Some programming models to derive priority weights from additive interval fuzzy preference relation

Wang, Jun; Lan, Jibin; Ren, Peiyu; Luo, Yuyan

doi:10.1016/j.knosys.2011.12.001

Cited by 40 publications

(45 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, Li et al [38] pointed out that the definition in [37] was technically deficient and yielded contradictory results for the same judgment matrix after the alternatives are re-labeled. Wang et al [55] put forward a new method with a parameter to obtain priority weights from an FPR, and defined a new definition for additive consistency in an IFPR. Based on the new definition, linear programming models for deriving interval priority weights from both a consistent and an inconsistent IFPR were proposed.…”

Section: Saaty and Vargasmentioning

confidence: 99%

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

Yin

Cheng

et al. 2017

Symmetry

View full text Add to dashboard Cite

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.

show abstract

Section: Saaty and Vargasmentioning

confidence: 99%

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

Yin

Cheng

et al. 2017

Symmetry

View full text Add to dashboard Cite

show abstract

“…According to additive or multiplicative transitivity, different prioritization methods have been developed for obtaining an interval-valued priority vector from a complete interval reciprocal comparison matrices such as linear programs (Arbel, 1989;Gou & Wang, 2012;Hu, Ren, Lan, Wang, & Zheng, 2014;Kress, 1991;Wang, Lan, Ren, & Luo, 2012;Xu & Chen, 2008), nonlinear programs (Xia & Xu, 2014), and goal programs (Wang & Elhag, 2007;Wang & Li, 2012;Wang, Yang, & Xu, 2005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 5 and the group IARCM. Finally, by putting the foresaid models together, an algorithm is proposed for solving GDM problems with incomplete IARCMs.…”

Section: Introductionmentioning

confidence: 99%

A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

Wang

2015

European Journal of Operational Research

View full text Add to dashboard Cite

“…Dubois and Prade (2012) pointed out that interval fuzzy values can clearly capture the idea of uncertain and imprecise ratings. Recently, IFPRs have been receiving increasing research interest and application in preference modelling and MCDM analysis (Genç et al 2010;Liu and Zhang 2014;Wang et al 2012;Wang and Chen 2014;Wang and Li 2012a;Xia and Xu 2014;Xu et al 2014a, b;Xu 2011). An important research issue is to elicit priority weights from IFPRs.…”

Section: Introductionmentioning

confidence: 99%

“…As such, new additive consistency definitions and priority methods have been put forward for IFPRs. Wang et al (2012) introduced a logarithmic feasible region model to define additively consistent IFPRs. Hu et al (2014) pointed out the drawback of Xu and Chen (2008)'s method and proposed the improved linear programs by setting α = (n−1)/2.…”

Section: Introductionmentioning

confidence: 99%

A two-stage linear goal programming approach to eliciting interval weights from additive interval fuzzy preference relations

Wang

2015

Soft Comput

View full text Add to dashboard Cite

This article presents a linear goal programming framework to obtain normalized interval weights from interval fuzzy preference relations (IFPRs). A parameterized transformation equation is put forward to convert a normalized interval weight vector into IFPRs with additive consistency. Based on a linearization approximate relation of the transformation equation, a two-stage linear goal programming approach is developed to elicit interval weights and determine an appropriate parameter value from an additive IFPR. The first stage devises a linear goal programming model to generate optimal interval weight vectors by minimizing the absolute deviation between sides of the parameterized linearization approximate relation. The second stage aims to find a benchmark among the optimal solutions derived from the previous stage by minimizing the absolute deviation between the parameter and 1. The obtained benchmark is the closest to the original IFPR and can sufficiently reflect uncertainty of original judgments. A procedure is further proposed for solving group decision making problems with IFPRs. Two numerical examples including a comparative study with existing approaches are provided to illustrate validity and practicality of the proposed model.

show abstract

Some programming models to derive priority weights from additive interval fuzzy preference relation

Cited by 40 publications

References 31 publications

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

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

A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

A two-stage linear goal programming approach to eliciting interval weights from additive interval fuzzy preference relations

Contact Info

Product

Resources

About