scholarly journals Group Decision-Making Approach without Weighted Aggregation Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Min Jiang ◽  
Zhiqing Meng ◽  
Rui Shen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Equilibrium Solution ◽  
Group Decision ◽  
Optimal Solution ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Practical Significance ◽  
Number Of Individuals ◽  
Model Approach

This paper introduces an approach for group decision-making problems (GDMP) without weighted aggregation operators. This approach is more suitable for scenarios with infinite number of individuals. A mathematical model approach is established based on the new concept of s⁎-optimal concession equilibrium solution without weighted aggregation operators for group decision-making problems. It is of practical significance for all decision-makers (experts) to find an optimal solution or to sort out all the candidate solutions. We prove that the s⁎-optimal concession equilibrium solution is equivalent to solving a single objective optimization problem, and, under certain conditions, the s⁎-optimal equilibrium solution always exists. Moreover, it is proven that the s⁎-optimal concession equilibrium solution is equivalent to the robust optimal solution of the group weight aggregation and the optimal solution under the worst weighted aggregation operators.

scholarly journals A Concession Equilibrium Solution Method without Weighted Aggregation Operators for Multiattribute Group Decision-Making Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Min Jiang ◽  
Rui Shen ◽  
Zhiqing Meng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Equilibrium Solution ◽  
Group Decision ◽  
Optimal Solution ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Practical Significance ◽  
New Approach ◽  
Alternative Solutions

This paper introduces a concession equilibrium solution without weighted aggregation operators to multiattribute group decision-making problems (in short MGDMPs). It is of practical significance for all decision-makers to find an optimal solution to MGDMPs or to sort out all candidate solutions to MGDMPs. It is proved that under certain conditions the optimal concession equilibrium solution does exist, and on this important result the optimal concession equilibrium solution is obtained by solving a single objective optimization problem. Moreover, the optimal concession equilibrium solution is equivalent to the robust optimal solution with the group weight aggregation under the worst weight condition. Finally, it is proved that the concession equilibrium solution is equivalent to a complete order, i.e. all candidate alternatives can be sorted by concession equilibrium solution. By defining the triangular fuzzy numbers of target concession value, the optimal concession equilibrium solution or the order of the alternative solutions can be obtained in the range of objective concession ambiguity. Numerical experiment shows that the solution can balance the evaluations of multiattribute group decision makers. This paper provides a new approach to solving multiattribute group decision-making problems.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

2016 ◽  
Vol 15 (05) ◽  
pp. 1055-1114 ◽  
Author(s):  
Sheng-Hua Xiong ◽  
Zhen-Song Chen ◽  
Yan-Lai Li ◽  
Kwai-Sang Chin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Individual Decision ◽  
Hesitant Fuzzy Sets ◽  
Variable Power ◽  
Interval Valued

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.

scholarly journals Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-33 ◽  
Author(s):  
Yuchu Qin ◽  
Xiaolan Cui ◽  
Meifa Huang ◽  
Yanru Zhong ◽  
Zhemin Tang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Number ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Intuitionistic Fuzzy Number ◽  
Fuzzy Information ◽  
Qualitative And Quantitative ◽  
Multicriteria Group Decision Making

q-Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all-in-one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T-norm and T-conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q-rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.

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

2014 ◽  
Vol 22 (05) ◽  
pp. 717-735 ◽  
Author(s):  
Hu-Chen Liu ◽  
Qing-Lian Lin ◽  
Jing Wu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Linguistic Variables ◽  
Preference Information ◽  
Operational Laws ◽  
Multiple Attribute

Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches.

scholarly journals Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean

2021 ◽  
Author(s):  
Wuhuan Xu ◽  
Xiaopu Shang ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Distance Measure ◽  
Group Decision ◽  
Comparison Method ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Pythagorean Fuzzy Sets ◽  
Multiple Attribute

AbstractThe linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.

scholarly journals Application of the Bipolar Neutrosophic Hamacher Averaging Aggregation Operators to Group Decision Making: An Illustrative Example

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 698 ◽  
Author(s):  
Muhammad Jamil ◽  
Saleem Abdullah ◽  
Muhammad Yaqub Khan ◽  
Florentin Smarandache ◽  
Fazal Ghani
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Neutrosophic Set ◽  
Ordered Weighted Averaging ◽  
New Methods

The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life.

scholarly journals Prioritized Linguistic Interval-Valued Aggregation Operators and Their Applications in Group Decision-Making Problems

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 209 ◽  
Author(s):  
Kamal Kumar ◽  
Harish Garg
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Efficient Tool ◽  
Intuitionistic Fuzzy ◽  
Quantitative Manner ◽  
Interval Valued

The linguistic interval-valued intuitionistic fuzzy (LIVIF) set is an efficient tool to represent data in the form of interval membership degrees in a qualitative rather than a quantitative manner. The LIVIF set combines the features of interval-valued intuitionistic fuzzy sets (IFSs) and the linguistic variables (LV) and hence provides more freedom to decision-makers. Under this environment, the main objective of this manuscript is to propose some new aggregation operators by capturing the prioritized relationship between the objects. For this, different weighted averaging and geometric aggregation operators are proposed in which preferences related to each object are expressed in terms of LIVIF numbers. Desirable properties of the proposed operators are studied. Further, a group decision-making (DM) approach is presented to solve the multi-attribute DM problems, and its efficiency has been verified with an illustrative example.

CPT-MABAC method for spherical fuzzy multiple attribute group decision making and its application to green supplier selection

2021 ◽  
pp. 1-11
Author(s):  
Huiyuan Zhang ◽  
Guiwu Wei ◽  
Xudong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Supplier Selection ◽  
Group Decision ◽  
Comparison Method ◽  
Entropy Method ◽  
Decision Makers ◽  
Green Supplier Selection ◽  
Multiple Attribute ◽  
Psychological Perceptions

The green supplier selection is one of the popular multiple attribute group decision making (MAGDM) problems. The spherical fuzzy sets (SFSs) can fully express the complexity and fuzziness of evaluation information for green supplier selection. Furthermore, the classic MABAC (multi-attributive border approximation area comparison) method based on the cumulative prospect theory (CPT-MABAC) is designed, which is an optional method in reflecting the psychological perceptions of decision makers (DMs). Therefore, in this article, we propose a spherical fuzzy CPT-MABAC (SF-CPT-MABAC) method for MAGDM issues. Meanwhile, considering the different preferences of DMs to attribute sets, we obtain the objective weights of attributes through entropy method. Focusing on the current popular problems, this paper applies the proposed method for green supplier selection and proves for green supplier selection based on SF-CPT-MABAC method. Finally, by comparing existing methods, the effectiveness of the proposed method is certified.

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