Fuzzy numbers are the only fuzzy sets that keep invertible operations invertible
✍ Scribed by Bernadette Bouchon-Meunier; Olga Kosheleva; Vladik Kreinovich; Hung T. Nguyen
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 659 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0165-0114
No coin nor oath required. For personal study only.
✦ Synopsis
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 -t-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 ofatl fuzzy numbers.