Kermack–McKendrick theory: Difference between revisions

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{{unreferenced|date=July 2012}}
Nicole is the title my parents gave me although it's not the most feminine of names. Distributing manufacturing is what I do. The thing I adore most fishing and now I'm trying to make cash with it. North Dakota is exactly where he and his wife reside. She's been working on her web site for some time now. Check it out here: http://www.[http://www.youtube.com/watch?v=jOGgdu4f-H8 youtube.com]/watch?v=jOGgdu4f-H8
 
In mathematics, the '''Sugeno integral''', named after M. Sugeno, is a type of integral with respect to a [[fuzzy measure theory|fuzzy measure]].
 
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]].
 
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:
:: <math>
\int_A h(x) \circ g
= {\sup_{E\subseteq X}} \left[\min\left(\min_{x\in E} h(x), g(A\cap E)\right)\right]
= {\sup_{\alpha\in [0,1]}} \left[\min\left(\alpha, g(A\cap F_\alpha)\right)\right]
</math>
where <math>F_\alpha = \left\{x | h(x) \geq \alpha \right\}</math>.
 
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:
 
: <math>
\int_A h(x) \circ g
= \int_X \left[h_A(x) \wedge h(x)\right] \circ g
</math>
 
where <math>h_A(x)</math> is the membership function of the fuzzy set <math>\tilde{A}</math>.
 
[[Category:Fuzzy logic]]
[[Category:Measure theory]]

Latest revision as of 01:46, 6 January 2015

Nicole is the title my parents gave me although it's not the most feminine of names. Distributing manufacturing is what I do. The thing I adore most fishing and now I'm trying to make cash with it. North Dakota is exactly where he and his wife reside. She's been working on her web site for some time now. Check it out here: http://www.youtube.com/watch?v=jOGgdu4f-H8

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