Some improved pythagorean fuzzy Dombi power aggregation operators with application in multiple-attribute decision making

2021 ◽  
pp. 1-21
Author(s):  
Peide Liu ◽  
Qaisar Khan ◽  
Tahir Mahmood ◽  
Rashid Ali Khan ◽  
Hidayat Ullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Multiple Attribute ◽  
General Parameter ◽  
Pythagorean Fuzzy Numbers

Pythagorean fuzzy set (PyFS) is an extension of various fuzzy concepts, such as fuzzy set (FS), intuitionistic FS, and it is enhanced mathematical gizmo to pact with uncertain and vague information. In this article, some drawbacks in the Dombi operational rules for Pythagorean fuzzy numbers (PyFNs) are examined and some improved Dombi operational laws for PyFNs are developed. We also find out that the value aggregated using the existing Dombi aggregation operators (DAOs) is not a PyFN. Furthermore, we developed two new aggregations, improved existing aggregation operators (AOs) for aggregating Pythagorean fuzzy information (PyFI) and are applied to multiple-attribute decision making (MADM). To acquire full advantage of power average (PA) operators proposed by Yager, the Pythagorean fuzzy Dombi power average (PyFDPA) operator, the Pythagorean fuzzy Dombi weighted power average (PyFDWPA) operator, Pythagorean fuzzy Dombi power geometric (PyFDPG) operator, Pythagorean fuzzy Dombi weighted geometric (PyFDPWG) operator, improved the existing AOs and their desirable properties are discussed. The foremost qualities of these developed Dombi power aggregation operators is that they purge the cause of discomfited data and are more supple due to general parameter. Additionally, based on these Dombi power AOs, a novel MADM approach is instituted. Finally, a numerical example is given to show the realism and efficacy of the proposed approach and judgment with the existing approaches is also specified.

scholarly journals Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chunyong Wang ◽  
Qingguo Li ◽  
Xiaoqiang Zhou ◽  
Tian Yang
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Special Cases ◽  
Fuzzy Aggregation

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

scholarly journals Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1150 ◽  
Author(s):  
Na Li ◽  
Harish Garg ◽  
Lei Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Multiple Attribute ◽  
The Given ◽  
Pythagorean Fuzzy Numbers

A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method.

scholarly journals Multiple Attribute Decision Making Based on Hesitant Fuzzy Einstein Geometric Aggregation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoqiang Zhou ◽  
Qingguo Li
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Information ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Geometric Operator

We first define an accuracy function of hesitant fuzzy elements (HFEs) and develop a new method to compare two HFEs. Then, based on Einstein operators, we give some new operational laws on HFEs and some desirable properties of these operations. We also develop several new hesitant fuzzy aggregation operators, including the hesitant fuzzy Einstein weighted geometric (HFEWGε) operator and the hesitant fuzzy Einstein ordered weighted geometric (HFEWGε) operator, which are the extensions of the weighted geometric operator and the ordered weighted geometric (OWG) operator with hesitant fuzzy information, respectively. Furthermore, we establish the connections between the proposed and the existing hesitant fuzzy aggregation operators and discuss various properties of the proposed operators. Finally, we apply the HFEWGεoperator to solve the hesitant fuzzy decision making problems.

Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making

2020 ◽  
Vol 8 (6) ◽  
pp. 524-548
Author(s):  
Qian Yu ◽  
Jun Cao ◽  
Ling Tan ◽  
Yubing Zhai ◽  
Jiongyan Liu
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Definition Of

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.

scholarly journals Analysis of Social Networks by Using Pythagorean Cubic Fuzzy Einstein Weighted Geometric Aggregation Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Tehreem ◽  
Amjad Hussain ◽  
Jung Rye Lee ◽  
Muhammad Sajjad Ali Khan ◽  
Dong Yun Shin
Keyword(s):  
Decision Making ◽  
Social Networks ◽  
Fuzzy Set ◽  
Group Decision ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Analysis Of Social Networks ◽  
Interval Valued

Pythagorean cubic set (PCFS) is the combination of the Pythagorean fuzzy set (PFS) and interval-valued Pythagorean fuzzy set (IVPFS). PCFS handle more uncertainties than PFS and IVPFS and thus are more extensive in their applications. The objective of this paper is under the PCFS to establish some novel operational laws and their corresponding Einstein weighted geometric aggregation operators. We describe some novel Pythagorean cubic fuzzy Einstein weighted geometric (PCFEWG) operators to handle multiple attribute group decision-making problems. The desirable relationship and the characteristics of the proposed operator are discussed in detail. Finally, a descriptive case is given to describe the practicality and the feasibility of the methodology established.

scholarly journals Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yong Liu ◽  
Yongfeng Pang ◽  
Ruiyue Lin
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Investment Company ◽  
Pythagorean Fuzzy Set ◽  
Bonferroni Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
Geometric Bonferroni Mean

The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.

scholarly journals AN APPROACH TO MULTIPLE ATTRIBUTE DECISION MAKING BASED ON THE INDUCED CHOQUET INTEGRAL WITH FUZZY NUMBER INTUITIONISTIC FUZZY INFORMATION

2014 ◽  
Vol 15 (2) ◽  
pp. 277-298 ◽  
Author(s):  
Guiwu Wei ◽  
Rui Lin ◽  
Xiaofei Zhao ◽  
Hongjun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Choquet Integral ◽  
Score Function ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Multiple Attribute

In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Firstly, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: induced fuzzy number intuitionistic fuzzy choquet ordered averaging (IFNIFCOA) operator and induced fuzzy number intuitionistic fuzzy choquet ordered geometric (IFNIFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method.

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

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 594 ◽  
Author(s):  
Mi Jung Son ◽  
Jin Han Park ◽  
Ka Hyun Ko
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Multiple Attribute

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.

scholarly journals Generalized Linguistic Hesitant Intuitionistic Fuzzy Hybrid Aggregation Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yongfeng Pang
Keyword(s):  
Decision Making ◽  
Geometric Mean ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
New Method ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Special Cases

Some hybrid aggregation operators have been developed based on linguistic hesitant intuitionistic fuzzy information. The generalized linguistic hesitant intuitionistic fuzzy hybrid weighted averaging (GLHIFHWA) operator and the generalized linguistic hesitant intuitionistic fuzzy hybrid geometric mean (GLHIFHGM) operator are defined. Some special cases of the new aggregation operators are studied and many existing aggregation operators are special cases of the new operators. A new multiple attribute decision making method based on the new aggregation operators is proposed and a practical numerical example is presented to illustrate the feasibility and practical advantages of the new method.

scholarly journals Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 943
Author(s):  
Min Feng ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variable ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Input Parameters ◽  
Cognitive Information

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Sign in / Sign up

Export Citation Format

Share Document