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Boolean fuzzy sets and possibility measures. (English) Zbl 1096.94538
B-possibility and B-necessity measures are defined as the qualitative analogues of the well known \([0, 1]\)-measures. Their connection to B-fuzzy sets (Boolean fuzzy sets) is established. It is also proved that B-fuzzy sets define B-possibility and B-necessity measures by their membership function. We also introduce the possibility of a B-fuzzy set and prove that it is the extension of the possibility measure defined on crisp sets. This extension can be defined in two ways which are proved to be equivalent.
MSC:
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03E72 Theory of fuzzy sets, etc.
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