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Article Dans Une Revue Fuzzy Sets and Systems Année : 1997

Fuzzy Numbers are the Only Fuzzy Sets that Keep Invertible Operations Invertible

Résumé

In standard arithmetic, if we, e.g., accidentally add a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x + y. In this paper, we prove the following two results:
  • First, a similar possibility to invert (undo) addition holds for fuzzy numbers (although in case of fuzzy numbers, we cannot simply undo addition by subtracting y from the sum).
  • Second, if we add a single fuzzy set that is not a fuzzy number, we lose invertibility.
Thus, invertibility requirement leads to a new characterization of the class of all fuzzy numbers.

Dates et versions

hal-01184898 , version 1 (18-08-2015)

Identifiants

Citer

Bernadette Bouchon-Meunier, Olga Kosheleva, Vladik Kreinovich. Fuzzy Numbers are the Only Fuzzy Sets that Keep Invertible Operations Invertible. Fuzzy Sets and Systems, 1997, 91 (2), pp.155-163. ⟨10.1016/S0165-0114(97)00137-1⟩. ⟨hal-01184898⟩
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