Deriving priority weights from intuitionistic fuzzy multiplicative preference relations

Meng, Fanyong; Tang, Jie; Zhang, Xu

doi:10.1002/int.22179

Cited by 13 publications

(41 citation statements)

References 54 publications

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“…In the following, we shall adopt formulation (2). Index GCI has been studied (Aguarón and Moreno-Jiménez, 2003;Aguarón et al, 2016) and extended to other representations of preferences as, for instance, interval-valued pairwise comparisons (Meng et al, 2015;Wang, 2015). Peláez and Lamata (2003) proposed another index in the following form,…”

Section: Pairwise Comparisons and Inconsistency Indicesmentioning

confidence: 99%

A general formulation for some inconsistency indices of pairwise comparisons

Brunelli

Fedrizzi

2018

Ann Oper Res

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In this paper, we propose a unifying approach to the problem of measuring the inconsistency of judgments. More precisely, we define a general framework that allow several well-known inconsistency indices to be expressed as special cases of our formulation. Our proposal defines an inconsistency index as an aggregation of 'local', i.e. triple-based, inconsistencies. We prove that some simple and reasonable assumptions on the local inconsistency evaluation and on the aggregation rules guarantee a set of good properties for the obtained general inconsistency index. We show that OWA functions and t-conorms are suitable examples of aggregation functions for the local inconsistencies. We argue that the flexibility of our proposal is a relevant property for inconsistency evaluation that allows a suitable tuning of some important characteristics of the index. For example, by using different types of OWA functions, it is possible to obtain the desired balance between an averaging behavior and a 'largest inconsistency focused' behavior. We show that our proposal can be formulated in an equivalent way for the additive representation of local inconsistencies too. Under this representation, we prove a property of Pareto-efficiency for our general, aggregation-based inconsistency index.

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Section: Pairwise Comparisons and Inconsistency Indicesmentioning

confidence: 99%

A general formulation for some inconsistency indices of pairwise comparisons

Brunelli

Fedrizzi

2018

Ann Oper Res

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“…(2013) proposed the definition of intuitionistic multiplicative preference relations (IMPRs), whose elements are intuitionistic multiplicative numbers (IMNs), that is, three values in [1/9, 9] to quantify the judgments of an alternative over another from the membership, nonmembership and the hesitancy degree. Due to the advantages of IMPR in describing the uncertainty of the pairwise judgments between alternatives, it has aroused great interest of scholars (Garg, 2017a, b, 2018a, b, 2020, 2021a, 2022; Jiang et al ., 2013, 2015; Jiang and Xu, 2014; Xia and Xu, 2013; Xu, 2013; Meng et al. , 2019; Zhang and Pedrycz, 2017, 2018; Zhang et al.…”

Section: Introductionmentioning

confidence: 99%

“…'s consistency concept for IMPRs and proposed a new one. Meanwhile, Meng et al. (2019) also proposed another consistency definition of IMPRs.…”

Section: Introductionmentioning

confidence: 99%

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A new group decision-making method with incomplete intuitionistic multiplicative preference relations

Hao³

2022

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PurposeConsistency and consensus are two important research issues in group decision-making (GDM). Considering some drawbacks associated with these two issues in existing GDM methods with intuitionistic multiplicative preference relations (IMPRs), a new GDM method with complete IMPRs (CIMPRs) and incomplete IMPRs (ICIMPRs) is proposed in this paper.Design/methodology/approachA mathematically programming model is constructed to judge the consistency of CIMPRs. For the unacceptably consistent CIMPRs, a consistency-driven optimization model is constructed to improve the consistency level. Meanwhile, a consistency-driven optimization model is constructed to supplement the missing values and improve the consistency level of the ICIMPRs. As to GDM with CIMPRs, first, a mathematically programming model is built to obtain the experts' weights, after that a consensus-driven optimization model is constructed to improve the consensus level of CIMPRs, and finally, the group priority weights of alternatives are obtained by an intuitionistic fuzzy programming model.FindingsThe case analysis of the international exchange doctoral student selection problem shows the effectiveness and applicability of this GDM method with CIMPRs and ICIMPRs.Originality/valueFirst, a novel consistency definition of CIMPRs is presented. Then, a consistency-driven optimization model is constructed, which supplements the missing values and improves the consistency level of ICIMPRs simultaneously. Therefore, this model greatly improves the efficiency of consistency improving. Experts' weights determination method considering the subjective and objective information is proposed. The priority weights of alternatives are determined by an intuitionistic fuzzy (IF) programming model considering the risk preference of experts, so the method determining priority weights is more flexible and agile. Based on the above theoretical basis, a new GDM method with CIMPRs and ICIMPRs is proposed in this paper.

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“…Clustering has been intensively studied by combing information to categorize unlabelled data items into appropriate groups 1‐16 . With increasing data collection, many data in the real‐world could be presented from different perspectives, which are termed multiview data in the literature.…”

Section: Introductionmentioning

confidence: 99%

Partial multiview clustering with locality graph regularization

Lian

Wang

et al. 2021

Int J Intell Syst

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Multiview clustering (MVC) collects complementary and abundant information, which draws much attention in machine learning and data mining community. Existing MVC methods usually hold the assumption that all the views are complete. However, multiple source data are often incomplete in real‐world applications, and so on sensor failure or unfinished collection process, which gives rise to incomplete multiview clustering (IMVC). Although enormous efforts have been devoted in IMVC, there still are some urgent issues that need to be solved: (i) The locality among multiple views has not been utilized in the existing mechanism; (ii) Existing methods inappropriately force all the views to share consensus representation while ignoring specific structures. In this paper, we propose a novel method termed partial MVC with locality graph regularization to address these issues. First, followed the traditional IMVC approaches, we construct weighted semi‐nonnegative matrix factorization models to handle incomplete multiview data. Then, upon the consensus representation matrix, the locality graph is constructed for regularizing the shared feature matrix. Moreover, we add the coefficient regression term to constraint the various base matrices among views. We incorporate the three aforementioned processes into a unified framework, whereas they can negotiate with each other serving for learning tasks. An effective iterative algorithm is proposed to solve the resultant optimization problem with theoretically guaranteed convergence. The comprehensive experiment results on several benchmarks demonstrate the effectiveness of the proposed method.

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Deriving priority weights from intuitionistic fuzzy multiplicative preference relations

Cited by 13 publications

References 54 publications

A general formulation for some inconsistency indices of pairwise comparisons

A general formulation for some inconsistency indices of pairwise comparisons

A new group decision-making method with incomplete intuitionistic multiplicative preference relations

Partial multiview clustering with locality graph regularization

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