Multicriteria correlation preference information (MCCPI) with nonadditivity index for decision aiding

Abstract

MCCPI (Multiple Criteria Correlation Preference Information) is a kind of 2 dimensional decision preference information obtained by pairwise comparison on the importance and interaction of decision criteria. In this paper, we introduce the nonadditivity index to replace the Shapley simultaneous interaction index and construct an undated MCCPI based decision scheme. We firstly propose a diagram to help decision maker obtain the nonadditivity index type MCCPI, then establish transform equations to normalize them into desired capacity and finally adopt a random generation MCCPI based comprehensive decision aid algorithm to explore the dominance relationships and creditable ranking orders of all decision alternatives. An illustrative example is also given to demonstrate the feasibility and effectiveness of the proposed decision scheme. It’s shown that based on some good properties of nonadditivity index in practice, the updated MCCPI model can deal with the internal interaction among decision criteria with relatively less model construction and calculation effort.

Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure

“…This is why authors have continued to research the additive representations of fuzzy measures. These can be nonadditivity indexes [9][10][11][12] or the degrees of defectiveness of nonadditivity [2], importance values, interaction indexes [7,[13][14][15][16], and other parameters. We especially highlight the probabilistic representations of a fuzzy measure [8,[17][18][19] as the main object of our research.…”

“…In [12], this index is used to indicate the range of advantages with respect to the alternatives of a decision-maker. In [9], the nonadditivity index for replacement of the Shapley concurrent interaction index and construction of an undated MAGDM-based decision scheme was introduced. In the work, a scheme was developed to calculate the nonadditivity index.…”

“…It should be noted that the use of the CBR for practical purposes was presented to a higher degree than the MSR. This is related to the more "flexible" structure of the CBR and the ability to easily embed its APC in problems such as fuzzy measure identification [13][14][15][16] and MAGDM modeling of the Shapley values and interaction indices of interacting attributes of the environment [9,22,[26][27][28]. The main motivation for this study was to establish links between these two probabilistic representations and to obtain evidence for representations of the Choquet integral in the MSR environment as the Choquet integral is the main aggregation tool in MAGDM modeling, which considers the interactions between attributes.…”