Interval possibility measures: basic concepts and conditioning
This paper deals with the theoretical analysis of the notion of interval valued fuzzy sets (IVFS) applied to possibility measures. This permits to provide interval valued possibility measure (IVPM) and interval valued necessity measure (IVNM) as well as interval valued possibility distribution (IVPD). Particularly, two kinds of IVPM will be provided. The first one assumes a conjunctive normal form and a disjunctive normal form pertaining to a logical assertion. While, the second one considers a logical AND and a logical OR as an essence to construct the underlying interval. The properties of both representations are investigated Also, some basic mode operations involving conjunction and disjunction combinations are examined Conditioning in the setting of IVPM is introduced considering either a canonical extension of well established rules, or more interestingly by solving the underlying Cox's axiomatic equation. Finally, some further extensions using general class of t-norms operators are discussed.
fuzzy sets cybernetics