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Kybernetika 41(3):397-422, 2005.

Multiplication, Distributivity and Fuzzy-integral I

Wolfgang Sander and Jens Siedekum


Abstract:

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.


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:2005:3:397-422,

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

title = {Multiplication, Distributivity and Fuzzy-integral I},

journal = {Kybernetika},

volume = {41},

year = {2005},

number = {3},

pages = {397-422}

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

}


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