On linguistic approximation of subnormal fuzzy sets

Fuzzy systems including fuzzy decision support and fuzzy control systems often provide outputs in the form of subnormal fuzzy sets or fuzzy sets consisting of a number of sub/normal segments. Linguistic interpretation of such outputs by means of linguistic approximation using sets of predefined primary terms, linguistic modifiers and connectives may sometimes produce ambiguous results. It is mainly due to normalization of the approximated subnormal fuzzy sets (or segments) and/or combination of primary terms predefined as normal fuzzy subsets commonly used in the existing linguistic approximation methods. Some aspects of linguistic approximation of such fuzzy sets are discussed and an approach taking into account their subnormality in linguistic approximation is proposed