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Evaluations of fuzzy sets based on orderings and measures.

Aldo Ventre, Siegfried Weber (1987)

Stochastica

Total orderings in the range of fuzzy sets can serve as choice criteria for fuzzy sets, a wide class of orderings based on functions is proposed (section 2). Decomposable measures are taken to measure the items on which the fuzzy sets are given (section 3). Combining the two levels of measurement by means of the integral introduced by the second author we obtain evaluations of fuzzy sets as functionals with appropriate properties, the concepts of energy and fuzziness are included (section 4).

Extension of measures: a categorical approach

Roman Frič (2005)

Mathematica Bohemica

We present a categorical approach to the extension of probabilities, i.e. normed σ -additive measures. J. Novák showed that each bounded σ -additive measure on a ring of sets 𝔸 is sequentially continuous and pointed out the topological aspects of the extension of such measures on 𝔸 over the generated σ -ring σ ( 𝔸 ) : it is of a similar nature as the extension of bounded continuous functions on a completely regular topological space X over its Čech-Stone compactification β X (or as the extension of continuous...

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