Convex combinations in terms of triangular norms: A characterization of idempotent, bisymmetrical and self-dual compensatory operators
✍ Scribed by Bernhard Moser; Elena Tsiporkova; Erich Peter Klement
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 827 KB
- Volume
- 104
- Category
- Article
- ISSN
- 0165-0114
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✦ Synopsis
It is observed that most of the well-known compensatory operators are defined in terms of convex transformations of the values of triangular norms and conorms or other operators. In this paper, the characterization and the applicability of paramelrized operators constructed again in terms of triangular norms and conorms, but as transformations of their arguments, are studied. It turns out that these operators are closely related to the ordinary convex combination. Moreover, when idempotency is required, these operators can be characterized algebraically as bisymmetrical and self-dual operators that satisfy the cancellation law.