Geodesic
Multiplication, distributivity and fuzzy-integral. II
Kybernetika, Tome 41 (2005) no. 4, pp. 469-496 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 (which are not necessarily Archimedean) and prove their essential properties.
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 (which are not necessarily Archimedean) and prove their essential properties.
Classification : 20M30, 28A12, 28A25, 28E10
Keywords: fuzzy measures; distributivity law; restricted domain; pseudo- addition; pseudo-multiplication; Choquet integral; Sugeno integral 
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Sander, Wolfgang; Siedekum, Jens. Multiplication, distributivity and fuzzy-integral. II. Kybernetika, Tome 41 (2005) no. 4, pp. 469-496. http://geodesic.mathdoc.fr/item/KYB_2005_41_4_a3/

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