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A reflection on what is a membership function.

Enric Trillas, Claudi Alsina (1999)

Mathware and Soft Computing

This paper is just a first approach to the idea that the membership function μP of a fuzzy set labelled P is, basically, a measure on the set of linguistic expressions x is P for each x in the corresponding universe of discourse X. Estimating that the meaning of P (relatively to X) is nothing else than the use of P on X, these measures seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the...

A remark on a theorem of Solecki

Petr Holický, Luděk Zajíček, Miroslav Zelený (2005)

Commentationes Mathematicae Universitatis Carolinae

S. Solecki proved that if ℱ is a system of closed subsets of a complete separable metric space X , then each Suslin set S ⊂ X which cannot be covered by countably many members of ℱ contains a G δ set which cannot be covered by countably many members of ℱ . We show that the assumption of separability of X cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the σ -ideal generated by ℱ is locally determined. Using Solecki’s arguments, our result can be used...

A remark on weak McShane integral

Kazushi Yoshitomi (2019)

Czechoslovak Mathematical Journal

We characterize the weak McShane integrability of a vector-valued function on a finite Radon measure space by means of only finite McShane partitions. We also obtain a similar characterization for the Fremlin generalized McShane integral.

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