two operators are also discussed. Finally, an approach for solving MCGDM problems is explored by applying the power aggreg...

INTUITIONISTIC UNCERTAIN LINGUISTIC POWERED EINSTEIN AGGREGATION OPERATORS AND THEIR APPLICATION TO MULTI-ATTRIBUTE GROUP DECISION MAKING

The intuitionistic 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. At the same time, Einstein operations are a kind of various t-norms and <i>t</i>-conorms families which can be used to perform the corresponding intersections and unions of intuitionistic fuzzy sets (IFSs). In this paper, we will combine the PA operator and Einstein operations to intuitionistic uncertain linguistic environment, and propose some new PA operators. Firstly, the definition and some basic operations of intuitionistic uncertain linguistic number (IULN), power aggregation (PA) operator and Einstein operations are introduced. Then, we propose intuitionistic uncertain linguistic fuzzy powered Einstein averaging (IULFPEA) operator, intuitionistic uncertain linguistic fuzzy powered Einstein weighted (IULFPEWA) operator, intuitionistic uncertain linguistic fuzzy Einstein geometric (IULFPEG) operator and intuitionistic uncertain linguistic fuzzy Einstein weighted geometric (IULFPEWG) operator, and discuss some properties of them in detail. Furthermore, we develop the decision making methods for multi-attribute group decision making (MAGDM) problems with intuitionistic 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.

Methods for multiple attribute decision making with hesitant fuzzy uncertain linguistic information and their application for evaluating the college English teachers' professional development competence

In this paper, we investigate the multiple attribute decision making MADM problems for evaluating the college English teachers' professional development competence with hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional power aggregation operator, we have developed the hesitant fuzzy uncertain linguistic power weighted average HFULPWA operator. Then, we have utilized hesitant fuzzy uncertain linguistic power weighted average HFULPWA operator to develop some approaches to solve the hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for evaluating the college English teachers' professional development competence is given to verify the developed approach and to demonstrate its practicality and effectiveness.

2-Tuple Linguistic Power Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

Aims: The aim of this paper is to develop several 2-tuple linguistic power aggregation operators for aggregating 2-tuple linguistic information. Study Design: We first introduce several power aggregation operators and then extend these operators to 2-tuple linguistic environments. Place and Duration of Study: We investigate several useful properties of the developed operators and discuss the relationships between them. Methodology: Furthermore, the new aggregation operators are utilized to develop two approaches to multiple attribute group decision making with 2-tuple linguistic information. Results: We develop several 2-tuple linguistic power aggregation operators to aggregate input arguments taking the form of 2-tuples. Conclusion: Finally, two practical examples are provided to illustrate the effectiveness and practicality of the proposed approaches.

An Extension of the MULTIMOORA Method for Multiple Criteria Group Decision Making Based upon Hesitant Fuzzy Sets

In order to determine the membership of an element to a set owing to ambiguity between a few different values, the hesitant fuzzy set (HFS) has been proposed and widely diffused to deal with vagueness and uncertainty involved in the process of multiple criteria group decision making (MCGDM) problems. In this paper, we develop novel definitions of score function and distance measure for HFSs. Some examples are given to illustrate that the proposed definitions are more reasonable than the traditional ones. Furthermore, our study extends the MULTIMOORA (Multiple Objective Optimization on the basis of Ratio Analysis plus Full Multiplicative Form) method with HFSs. The proposed method thus provides the means for multiple criteria decision making (MCDM) regarding uncertain assessments. Utilization of hesitant fuzzy power aggregation operators also enables facilitating the process of MCGDM. A numerical example of software selection demonstrates the possibilities of application of the proposed method.

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

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic arithmetic aggregation operators, hesitant fuzzy linguistic geometric aggregation operators, hesitant fuzzy linguistic correlated aggregation operators, induced hesitant fuzzy linguistic aggregation operators, induced hesitant fuzzy linguistic correlated aggregation operators, hesitant fuzzy linguistic prioritized aggregation operators, hesitant fuzzy linguistic power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach.

Approaches for multi-attribute group decision making based on intuitionistic trapezoid fuzzy linguistic power aggregation operators

Approaches for multi-attribute group decision making based on intuitionistic trapezoid fuzzy linguistic power aggregation operators