A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees

Wan, Shouhong; Yingli, Qin; Dong, Jiuying

doi:10.1016/j.knosys.2017.10.002

Cited by 64 publications

(50 citation statements)

References 41 publications

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“…Multiple criteria decision analysis (MCDA) is the process of ranking discrete candidate alternatives and finding the best compromise solution based on the decision maker's subjective assessments of multiple evaluative criteria. 1 In particular, the growing strategic consideration within the intricate and unpredictable environment has contributed to the greater complexity and difficulty of subjective assessments. Great uncertainties in changeable decision-making situations increase the vagueness and ambiguity in multiple criteria evaluation processes.…”

Section: Introductionmentioning

confidence: 99%

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Chen

2018

Int J Intell Syst

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The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson‐like correlation‐based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval‐valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real‐life decision‐making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well‐known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson‐like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation‐based closeness coefficients to simultaneously measure the relative closeness to the positive‐ideal PF/IVPF solutions and the relative remoteness from the negative‐ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson‐like correlation‐based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.

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Section: Introductionmentioning

confidence: 99%

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Chen

2018

Int J Intell Syst

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“…In Step I.4, this paper employed Eqs. (14) and (15) to identify the displaced reference points p k * j and p k #j , respectively, in connection with c j ∈ C for each e k . The determination results of the positiveand negative-ideal reference points are revealed in Tables 5 and 6 Table 7.…”

Section: Practical Applicationmentioning

confidence: 99%

“…with hesitant fuzzy ratings of alternatives and pairwise judgments between alternatives using interval numbers. Wan et al [14] developed a hesitant fuzzy mathematical programming model to deal with hybrid MCGDM involving hesitant fuzzy truth degrees and incomplete criteria weight information. Xu et al [15] combined hesitant fuzzy linguistic term sets with LINMAP to provide a hesitant fuzzy linguistic LINMAP method.…”

Section: Introductionmentioning

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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“…Further, Wan and Li [22] and Wan and Dong [23] developed IVIF mathematical programming methods to solve hybrid MCDM and MCGDM problems with IVIF truth degrees, respectively. Wan and Qing [24] developed a HF mathematical programming method to solve hybrid MCGDM problems with HF truth degrees. Wan et al [25] extended LINMP method for MCGDM in which all the criteria values of alternatives and truth degrees of alternatives' comparisons are in the form of Pythagorean fuzzy sets (PFSs).…”

Section: Introductionmentioning

confidence: 99%

A Novel Three-Phase LINMAP Method for Hybrid Multi-Criteria Group Decision Making With Dual Hesitant Fuzzy Truth Degrees

Dong

Wan

2020

IEEE Access

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Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented here for solving hybrid multicriteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection.

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A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees

Cited by 64 publications

References 41 publications

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

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

A Novel Three-Phase LINMAP Method for Hybrid Multi-Criteria Group Decision Making With Dual Hesitant Fuzzy Truth Degrees

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