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Abstract
The purpose of this paper is to enrich the decision preference information inconsistency check and adjustment method in the context of capacity-based multiple criteria decision making. We first show that almost all the preference information of a decision maker can be represented as a collection of linear constraints. By introducing the positive and negative deviations, we construct the the multiple goal linear programming (MGLP)-based inconsistency recognition model to find out the redundant and contradicting constraints. Then, based on the redundancy and contradiction degrees, we propose three types of adjustment strategies and accordingly adopt some explicit and implicit indices w.r.t. the capacity to test the implementation effect of the adjustment strategy. The empirical analyses verify that all the strategies are competent in the adjustment task, and the second strategy usually costs relatively less effort. It is shown that the MGLP-based inconsistency recognition and adjustment method needs less background knowledge and is applicable for dealing with some complicated decision preference information.
Highlights
In the context of multiple criteria decision making, the probability measure or the weight vector mainly reflects the importance relationship of decision criteria and assumes all the criteria are absolutely independent of each other
Replacing the additivity of the probability measure by the monotonicity w.r.t. set inclusion, capacity [1], or the fuzzy measure [2], we obtain the powerful ability to construct a variety of nonadditivity situations to represent the complex interaction phenomena among decision criteria [3,4,5,6]
The p-symmetric capacity means that the decision criteria consist of p classes of indifferent criteria [7,8]; the k-additive capacity takes into account the interaction among at most k criteria and has a simple structure [3,9]; the k-tolerant and k-intolerant capacity respectively express that any k criterion is enough to favor or vote for an alternative [10]; the k-maxitive and -minitive capacities respectively focus on the lower and upper k-order subsets’ capacity values concerning only the micro and macro view of decision criteria [5,11,12,13]
Summary
In the context of multiple criteria decision making, the probability measure or the weight vector mainly reflects the importance relationship of decision criteria and assumes all the criteria are absolutely independent of each other. The third category of approaches is to adopt the fuzzy integral [18], most commonly the Choquet integral [1], to show directly the decision maker’s preference for some typical alternatives, which can be carried out by the desired overall evaluations or the partial order on alternatives [19,20,21] These three approaches provide a systematic scheme to show comprehensively the decision preference information, and most of them can be established in terms of linear constraints. We will focus on the second branch and enhance the MGLP model with programmable steps and detailed adjustment strategies The advantage of this enhanced method is that it (a) does not need much prior knowledge of the decision preference, but (b) can figure out the inconsistency degrees of all constraints simultaneously even when they are established in quite different kinds of indices or representations, and (c) can flexibly customize the adjustment measures according to the contradictory and redundancy degrees of the inconsistent constraints.
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