A Prototype Theory Interpretation of Label Semantics

Using words rather than numbers to convey vague information as part of uncertain reasoning is a sophisticated human activity. The theory of fuzzy sets is now a popular tool for computing with words^[12] which attempts to formally capture this human reasoning process^[3–4] Furthermore, linguistic modeling based on fuzzy IF-THEN rules ^[6–8] has achieved promising results in many application areas. However, the currently proposed interpretations of the membership function in fuzzy set theory are not consistent with the truth-functional calculus of fuzzy logic^[9]. Alternatively, from the philosophical viewpoint of the epistemic stance, Lawry proposed a functional (but non-truth functional) calculus, label semantics, for computing with words^[10,11]. In this framework, the meaning of linguistic labels is encoded by mass functions which represent the subjective probabilities that a given set of labels is appropriate to describe a given instance. Label semantics is a powerful new tool for modelling with vague concepts, the possible applications of which include knowledge fusion^[12], decision tree learning^[13], linguistic rule induction^[14], and collective decision making^[15,16].