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Averaging operators on the unit interval

✍ Scribed by Mai Gehrke; Carol Walker; Elbert Walker

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
221 KB
Volume
14
Category
Article
ISSN
0884-8173

No coin nor oath required. For personal study only.

✦ Synopsis

In working with negations and t-norms, it is not uncommon to call upon the arithmetic of the real numbers even though that is not part of the structure of the unit interval as a bounded lattice. To develop a self-contained system, we incorporate an averaging Ε½ . operator, which provides a continuous scaling of the unit interval that is not available from the lattice structure. The interest here is in the relations among averaging operators and t-norms, t-conorms, negations, and their generators.

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