Non-specificity and interval-valued fuzzy sets

Non-specificity is a characteristic of interval-valued fuzzy sets. Vagueness is represented by fuzzy sets which capture the meaning representation of linguistic terms or linguistic variables. This is Type I semantic uncertainty. Combinations of two or more vague linguistic terms with vague linguistic operators generate semantic uncertainty when disjunctive and conjunctive combinations of concepts are formed. In particular, disjunctive and conjunctive normal form expressions of combined concepts generate an interval of uncertainty. This is Type II semantic uncertainty. The size, i.e., the cardinality, of this interval provides a foundation for the fuzzy measure-theoretical investigation of the combination of vagueness associated with two or more linguistic concepts and the operators that combine them. In particular, the length of the interval provides the ''non-specificity'' measure for interval-valued fuzzy sets. Thus, non-specificity generated by interval-valued fuzzy sets forms an essential linkage for the development of evidence theory with fuzzy sets.