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Open AccessArticle

An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

1
Labuan Faculty of International Finance, Universiti Malaysia Sabah, Labuan 87000, Malaysia
2
School of Quantitative Sciences, Universiti Utara Malaysia, Kedah 06000, Malaysia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1708; https://doi.org/10.3390/sym12101708
Received: 10 September 2020 / Revised: 13 October 2020 / Accepted: 14 October 2020 / Published: 16 October 2020
(This article belongs to the Section Computer and Engineer Science and Symmetry)
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. View Full-Text
Keywords: Choquet integral; distance correlation; fuzzy measure; hospital website evaluation; multi-attribute decision making; Shannon entropy Choquet integral; distance correlation; fuzzy measure; hospital website evaluation; multi-attribute decision making; Shannon entropy
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Krishnan, A.R.; Mat Kasim, M.; Hamid, R. An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure. Symmetry 2020, 12, 1708.

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