Interval weight generation approaches based on consistency test and interval comparison matrices

Wang, Ying‐Ming; Yang, Jian‐Bo; Xu, Dong-Ling

doi:10.1016/j.amc.2004.06.080

Cited by 123 publications

(58 citation statements)

References 28 publications

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“…In fact, this definition of consistency for interval matrices is similar to the one introduced in [30], as recalled in Theorem 1. Indeed, this definition means that a vector − → w = (w 1 , w 2 , .…”

Section: Definition 1 (Alpha-matrix Consistency)mentioning

confidence: 68%

Knowledge-based consistency index for fuzzy pairwise comparison matrices

Kubler¹,

Derigent²,

Voisin³

et al. 2017

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Abstract-Fuzzy AHP is today one of the most used Multiple Criteria Decision-Making (MCDM) techniques. The main argument to introduce fuzzy set theory within AHP lies in its ability to handle uncertainty and vagueness arising from decision makers (when performing pairwise comparisons between a set of criteria/alternatives). As humans usually reason with granular information rather than precise one, such pairwise comparisons may contain some degree of inconsistency that needs to be properly tackled to guarantee the relevance of the result/ranking. Over the last decades, several consistency indexes designed for fuzzy pairwise comparison matrices (FPCMs) were proposed, as will be discussed in this article. However, for some decision theory specialists, it appears that most of these indexes fail to be properly "axiomatically" founded, thus leading to misleading results. To overcome this, a new index, referred to as KCI (Knowledge-based Consistency Index) is introduced in this paper, and later compared with an existing index that is axiomatically well founded. The comparison results show that (i) both indexes perform similarly from a consistency measurement perspective, but (ii) KCI contributes to significantly reduce the computation time, which can save expert's time in some MCDM problems.

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Section: Definition 1 (Alpha-matrix Consistency)mentioning

confidence: 68%

Knowledge-based consistency index for fuzzy pairwise comparison matrices

Kubler¹,

Derigent²,

Voisin³

et al. 2017

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

View full text Add to dashboard Cite

show abstract

“…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%

“…Wang [31] showed that the weights and rankings obtained from upper and lower triangular judgments using Islam's method are different. Wang et al [32] defined the consistency of an IMPR based on a feasible region restricted by interval judgments. They developed an eigenvector method-based nonlinear programming model to derive interval weights from inconsistent IMPRs.…”

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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“…Similarly, the sensitivity analyses for the indices of technology maturity risk (s 22 ), different location (s 32 ) and natural environment (s 52 ) are executed, as shown in Figures 6, 7 and 8. Through sensitivity analysis of dynamic alliance, we know that same risk factors have different impacts on enterprises.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Four indices, opportunity identification risk (s 11 ), technology maturity risk (s 22 ), different location (s 32 ) and natural environment (s 52 ) have been selected as they have greater weights.…”

Section: Sensitivity Analysismentioning

confidence: 99%