A theoretical approach to ranking of parametric fuzzy numbers using value and left-right ambiguity

In this paper, a new method of ranking fuzzy numbers has been proposed. The method is being developed using the ill-defined quantity value as well as the quantities, left ambiguity and right ambiguity of a fuzzy number. It is seen that there are several methods on ranking fuzzy numbers, but in most of the studies, the ranking methods fail to rank some of the fuzzy numbers. Hence, in this paper, a new ranking method has been introduced to overcome these limitations. The ranking index is formulated by using ill-defined quantity value and by the convex combination of left ambiguity and right ambiguity of a fuzzy number with index of optimism. A quantity theta is also introduced, which decides the inclusion and exclusion of the ambiguity in the ranking index. Further, the rationality validation of the proposed ranking method is also checked, by proving the Wang and Kerre's reasonable properties. Furthermore, a comparative study is being performed to show the outperformance of the proposed method.