scholarly journals Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Naeem ◽  
Shahzaib Ashraf ◽  
Saleem Abdullah ◽  
F. M. AL‐Harbi
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Numerical Application ◽  
Operational Laws ◽  
Maclaurin Symmetric Mean ◽  
Definition Of ◽  
Improved Algorithm

In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique.

scholarly journals EDAS METHOD FOR MULTIPLE CRITERIA GROUP DECISION MAKING WITH PICTURE FUZZY INFORMATION AND ITS APPLICATION TO GREEN SUPPLIERS SELECTIONS

2019 ◽  
Vol 25 (6) ◽  
pp. 1123-1138 ◽  
Author(s):  
Siqi Zhang ◽  
Guiwu Wei ◽  
Hui Gao ◽  
Cun Wei ◽  
Yu Wei
Keyword(s):  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Score Function ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Operational Laws ◽  
Definition Of ◽  
Green Suppliers ◽  
Picture Fuzzy Sets

In this paper, we construct picture fuzzy EDAS model based on traditional EDAS (Evaluation based on Distance from Average Solution) model. Firstly, we briefly review the definition of picture fuzzy sets (PFSs) and introduce the score function, accuracy function and operational laws of picture fuzzy numbers (PFNs). Then, we combine traditional EDAS model for MCGDM with PFNs. In our model, it’s more accuracy and effective for considering the conflicting attributes. Finally, a numerical example for green supplier selection has been given to illustrate this new model and some comparisons between EDAS model with PFNs and PFWA, PFWG aggregation operators are also conducted to further illustrate advantages of the new method.

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 Decision Support System For Energy Source Selection Based On Credibility Fuzzy Information.

2021 ◽  
Author(s):  
Saleem Abdullah ◽  
Muhammad Yahya
Keyword(s):  
Energy Source ◽  
Decision Making ◽  
Decision Support ◽  
Support System ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Source Selection ◽  
Operational Laws

Abstract This main objective of this work is to define some new operations of credibility fuzzy numbers using Hamacher t-norm and t-conorm. These operation are more generalized operation for credibility fuzzy numnbers, we apply these operations to aggregation operators for credibility fuzzy numbers. Furthermore, using the basic operational laws of Hamacher t-norm and t-conorm, we develop a series of credibility fuzzy Hamacher aggregation operators like credibility fuzzy Hamacher weighted averaging (CFHWA) and credibility fuzzy Hamacher geometric (CFHWG) aggregation operators. we also explained some of the proposed Hamacher aggregation operators properties like commutativity, idempotency and monotonicity. In order to validate the proposed Hamacher aggregation operators for credibility fuzzy numbers, we develop general algorithm for decision making technique under credibility fuzzy numbers and using these operators. The proposed algorithm is apply to electricity crises in Pakistan problems. Finally a comparison with other existing methods is done to check the accuracy and validation of the proposed methods. At rest the proposed method is verified by other well known methods.

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.

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.

Prioritized weighted aggregation operators under complex pythagorean fuzzy information

2020 ◽  
Vol 39 (3) ◽  
pp. 4763-4783
Author(s):  
Muhammad Akram ◽  
Xindong Peng ◽  
Ahmad N. Al-Kenani ◽  
Aqsa Sattar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Two Dimensional ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Priority Level ◽  
Prioritized Aggregation Operators

Complex Pythagorean fuzzy (CPF), a worthwhile generalization of Pythagorean fuzzy set, is a powerful tool to deal with two-dimensional or periodic information. In this paper, we develop two prioritized aggregation operators (AOs) under CPF environment, namely, complex Pythagorean fuzzy prioritized weighted averaging (CPFPWA) operator and complex Pythagorean fuzzy prioritized weighted geometric (CPFPWG) operator. We consider the prioritization relationship among criteria and decision makers (DMs) to make our result more accurate as in real decision making (DM) problems, the criteria and DMs have different priority level. Further, we discuss remarkable properties of our proposed AOs. Moreover, we promote the evolution of MCDM problem by investigating an algorithm in CPF environment with its flow chart. Finally, to check the superiority and validity of proposed operators, we compare the computed results with the different existing techniques.

scholarly journals Some T-Spherical Fuzzy Einstein Interactive Aggregation Operators and Their Application to Selection of Photovoltaic Cells

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Shouzhen Zeng ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Muhammad Naeem
Keyword(s):  
Fuzzy Set ◽  
Photovoltaic Cells ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Selection Of

In this article, it is pointed out that the existing intuitionistic fuzzy and T-spherical fuzzy Einstein averaging and geometric operators have some limitations. To overcome these limitations, we proposed some new averaging and geometric operators in the T-spherical fuzzy environment instead of the intuitionistic fuzzy environment because the T-spherical fuzzy set is the most generalized form and the proposed operators can be particularized to the intuitionistic fuzzy environment. First, new operational laws for T-spherical fuzzy information are defined, on the basis of which Einstein geometric interaction operators and Einstein averaging interactive aggregation operators are then proposed. Some basic properties and advantages of proposed aggregation operators are also discussed. Moreover, the proposed operators are applied to the MADM problem to check their reliability. The superiority of the proposed operators over existing work is checked with the help of an example.

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 Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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