Download Information Fusion in Data Mining by Vicenç Torra (auth.), Prof. Vicenç Torra (eds.) PDF

By Vicenç Torra (auth.), Prof. Vicenç Torra (eds.)

Information fusion is changing into an immense want in information mining and information discovery in databases. This publication provides a few contemporary fusion options which are at the moment in use in info mining, in addition to facts mining purposes that use info fusion. distinct concentration of the booklet is on details fusion in preprocessing, version development and data extraction with quite a few purposes.

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Definition 4 [3,14] Let p be a fuzzy measure on (X,2X). The Choquet integral of x E [0, l]n with respect to p is defined by Cp,(x) := where px(r) = p({Xi ~ 1 00 px(r)dr, r}). Using the i-th order statistics, the Choquet integral is written as n Cp,(x) = ~)x(i) - x(i-l))p({(i) ... (n)}), i=l where we define Theorem 5 [5] expression hold: x(O) := O. Let p be a fuzzy measure on (X,2X), then the following 1. (positive homogeneity) for x E X and a positive real number a E [0, 1]. 30 Yasuo Narukawa and Toshiaki Murofushi 2.

B( i) 1£ for each i, using any parametric average operator FAYE. We then aggregate over i using the standard OWA operator. Mathematically the process defines a second type of PWOWA operator: Probabilistic WOWA Operator 49 M FpWOWA = I : WiQ(i) , (31) i=1 where (32) There are many different possible choices for FAVE. Two simple choices are the arithmetic mean and the median operator. Using these operators in (29) and (31) we obtain four PWOWA operators L • • M F~U,OWA = ± I : (I: Wib(i)ll) 1=1 i=l F~UrOWA (33) , M = M median (I: Wi b (i)11, i=l M M I : Wi b (i)12, ...

We show that, from a purely mathematical view, the essential integral operation are only Choquet integral and Sugeno type integral. lv whenever x ::; u and y ::; v. lz). A t-conorm is said to be strict if and only if it is continuous on [0, 1] and strictly increasing in each of its places. lx > x for all x E (0,1). Example 2 1. The maximum operator x V y is a non Archimedean t-conorm. 2. The bounded sum x+y := 1/\ (x + y) is an Archimedean t-conorm. 3. Sugeno operator x +>. Y 1/\ (x + y + AXY) (-1 < A < 00) is an Archimedean t-conorm.

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