Ranking of fuzzy numbers by using value and angle in the epsilon-deviation degree method

Abstract

In this paper, a modified epsilon-deviation degree method of ranking fuzzy numbers is proposed. The epsilon-deviation degree method and other ranking methods are available in the literature and applied in the field of decision-making. Despite of the merits, some limitations and shortcomings are observed in these methods. Namely, (1) these methods cannot distinguish fuzzy numbers sharing the same support and different cores, (2) these methods cannot distinguish crisp-valued fuzzy numbers with different heights, (3) these methods also cannot make a preference between a crisp-valued fuzzy number and an arbitrary fuzzy number, (4) if the expectation values of the centroid points are the same for the fuzzy numbers to be compared, then these methods give an incorrect ranking, (5) if fuzzy numbers depict compensation of areas, then these methods fail to give a proper ranking, and (6) further inconsistency in ranking the fuzzy numbers and their images is also observed. Hence, a modified epsilon-deviation degree method is developed, based on the concept of the ill-defined magnitude ‘value’ and the angle of the fuzzy set. The proposed method bears all the properties of epsilon-deviation degree method and overcome all the limitations and shortcomings of this method and other existing methods. Various sets of fuzzy numbers are considered for comparative study between the existing ranking methods and the proposed method for validation. Further, the proposed method seems to outperform in all situations. Risk analysis problem under uncertain environment are often studied under fuzzy domain. Hence, a study is done by applying the proposed method to risk analysis in poultry farming.