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...