Ranking interval type-2 fuzzy number based on a novel value-ambiguity ranking index and its application in risk analysis

Abstract

Consequence of decision making problems under fuzzy domain mostly necessitate choosing the best alternative among the sets of alternatives. This requirement is generally fulfilled through the methodology called the ranking of fuzzy numbers. In this paper, an attempt under fuzzy domain to develop a coherent methodology of ordering fuzzy numbers is thrived. The ill-defined quantity ‘value’ and the amount of uncertainty in the ill-defined quantity ‘ambiguity’ of a fuzzy number constituted the important tools in ranking fuzzy numbers. As such, an effort has been made to employ these quantities in ranking interval type-2 fuzzy numbers constructing a novel value-ambiguity ranking index. A through comparative study with the existing method and the present method is executed to exhibit the essence of the proposed ranking method. The comparative study exhibit the superiority of the present method of ranking interval type-2 fuzzy numbers over the existing method. Further, the method is not just limited to interval type-2 fuzzy numbers, it can be broadly applied to arbitrary fuzzy numbers. Finally, a risk analysis problem has been discussed and the proposed novel value-ambiguity ranking index of ranking interval type-2 fuzzy numbers has been applied successfully.