Prospect-regret theory based decision-making approach for incomplete probabilistic hesitant fuzzy environment: An application to medical field

Abstract

In the era of uncertainty and indeterminacy, probabilistic hesitant fuzzy sets (PHFS) an extension of hesitant fuzzy sets (HPS) have received much attention due to their ability to increase the reliability of information by considering the occurrence probabilities of each opinion. Considering the studies of PHFS following points can be identified, (i) preferences are aggregated without considering the inter-relationship among arguments, (ii) occurrence probabilities are not always prior known, (iii) approaches for attribute weights do not consider interactions among attributes (iv) decision-makers are not completely rational. Thus, we present a decision-making approach in which incomplete probabilities are estimated using the Shannon entropy optimization model. A projection entropy-based Shapley value method is used to attain attribute weights. Heronian operator (HM) is extended under the PHFS environment to capture the inter-relationship among arguments. Considering the psychological behavior of decision-makers, final ranking is provided combining the merits of prospect and regret theory. Finally, the proposed framework is applied to a real case study from the medical field. Comparative analysis verifies the effectiveness, and the sensitivity analysis determines the stability of the proposed approach.