Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study

Meng, Fanyong; Tan, Chunqiao; Chen, Xiaohong

doi:10.1016/j.omega.2016.05.006

Cited by 81 publications

(32 citation statements)

References 61 publications

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“…The soundness of such consistency condition has thus been questioned in recent papers [33,42,32] as it seems to violate a principle according to which a simple reordering of alternatives which leaves the preferences unchanged shall not affect the consistency of these latter ones [6]. Consequently, to overcome this issue, more recent formulations of consistency conditions for IPCMs are invariant under permutations of alternatives.…”

Section: Liu's [G]-consistencymentioning

confidence: 99%

A general unified framework for interval pairwise comparison matrices

Cavallo

Brunelli

2018

International Journal of Approximate Reasoning

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Interval Pairwise Comparison Matrices has been widely used to account for uncertain statements concerning the preferences of decision makers. Several approaches have been proposed in the literature, such as multiplicative and fuzzy interval matrices. In this paper, we propose a general unified approach to Interval Pairwise Comparison Matrices, based on Abelian linearly ordered groups. In this framework, we generalize some consistency conditions provided for multiplicative and/or fuzzy interval pairwise comparison matrices and provide inclusion relations between them. Then, we provide a concept of distance between intervals that, together with a notion of mean defined over real continuous Abelian linearly ordered groups, allows us to provide a consistency index and an indeterminacy index. In this way, by means of suitable isomorphisms between Abelian linearly ordered groups, we will be able to compare the inconsistency and the indeterminacy of different kinds of Interval Pairwise Comparison Matrices, e.g. multiplicative, additive, and fuzzy, on a unique Cartesian coordinate system

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Section: Liu's [G]-consistencymentioning

confidence: 99%

A general unified framework for interval pairwise comparison matrices

Cavallo

Brunelli

2018

International Journal of Approximate Reasoning

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“…Zhang [44] developed a logarithmic least square method based on a parameterized transformation formula which converts a normalized interval weight vector into a consistent IMPR to derive interval weights. Meng et al [45,46] proposed a new formulation of consistency for an IMPR that is based on the definition of a quasi-IMPR, and they analyzed the relationship between their definition, Liu's definition [37], and Wang et al's definition [32]. Based on the analysis of existing definitions of consistency, Krejčí [47] proposed a new definition which was invariant to the permutation of objects for an IMPR.…”

Section: Saaty and Vargasmentioning

confidence: 99%

The Interval Cognitive Network Process for Multi-Attribute Decision-Making

Yin

Cheng

et al. 2017

Symmetry

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Aiming at combining the good characteristics of a differential scale in representing human cognition and the favorable properties of interval judgments in expressing decision-makers' uncertainty, this paper proposes the interval cognitive network process (I-CNP) to extend the primitive cognition network process (P-CNP) to handle interval judgments. The key points of I-CNP include a consistency definition for an interval pairwise opposite matrix (IPOM) and a method to derive interval utilities from an IPOM. This paper defines a feasible region-based consistency definition and a transitivity based consistency definition for an IPOM. Both of the two definitions are equivalent to the consistency definition for a crisp pairwise opposite matrix (POM) when an IPOM is reduced to a POM. Two methods that are able to derive interval utilities from both consistent and inconsistent IPOMs are developed based on the two definitions. Four numerical examples are used to illustrate the proposed methods and to compare I-CNP to interval analytic hierarchy process (IAHP). The results show that I-CNP reflects the decision-makers' cognition better, and that the suggestions provided by I-CNP are more convincing. I-CNP provides new useful alternative tools for multi-attribute decision-making problems.

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“…A partir de ella proporcionan un modelo de programación lineal para construir una relación consistente a partir de una relación de preferencias fuzzy intervalar. Paralelamente en (Meng et al, 2017b) se propone una definición de consistencia multiplicativa.…”

Section: )unclassified

“…Xu (2006Xu ( , 2007 introdujo el concepto de relación de preferencia fuzzy intervalar incompleta. Desde entonces, muchas de las referencias señaladas anteriormente abordan el problema de información incompleta, centrándose en métodos de compleción, para estimar los datos no facilitados por los expertos (Genç et al, 2010;Wang y Li, 2012;Liu et al, 2012b;Xu et al, 2014c;Xia y Xu, 2014;Wang y Li, 2015;Meng et al, 2016Meng et al, , 2017aMeng et al, , 2017b.…”

Section: )unclassified

“…En Wan et al (2018a) se propone uníndice de consistencia geométrica para medir el nivel de consistencia de una relación de preferencia fuzzy intervalar. En (Meng et al, 2017b) y en (Meng et al, 2017a) se defineníndices de consenso de grupo para relaciones de preferencia fuzzy cuasiintervalares para el modelo multiplicativo y aditivo de preferencias, respectivamente.…”

Section: Modelo Computacionalunclassified

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Métodos y algoritmos en problemas de decisión de grupo a partir de relaciones de preferencia fuzzy

Céspedes¹,

Luisa²

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Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study

Cited by 81 publications

References 61 publications

A general unified framework for interval pairwise comparison matrices

A general unified framework for interval pairwise comparison matrices

The Interval Cognitive Network Process for Multi-Attribute Decision-Making

Métodos y algoritmos en problemas de decisión de grupo a partir de relaciones de preferencia fuzzy

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