Gradual Numbers and Their Application to Fuzzy Interval Analysis

Abstract-- We introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual numbers basically have the same algebraic properties as real numbers, but they are functions. A fuzzy interval is then viewed as a pair of fuzzy thresholds, which are monotonic gradual real numbers. This view enable interval analysis to be directly extended to fuzzy intervals, without resorting to

• Type: Journal
• Year: 2008
• Where: TFS
• Authors: Jérôme Fortin, Didier Dubois, Hélène Fargier
• Keywords: Fuzzy Interval, Interval Analysis, Real Numbers, TFS 2008