Displaying similar documents to “Twofold integral and multi-step Choquet integral”

Numerical experimentation and comparison of fuzzy integrals.

Manuel Jorge Bolaños, Luis Daniel Hernández, Antonio Salmerón (1996)

Mathware and Soft Computing

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Sugeno and Choquet integrals have been widely studied in the literature from a theoretical viewpoint. However, the behavior of these functionals is known in a general way, but not in practical applications and in particular cases. This paper presents the results of a numerical comparison that attempts to be a basis for a better comprehension and usefulness of both integrals.

Mathematical aspects of the theory of measures of fuzziness.

Doretta Vivona (1996)

Mathware and Soft Computing

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After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.

General theory of the fuzzy integral.

Pietro Benvenuti, Doretta Vivona (1996)

Mathware and Soft Computing

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By means of two general operations + and x, called pan-operations'', we build a new kind of integral. This formulation contains, as particular cases, both Choquet's and Sugeno's integrals.

Evaluations of fuzzy sets based on orderings and measures.

Aldo Ventre, Siegfried Weber (1987)

Stochastica

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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...

Classes of fuzzy measures and distortion

Ľubica Valášková, Peter Struk (2005)

Kybernetika

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Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.

A collector for information without probability in a fuzzy setting

Doretta Vivona, Maria Divari (2005)

Kybernetika

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In the fuzzy setting, we define a collector of fuzzy information without probability, which allows us to consider the reliability of the observers. This problem is transformed in a system of functional equations. We give the general solution of that system for collectors which are compatible with composition law of the kind “inf”.