Považan, Jaroslav, Riečan, Beloslav
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Independently with [7] a corresponding fuzzy approach has been developed in [3-5] with applications in measure theory. One of the results the Egoroff theorem has been proved in an abstract form. In [1] a necessary and sufficient condition for holding the Egoroff theorem was presented in the case of a space with a monotone measure. By the help of [2] and [6] we prove a variant of the Egoroff theorem stated in [4].
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.
Wolfgang Sander, Jens Siedekum (2005)
Kybernetika
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Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.
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.
V. B. Kuz'min, S. I. Travkin (1998)
Mathware and Soft Computing
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The Shaffer's definition of the upper and lower expectations of fuzzy variables is considered with respect to randomized fuzzy sets. The notion of randomized fuzzy sets is introduced in order to evaluate fuzzy statistical indices for an arbitrary chosen fuzzy variable. Provided the distribution of the mathematical expectation of a randomized fuzzy variable is known, it is possible to adopt the traditional methods of testing statistical hypotheses for fuzzy variables. We show...
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.
Doretta Vivona, Maria Divari (2002)
Kybernetika
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In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.