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Kybernetika 41(4):469-496, 2005.

Multiplication, Distributivity and Fuzzy-Integral II

Wolfgang Sander and Jens Siedekum


Abstract:

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.


Keywords: fuzzy measures; distributivity law; restricted domain; pseudo-addition; pseudo-multiplication; Choquet integral; Sugeno integral;


AMS: 28A25; 20M30;


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BIB TeX

@article{kyb:2005:4:469-496,

author = {Sander, Wolfgang and Siedekum, Jens },

title = {Multiplication, Distributivity and Fuzzy-Integral II},

journal = {Kybernetika},

volume = {41},

year = {2005},

number = {4},

pages = {469-496}

publisher = {{\'U}TIA, AV {\v C}R, Prague },

}


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