MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making

Pérez-Domínguez, Luis; Rodríguez‐Picón, Luis Alberto; Alvarado‐Iniesta, Alejandro; Luviano-Cruz, David; Zhang, Xu

doi:10.1155/2018/2602376

Cited by 83 publications

(45 citation statements)

References 35 publications

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“…To be specific, Gündoǧdu [36] introduced a useful nine-point linguistic scale for facilitating the construction of the evaluation matrix based on PF sets and spherical fuzzy sets. Mete [37], Oz et al [38], and Pérez-Domínguez et al [39] employed an identical nine-point scale for expressing linguistic evaluations in PF settings. Rani et al [40] introduced a nine-point linguistic scale for assisting decision-makers' judgments concerning the performance evaluations of alternatives in terms of criteria.…”

Section: Mcgdm Problem Under Pf Uncertaintymentioning

confidence: 99%

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

Wang¹,

Chen²

2020

IJCIS

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A B S T R A C TThis paper presents a new compromising approach to multiple criteria group decision-making (MCGDM) for the treatment of uncertainty which is based on Pythagorean fuzzy (PF) sets. The present work intends to propose a novel linear programming technique for multidimensional analysis of preference (LINMAP) by way of some useful concepts related to PF dominance relations, individual consistency and inconsistency levels, and individual fit measurements. The concept of PF scalar function-based dominance measures is defined to conduct intracriterion comparisons concerning uncertain evaluation information based on Pythagorean fuzziness; moreover, several valuable properties are also investigated to demonstrate its effectiveness. For the assessment of overall dominance of alternatives, this paper provides a synthetic index, named a comprehensive dominance measure, which is the aggregation of the weighted dominance measures by combining unknown weight information and PF dominance measures of various criteria. For each decision-maker, this paper employs the proposed measures to evaluate the individual levels of rank consistency and rank inconsistency regarding the obtained overall dominance relations and the decision-maker's preference comparisons over paired alternatives. In the framework of individual fit measurements, this paper constructs bi-objective mathematical programming models and then provides their corresponding parametric linear programming models for generating the best compromise alternative. Realistic applications with some comparative analyses concerning railway project investment are implemented to demonstrate the appropriateness and usefulness of the proposed methodology in addressing actual MCGDM problems.However, the classical LINMAP methods cannot be directly employed to handle the decision-making problems involving fuzzy information because of the uncertainty contained in performance information or evaluation values of candidate alternatives in terms of criteria [8][9][10]. Accordingly, numerous studies have extended the classical LINMAP for conducting multiple criteria decision analysis in a variety of different fuzzy circumstances. For example, Wan and Li [11] emanated from LINMAP to construct an intuitionistic fuzzy programming method for handling heterogeneous MCGDM containing intuitionistic fuzzy truth degrees. Furthermore, Wan and Li [8] considered the hesitancy degrees about pairwise comparisons as interval-valued intuitionistic fuzzy sets to establish a fuzzy LINMAP-based method for conducting a heterogeneous decision analysis. Zhang et al. [12] utilized the LINMAP and Shapley values to develop an interval-valued intuitionistic fuzzy mathematical programming model to manage uncertain MCGDM problems. Moreover, Zhang et al.[13] established a mathematical programming-based approach to heterogeneous MCGDM involving aspirations and incomplete preference information. Zhang and Xu [10] applied the LINMAP structure to present an interval programming method for handling MCGDM problems

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Section: Mcgdm Problem Under Pf Uncertaintymentioning

confidence: 99%

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

Wang¹,

Chen²

2020

IJCIS

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“…This section introduces preliminaries on the concepts of PFS and IPFS and their operations. The concepts of PFSs originated from the work of Atanassov [25], with the name "intuitionistic fuzzy sets of second type" and with further development by Yager [28,29], similar to the latest research in decision making problems [30,31].…”

Section: Preliminariesmentioning

confidence: 99%

“…The PFS is equivalent to IFSs of second type and powerfully handles uncertain problems. Throughout the whole paper, we use the name "Pythagorean fuzzy sets" similar to various existing references [30,31].…”

Section: Introductionmentioning

confidence: 99%

An Interval Pythagorean Fuzzy Multi-criteria Decision Making Method Based on Similarity Measures and Connection Numbers

Cao

et al. 2019

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Interval Pythagorean fuzzy set (IPFS), which can handle imprecise and ambiguous information, has attracted considerable attention in both theory and practice. However, one of the main difficulties under IPFSs is the comparison between interval numbers. To overcome this shortcoming, connection number theory is first introduced, and interval numbers are transformed into connection numbers in the operating process. Considering that similarity measures play an important role in assessing the degree between ideal and proposal alternatives in the decision making process, this paper aims to develop new similarity measures with IPFSs and apply them to multi-criteria decision making (MCDM) problems. The main contributions of this paper are as follows: (1) introduction of a comparison method through transforming interval numbers into connection numbers; (2) development of three new similarity measures with IPFSs based on the minimum and maximum operators, and investigation of their properties; (3) calculation of the similarity measures considering weights of membership and non-membership degrees; (4) establishment of an interval Pythagorean fuzzy decision making method applying the presented similarity measures. A case study on selecting a project delivery system is made to show the applicability of the proposed approach.

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“…Xue et al [28] developed the LINMAP technique to track the best investment company in railway projects using PF information. Perez-Dominguez [29] developed a multi-objective optimization based on ratio analysis (MOORA) with PF set information and applied it to MAGDM problem. To solve an MAGDM problem with partially known weight information, Garg [30] introduced an improved score function, where the preferences of the attribute are taken in the form of IVPF sets.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

et al. 2019

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The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems.

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MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making

Cited by 83 publications

References 35 publications

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

An Interval Pythagorean Fuzzy Multi-criteria Decision Making Method Based on Similarity Measures and Connection Numbers

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

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