Abstract
This paper introduces a new pairwise comparison approach to ranking fuzzy numbers based on a probability comparison index for intervals and the measures of preference index sets. First, we compare level sets (intervals) by a probability method, which possesses good interpretability. Besides, three-way decision theory is introduced to give a new explanation of the ordering methodology. Second, the unit interval is divided into two disjoint subsets according to the comparison results of level sets. Then two fuzzy numbers are ordered based on a comparison of the two disjoint subsets from a perspective of Lebesgue measure. Transitivity of our proposed approach is proved, and a concept of extra degree, which is to measure the degree of precedence, is also defined. Besides, several well-used examples are displayed to demonstrate the effectiveness and reasonability of our approach. Finally, the proposed ranking approach, especially the extra degree, is used to evaluate the results of coalitions in conflict analysis.
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