On aggregation operators for ordinal qualitative information

Abstract

In many fuzzy systems applications, values to be aggregated are of a qualitative nature. In that case, if one wants to compute some type of average, the most common procedure is to perform a numerical interpretation of the values, and then apply one of the well-known (the most suitable) numerical aggregation operators. However, if one wants to stick to a purely qualitative setting, choices are reduced to either weighted versions of max-min combinations or to a few existing proposals of qualitative versions of ordered weighted average (OWA) operators. In this paper, we explore the feasibility of defining a qualitative counterpart of the weighted mean operator without having to use necessarily any numerical interpretation of the values. We propose a method to average qualitative values, belonging to a (finite) ordinal scale, weighted with natural numbers, and based on the use of finite t-norms and t-conorms defined on the scale of values. Extensions of the method for other OWA-like and Choquet integral-type aggregations are also considered.

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