Abstract
Classification of the divergence measure for fuzzy sets (FSs) has been a successful approach since it has been utilized in several disciplines, e.g., image segmentation, pattern recognition, decision making, etc. The objective of the manuscript is to show the advantage of the combined methodology. A comparison clearly shows the usefulness of the proposed technique over the existing ones under the fuzzy environment. This study presents novel exponential-type divergence measures with some elegant features, which can be applied to FSs. Next, a TODIM (an acronym in Portuguese for Interactive Multicriteria Decision Making) approach derived from prospect theory, Shapley function, and divergence measure for multi-criteria decision-making (MCDM) is proposed. Besides, for the reason of evaluating the dominance degree of the option, and the weights of the criteria, proposed divergence measures are implemented. Evaluating and selecting the service quality is the most important issue in management; it has a direct influence on the way the manufacturer performs its tasks. Selecting the service quality can be thought of as a problem of MCDM involving numerous contradictory criteria (whether of a quantitative or qualitative nature) for the evaluation processes. In recent years, the service quality assessment is becoming increasingly complex and uncertain; as a result, some criteria assessment processes cannot be efficiently done by numerical assessments. In addition, decision experts (DEs) may not always show full rationality in different real-life situations that need decision making. Here, a real service quality evaluation problem is considered to discuss the efficacy of the developed methods. The algorithm (TODIM based on the Shapley function and divergence measures) has a unique procedure among MCDM approaches, which is demonstrated for the first time in this paper.
Highlights
Shannon entropy [1] and Kullback–Leibler (K-L) [2] divergences are two critical measures in the information theory
TODIM was found to be efficient in the solution of the multi-criteria decision-making (MCDM)-related problems, especially in the conditions in which the behaviors of decision making (DM) are taken into consideration, the approach fails to solve the MCDM procedures directly under the fuzzy sets (FSs)
We proposed new exponential-type divergence measures for FSs and demonstrated many elegant properties, which were found to be capable of enhancing the usefulness of the proposed measure
Summary
Shannon entropy [1] and Kullback–Leibler (K-L) [2] divergences are two critical measures in the information theory. The base of this technique was the prospect theory, and it was used to explain the MCDM problem in cases where the psychological behaviors of decision experts (DEs) are considered. It has encouraged lots of scholars to design extended forms of TODIM as this method efficiently solves the MCDM problems in a variety of fuzzy settings. Many scholars have taken into account the divergence measure because of its effectiveness in the evaluation of uncertain information In such conditions, this is generally applied to acquiring the criteria weights for MCDM in uncertain environments [55,56].
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