Towards fuzzy differential calculus part 1: Integration of fuzzy mappings |
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Authors: | Didier Dubois Henri Prade |
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Institution: | Département d''Automatique, C.E.R.T., 31055 Toulouse, France;Langages et Systèmes Informatiques, Université Paul Sabatier, 31062 Toulouse, France |
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Abstract: | This paper deals with fuzzy-set-valued mappings of the real line, and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line. These mappings can also be viewed as fuzzy relations. Using Zadeh's extension principle, the integral of such fuzzy mappings over a crisp interval is defined. Provided a special analytical representation of the fuzzy mapping, the practical computation of such an integral is shown to be easy. Practically speaking, it yields the fuzzy surface of a fuzzily-bounded area. |
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Keywords: | Riemann integration Fuzzy mapping Fuzzy value |
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