A novel decision making approach based on weighted hesitant fuzzy rough set and its application in medical diagnosis problem

Abstract

Decision-making problems in complex real-world systems consist of uncertain, imprecise, insufficient, and incomplete information in their data sets. Fuzzy set, hesitant fuzzy set (HFS), rough set, and their hybrid generalizations, hesitant fuzzy rough set (HFRS) are among several specific tools in hand of decision makers to cope with nonprobabilistic uncertainty and imprecision of such systems to shape system's trajectory, goal achievements, performance, outcomes, and sustainable growth. Probabilistic hesitant fuzzy sets (PHFS) and weighted hesitant fuzzy set (WHFS) are extensions of hesitant fuzzy set (HFS), offering more flexibility in expressing uncertainty, but are distinct in concepts, representations, and have diversified applications backgrounds. PHFS deals with random uncertainty and reflects the likelihood of different evaluations by assigning probabilities to different membership values of each hesitant fuzzy element (HFE), while WHFS deals with subjective uncertainty, where weights show that the decision maker has distinct confidence, rather than randomness, in providing the possible values of the membership degree of each HFE. But HFS, PHFS, and WHFS based decision approaches fail to incorporate incomplete information in data sets of a complex system. However, the well-known HFRS and probabilistic HFRS (PHFRS) based decision-making models incorporate both uncertainties and incomplete information in data sets of such complex systems, but fail to consider weights or varying importance of different membership values of HFE. The fusion of concepts of WHFS and HFRS leads to a new hybrid concept, proposed here as the weighted hesitant fuzzy rough set (WHFRS) that incorporates uncertainty (through weights of HFE) and insufficient information inherent in the data set of a complex real-world system, while neither of the individual concepts, WHFS and HFRS handles both simultaneously. Finally, we have shown the application of WHFRS in medical diagnosis problems.