A Novel Defuzzification Approach of Ranking Parametric Fuzzy Numbers Based on the Value and Ambiguity Calculated at Decision Levels

Abstract

Generally, in every decision-making process under the fuzzy domain, ranking of fuzzy numbers is indispensable. Although such approaches are abundant, yet a universally accepted approach is not apparent. Hence, newer methodologies have been developed since its inception. In many instances, defuzzification techniques are being criticized as these methodologies are based on intuition and the geometry of the fuzzy numbers. Furthermore, in many instances the reasonable properties that a ranking method should follow are not being verified. However, in the current study, a novel defuzzification technique is being developed with the notion of value and multiple of a ambiguity inclusion-exclusion function, [Formula: see text], with ambiguity at various decision levels. The current method perfectly obeys the intuition and the geometry of the fuzzy numbers. Adding to this, it should be emphasized that the current methodology follows all the reasonable properties of a ranking method. Furthermore, new properties are stated and proved which illustrate the novelty of the present method. Furthermore, the shortcomings and drawbacks of the existing methods are overcome by the current methodology. Noteworthy, the current method ranks the fuzzy numbers and their corresponding images consistently, which was not evident in most of the existing methods.