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| {{unreferenced|date=July 2012}}
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| In mathematics, the '''Sugeno integral''', named after M. Sugeno, is a type of integral with respect to a [[fuzzy measure theory|fuzzy measure]].
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| Let <math>(X,\Omega)</math> be a [[measurable space]] and let <math>h:X\to[0,1]</math> be an <math>\Omega</math>-[[measurable function]].
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| The Sugeno integral over the [[crisp set]] <math>A \subseteq X</math> of the function <math>h</math> with respect to the fuzzy measure <math>g</math> is defined by:
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| :: <math>
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| \int_A h(x) \circ g
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| = {\sup_{E\subseteq X}} \left[\min\left(\min_{x\in E} h(x), g(A\cap E)\right)\right]
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| = {\sup_{\alpha\in [0,1]}} \left[\min\left(\alpha, g(A\cap F_\alpha)\right)\right]
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| </math>
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| where <math>F_\alpha = \left\{x | h(x) \geq \alpha \right\}</math>.
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| The '''Sugeno integral over the [[fuzzy set]] <math>\tilde{A}</math>''' of the function <math>h</math> with respect to the fuzzy measure <math>g</math> is defined by:
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| : <math>
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| \int_A h(x) \circ g
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| = \int_X \left[h_A(x) \wedge h(x)\right] \circ g
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| </math>
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| where <math>h_A(x)</math> is the membership function of the fuzzy set <math>\tilde{A}</math>.
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| [[Category:Fuzzy logic]]
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| [[Category:Measure theory]]
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Revision as of 01:59, 8 February 2014
There is nothing to write about me really.
Enjoying to be a part of wmflabs.org.
I just wish Im useful at all
Also visit my blog ... canon digital camera accessories canada - the full details,