Two new methods for deriving the priority vector from interval multiplicative preference relations

Tan

2017

Omega

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Section: Methods For Group Decision Making With Ifprsmentioning

confidence: 99%

“…Step 8: With respect to B, using formula (36), we obtain the following interval priority weight vector Step 9: Using the interval formulae in [56], the following preferred matrix is obtained. Summing each line of P, we derive r 1 ¼2.834, r 2 ¼1.636, r 3 ¼1.…”

Section: Two Practical Examplesmentioning

confidence: 99%

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

Tan

2017

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“…As we analysed in (Meng et al, 2015) for interval reciprocal preference relations, it is more rational to give the priority weights of the objects, respectively. Interested readers can refer to reference (Meng et al, 2015).…”

Section: Consistent Interval Linguistic Preference Relationsmentioning

confidence: 99%

“…Interested readers can refer to reference (Meng et al, 2015). When an interval linguistic preference relation R ¼ ðr ij Þ n n is consistent, we build the following two consistency-based linear programming models to derive the lower and upper bounds of the interval linguistic Fanyong Meng et al-A method to group decision making with interval linguistic preference relations variables for the object x d , d = 1,2,…,n.…”

Section: Consistent Interval Linguistic Preference Relationsmentioning

confidence: 99%

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Journal of the Operational Research Society

2016

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Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers' preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.

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“…The methods in [32,54] are both based on the concept of interval multiplicative preference relations introduced in [73]. Recently, Meng et al [58] developed two methods to calculate the priority vector from interval multiplicative preference relations, which consider the interval priorities of alternatives separately. First, let us review several basic concepts.…”

Section: Incomplete Interval Multiplicative Preference Relationsmentioning

confidence: 99%

An approach to incomplete multiplicative preference relations and its application in group decision making

2015

Information Sciences

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