Displaying similar documents to “Extension on the fuzzy integral based on -decomposable measure.”

Multiplication, distributivity and fuzzy-integral. II

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

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Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms...

Multiplication, distributivity and fuzzy-integral. III

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.

Multiplication, distributivity and fuzzy-integral. I

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

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The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.

Fuzzy-valued integrals based on a constructive methodology

Hsien-Chung Wu (2007)

Applications of Mathematics

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The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued...

Radon-Nikodym derivatives and conditioning in fuzzy measure theory.

Domenico Candeloro, Sabrina Pucci (1987)

Stochastica

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In the last twenty years many papers have appeared dealing with fuzzy theory. In particular, fuzzy integration theory had its origin in the well-known Thesis of Sugeno [7]. More recently, some authors faced this topic by means of some binary operations (see for instance [3], [8] and references): a fuzzy measure must be additive with respect to one of them, an the integral is to define in a way, which is very similar to the construction of the Lebesgue integral. On the contrary, we are...

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...