A Novel Divergence and Fuzzy Divergence Measure in an Uncertain Environment for Multi-Criteria Decision-Making Problems

Zadeh's fuzzy set notion has made a significant impact in a variety of disciplines. In reality, ambiguity is all around us. To deal with ambiguity and vagueness to deduce a meaningful conclusion in decision-making, entropy is an important factor, so we present a novel measure of directed divergence on fuzzy sets (FSs) in this paper. FSs have been expanded by several researchers by combining other concepts with a fuzzy theory in which several assumptions about the accuracy of various metric measures such as score and accuracy measure, similarity measure, distance measure, possibility measure, correlation coefficient, entropy measure, and so on have established. In this paper, we have proposed a technique for determining decision-making criteria and have provided an appropriate approach by using the suggested directed divergence measure for FSs, also we have addressed the effectiveness of the suggested measure. Multi-criteria decision-making (MCDM) is a useful technique that may use in a variety of situations in real-life problems, where we can identify the optimal option from the provided criteria utilizing MCDM. For MCDM problems, several researchers have widely used fuzzy directed divergence extensively previously; we have examined various challenges of existing measures and hence, proposed a new fuzzy directed divergence measure. To validate the same, a real-life MCDM problem has been formulated in a well-defined numerical example and solved effectively using the suggested measure.