Some sets of indistinguishability operators as multiresolution families. (English) Zbl 1390.68645
Summary: Multiresolution is a general mathematical concept that allows us to study a property by means of several changes of resolution. From a fixed resolution, a coarser projection can be calculated and then the changes between a finer resolution and a coarser one can be studied. That information can give a good knowledge about the problem under consideration. Also using multiresolution techniques it is possible to present information with a higher or a lower detail, given a way to get the adequate granularity or abstraction for a context.{
}The granularity of a system can be obtained or modeled by the use of indistinguishability operators. In this work the relation between indistinguishability operators and multiresolution theory is studied and several methods to build families of indistinguishability operators with multiresolution capacities are given.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
indistinguishability operator; fuzzy similarity; multiresolution system; granular computing; fuzzy set theoryReferences:
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