Geodesic
Multiplication, distributivity and fuzzy-integral. II
Kybernetika, Tome 41 (2005) no. 4, pp. 469-496

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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 
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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     title = {Multiplication, distributivity and fuzzy-integral. {II}},
     journal = {Kybernetika},
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     number = {4},
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     zbl = {1249.28029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2005_41_4_a3/}
}
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