Abstract
λ0-measure is a special type of fuzzy measure. In the context of multi-attribute decision making (MADM), the measure can be used together with Choquet integral to model the interdependencies that usually present between the decision attributes. Unfortunately, the range of techniques available to estimate λ0-measure values is too limited i.e., only four techniques are available to this date. Besides, the review on literature shows that each of these existing techniques either requires some initial data from the decision-makers or misrepresents the actual interdependencies held by the attributes. Thus, an alternate unsupervised technique is needed for the estimation of λ0-measure values. This study has developed such a technique by integrating the idea of distance correlation and Shannon entropy. In this technique, the two inputs required to estimate λ0-measure values, namely, the interdependence degrees and fuzzy densities are determined by utilizing the distance correlation measures and entropy weights, respectively. An evaluation to rank the websites owned by five different hospitals located in Sabah, Malaysia, was conducted to illustrate the usage of the technique. A similar evaluation was also performed with a few selected MADM techniques for comparison purposes, where the proposed technique is found to have produced the most consistent ranking. From the literature perspective, this study has contributed an alternate unsupervised technique that can estimate λ0-measure values without necessitating any additional data from the decision-makers, and at the same time can better capture the interdependencies held by the attributes.
Highlights
The evaluation on a finite set of alternatives based on a predetermined set of attributes is known as a multi-attribute decision making (MADM) problem [1]
The use of Choquet integral in MADM problems is sometimes hampered by its complex fuzzy measure estimation procedure despite being known as an advantageous aggregation operator [23]
As for the proposed technique and Pearson correlation-based unsupervised (PCBU), worse complications may even occur as these techniques determined the interdependence degree that was based on the distance correlation and Pearson correlation measures respectively
Summary
The evaluation on a finite set of alternatives based on a predetermined set of attributes is known as a multi-attribute decision making (MADM) problem [1]. The available aggregation operators can be divided into two main categories, which are linear and non-linear operators [4] The linear operators such as simple weighted mean and ordered weighted average aggregate the scores with the assumption that there are no significant interdependencies between the evaluation attributes [5]. In other words, using linear operators in a problem involving interactive attributes may lead to incorrect aggregated scores and ranking of alternatives, which usually results in misleading decisions. In advance to computing the aggregated score of each teacher using the Choquet integral, the decision-maker will first need to estimate the values of the following subsets, g: {∅}, {c1 }, {c2 }, {c3 },. For any decision analysis involving n number of evaluation attributes, one will need to estimate the 2n values of fuzzy measure [14]. Further details on the motivation of this study are provided in the following subsection
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