Power Aggregation Operators Research Articles

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

An Approach to Multiple Attribute Group Decision Making Based on Intuitionistic Trapezoidal Fuzzy Power Generalized Aggregation Operator

AbstractWith respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, a new decision making analysis method is developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced, and the comparison method for the intuitionistic trapezoidal fuzzy numbers is proposed. Then, combined the power aggregation operator and the generalized aggregation operator, a power generalized average (PGA) operator is proposed, and some properties of the PGA operator, such as idempotency, boundary, commutativity, etc., are studied. At the same time, some special cases of the generalized parameters in PGA operator are analyzed. Furthermore, an intuitionistic trapezoidal fuzzy power generalized weighted average (ITFPGWA) operator is also proposed for the intuitionistic trapezoidal fuzzy information, and some properti...

2-Dimension uncertain linguistic power generalized weighted aggregation operator and its application in multiple attribute group decision making

The 2-dimension uncertain linguistic variables add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information. At the same time, the power average (PA) operator has the characteristic of capturing the correlations of the aggregated arguments. In this paper, we propose some power aggregation operators, including 2-dimension uncertain linguistic power generalized aggregation operator (2DULPGA) and 2-dimension uncertain linguistic power generalized weighted aggregation operator (2DULPGWA), and discuss some properties and special cases of them. Finally, with respect to the multiple attribute group decision making problems in which the attribute values take the form of the 2-dimension uncertain linguistic information, the method based on some power generalized aggregation operators is proposed, and two examples are given to verify the developed approach and to demonstrate its effectiveness.

FUZZY POWER AGGREGATION OPERATORS AND THEIR APPLICATION TO MULTIPLE ATTRIBUTE GROUP DECISION MAKING

The article investigates the multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of triangular fuzzy information. Motivated by the ideal of power aggregation, in this paper some power aggregation operators for aggregating triangular fuzzy information are developed and then applied in order to develop some models for multiple attribute group decision making with triangular fuzzy information. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Induced Power Aggregation Operators and their Applications in Group Decision Making

The power ordered weighted average (POWA) operator and the power ordered weighted geometric (POWG) operator are the two nonlinear weighted average aggregation tools whose weighting vectors depend on their input arguments. In this paper, as a more general type of POWA and POWG operators, respectively, we develop two induced power aggregation operators called the induced POWA (IPOWA) operator and the induced POWG (IPOWG) operator, respectively, and establish various properties of these induced power aggregation operators, and then apply them, respectively, to develop an approach to multiple attribute group decision making.

Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of hesitant interval-valued fuzzy information. Firstly, definition and some operational laws of hesitant interval-valued fuzzy elements and score function of hesitant interval-valued fuzzy elements are introduced. Then, we have developed some hesitant interval-valued fuzzy aggregation operators: hesitant interval-valued fuzzy weighted averaging (HIVFWA) operator, hesitant interval-valued fuzzy ordered weighted averaging (HIVFOWA) operator, the hesitant interval-valued fuzzy weighted geometric (HIVFWG) operator, hesitant interval-valued fuzzy ordered weighted geometric (HIVFOWG) operator, hesitant interval-valued fuzzy choquet ordered averaging (HIVFCOA) operator, hesitant interval-valued fuzzy choquet ordered geometric (HIVFCOG) operator, hesitant interval-valued fuzzy prioritized aggregation operators and hesitant interval-valued fuzzy power aggregation operators. We have applied the HIVFCOA and HIVFCOG operators to multiple attribute decision making with hesitant interval-valued fuzzy information. Finally an illustrative example has been given to show the developed method.

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

The hesitant fuzzy set is a useful generalization of the fuzzy set that is designed for situations in which it is difficult to determine the membership of an element to a set owing to ambiguity between a few different values. In this paper, we develop a wide range of hesitant fuzzy power aggregation operators for hesitant fuzzy information. We first introduce several power aggregation operators and then extend these operators to hesitant fuzzy environments, i.e., we introduce operators to aggregate input arguments that take the form of hesitant fuzzy sets. We demonstrate several useful properties of the operators and discuss the relationships between them. The new aggregation operators are utilized to develop techniques for multiple attribute group decision making with hesitant fuzzy information. Finally, some practical examples are provided to illustrate the effectiveness of the proposed techniques.