Areas covering algorithms that commonly require measurements of similarity within data include classification, ranking, decision-making and pattern-matching. A similarity measure can effectively substitute for a distance measure (e.g. Euclidean distance), making data types with defined similarity measures compatible with methods such as K-Nearest Neighbour [1, 2] and TOPSIS [3, 4, 5]. This study proposes a similarity measure for aggregate fuzzy numbers constructed from interval-valued data using the Interval Agreement Approach (IAA), that is when given two such fuzzy numbers the degree of similarity regarding them is computed. The experimental interval-valued data in recent literature is often an alternative representation of expert opinion.

This paper primarily presents two methods of ranking aggregated fuzzy numbers from intervals using the Interval Agreement Approach (IAA). The two proposed ranking methods within this study contain the combination and application of previously proposed similarity measures, along with attributes novel to that of aggregated fuzzy numbers from interval-valued data. The shortcomings of previous measures, along with the improvements of the proposed methods, are illustrated using both a synthetic and real-world application. The real-world application regards the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm, modified to include both the previous and newly proposed methods.