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Rough membership functions: a tool for reasoning with uncertainty

100%

Pawlak Z., Skowron A.

Banach Center Publications

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1993

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tom 28

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nr 1

135-150

EN

A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.

2

On a class of diffeomorphisms defined by integro-differential operators

81%

Idczak D., Skowron A., Walczak S.

Banach Center Publications

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2014

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tom 101

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nr 1

77-86

EN

We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.

3

Theory of computing systems

50%

Bartol W., Raś Z., Skowron A.

Banach Center Publications

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1977

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tom 2

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nr 1

101-165

Ograniczanie wyników

3 Banach Center Publications

3 Skowron A.

1 Bartol W.

1 Idczak D.

1 Pawlak Z.

1 Raś Z.

1 Walczak S.

1 2014

1 1993

1 1977

Rough membership functions: a tool for reasoning with uncertainty

On a class of diffeomorphisms defined by integro-differential operators

Theory of computing systems