Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations

Xu, Guizhi; Wan, Shouhong; Wang, Feng; Dong, Jiuying; Zeng, Yanjun

doi:10.1016/j.knosys.2015.12.007

Cited by 93 publications

(68 citation statements)

References 41 publications

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“…Except for the above quantitatively comparative analysis, this subsection implements a qualitatively comparative analysis by using the existing GDM methods [6,18].…”

Section: Comparison With Other Existing Methodsmentioning

confidence: 99%

“…(1) The concerns of these methods are different. Method [6] studied the consistent and consensus in GDM with IFPR, whereas Method [18] and the proposed algorithm concentrate on the multiplicative consistency of IVIFPR. The discrepancy is that Method [18] focused on the multiplicative transitivity of IVIFPR and improving the consistency of an inconsistent IVIFPR, while the proposed algorithm is devoted to judging and measuring the multiplicative consistency degree of an IVIFPR and address the GDM with IVIFPRs.…”

Section: Comparison With Other Existing Methodsmentioning

confidence: 99%

“…In order to reveal the superiority of our proposed method, this subsection concentrates on comparative analyses with Wan's method [12] and other existing GDM methods [6,18].…”

Section: Comparative Analysesmentioning

confidence: 99%

“…However, due to the uncertainty and complex information granularity, DMs may have difficulty in providing pairwise comparison judgments on alternatives with crisp numerical values. To address this issue, the intuitionistic fuzzy preference relation (IFPR) [5,6], interval-valued fuzzy preference relation (IVFPR) [7,8] and interval-valued intuitionistic fuzzy (IVIF) preference relation (IVIFPR) [9,10] appear one after another. Particularly, the elements in an IVIFPR consist of IVIF values (IVIFVs), where both the membership degree and non-membership degree are intervals.…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm for Interval-Valued Intuitionistic Fuzzy Preference Relations in Group Decision Making Based on Acceptability Measurement and Priority Weight Determination

Zhuang

Tang

2018

Algorithms

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Group decision making with intuitionistic fuzzy preference information contains two key issues: acceptability measurement and priority weight determination. In this paper, we investigate the above two issues with respect to multiplicative interval-valued intuitionistic fuzzy preference relation (IVIFPR). Firstly, a consistency index is defined to measure the multiplicative consistency degree of IVIFPR and an optimization model is established to improve the consistency degree of IVIFPR to an acceptable one. Next, in terms of priority weight determination, an error-analysis-based extension method is proposed to obtain priority weight vector from the acceptable IVIFPR. For GDM problems, decision makers' weights are derived by the proposed multiplicative consistency index. Subsequently, the collective IVIFPR is obtained by using an interval-valued intuitionistic fuzzy (IVIF) weighted averaging operator. Finally, a step-by step algorithm for GDM with IVIFPRs is given, and an example of enterprise innovation partner selection is analyzed, and comparative analyses with existing approaches are performed to demonstrate that the proposed algorithm is both effective and practical in dealing with GDM problems. Definition 1. [27] An IVFPR R on the alternative set X = {x 1 , x 2 , . . . , x n } is presented by an interval-valued fuzzy judgment matrix R = r ij n×n ⊂ X × X with r ij = r ij , r ij , where the preference degree to which alternative x i over x j is between r ij and r ij . Moreover, r ij and r ij fulfill the following conditions: 0 ≤ r ij ≤ r ij ≤ 1, r ij + r ji = 1, r ii = r ii = 0.5 for all i, j = 1, 2, . . . , n.

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“…Except for the above quantitatively comparative analysis, this subsection implements a qualitatively comparative analysis by using the existing GDM methods [6,18].…”

Section: Comparison With Other Existing Methodsmentioning

confidence: 99%

Section: Comparison With Other Existing Methodsmentioning

confidence: 99%

“…In order to reveal the superiority of our proposed method, this subsection concentrates on comparative analyses with Wan's method [12] and other existing GDM methods [6,18].…”

Section: Comparative Analysesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Algorithm for Interval-Valued Intuitionistic Fuzzy Preference Relations in Group Decision Making Based on Acceptability Measurement and Priority Weight Determination

Zhuang

Tang

2018

Algorithms

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“…Thus, in some cases, IFS theory is more appropriate to deal with inexact information present in real-world applications than the ordinary fuzzy set. Eventually, in less than three decades since its rst appearance, IFS theory has been investigated by many authors [18][19][20][21][22][23][24] and used for decision making [18,23,25], mathematical programming [20,24,[26][27][28], medical diagnosis [19], to name a few. With this viewpoint, the extension of all aforementioned aggregation operators to intuitionistic fuzzy environment has received considerable attention of many researchers [29,30].…”

Section: Introductionmentioning

confidence: 99%

Family of harmonic aggregation operators under inuitionistic fuzzy environment

Das

Guha

2017

Scientia Iranica

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Abstract. In the process of decision making, the necessity of aggregation of input arguments into a single output becomes a key step; as a result, the selection of an appropriate aggregation operator is a vital aspect. The aim of this contribution is threefold. First, we study algebraic operations of Trapezoidal Intuitionistic Fuzzy Numbers (TrIFNs), and then on the basis of these operational laws, we de ne four types of harmonic mean operators with TrIFNs. Second, the required properties of the proposed operators are reviewed. After that, an approach based on the proposed operators is introduced to solve a group decision making problem. Finally, a practical example is furnished to demonstrate the applicability of the proposed operators in the decision making context. The contribution ends by introducing comparative analysis of the obtained results.

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Multiplicative consistency analysis for q‐rung orthopair fuzzy preference relation

et al. 2019

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The q-rung orthopair fuzzy set is characterized by membership and nonmembership functions, and the sum of the qth power of them is less than or equal to one. Since it releases the constraints existed in both intuitionistic fuzzy set and Pythagorean fuzzy set, it has wide applications in real cases. However, so far, there is little research on the multiplicative consistency of q-rung orthopair fuzzy preference relation (q-ROFPR). To fill this vacancy, this paper provides a detailed analysis on the multiplicative consistency of q-ROFPR. First, we investigate the concept of multiplicative consistent q-ROFPR and its properties. Subsequently, two goal programming models are proposed to derive the priorities from individual and group q-ROFPRs, respectively. After that, a novel consistency-improving algorithm for q-ROFPR and a weight-generating method for decision-makers are discussed in detail, based on which, a novel group decision-making method is proposed. Finally, a case study concerning the evaluation of rehabilitation program selection is given to illustrate the applicability of the proposed method. The effectiveness and superiority of the proposed method are verified by comparing it with some existing methods. K E Y W O R D S multiple criteria decision making, multiplicative consistency, q-rung orthopair fuzzy preference relation, q-rung orthopair fuzzy priority weight, q-rung orthopair fuzzy set F I G U R E 1 The orthogonal projections of intuitionistic fuzzy set (IFS)/Pythagorean fuzzy set (PFS)/q-rung orthopair fuzzy set (q-ROFS) in μ and ν coordinates 2 ZHANG ET AL. | 39

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Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations

Cited by 93 publications

References 41 publications

An Algorithm for Interval-Valued Intuitionistic Fuzzy Preference Relations in Group Decision Making Based on Acceptability Measurement and Priority Weight Determination

An Algorithm for Interval-Valued Intuitionistic Fuzzy Preference Relations in Group Decision Making Based on Acceptability Measurement and Priority Weight Determination

Family of harmonic aggregation operators under inuitionistic fuzzy environment

Multiplicative consistency analysis for q‐rung orthopair fuzzy preference relation

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