Simplification Assumptions For Fuzzy Measures
Since fuzzy measures are defined on the power set (or, more formally, on the sigma algebra associated with ), even in discrete cases the number of variables can be quite high . For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively.
Read more about this topic: Fuzzy Measure Theory
Famous quotes containing the words assumptions, fuzzy and/or measures:
“All of the assumptions once made about a parent’s role have been undercut by the specialists. The psychiatric specialists, the psychological specialists, the educational specialists, all have mystified child development. They have fostered the idea that understanding children and promoting their intellectual well-being is too complex for mothers and requires the intervention of experts.”
—Elaine Heffner (20th century)
“What do you think of us in fuzzy endeavor, you whose directions are sterling, whose lunge is straight?
Can you make a reason, how can you pardon us who memorize the rules and never score?”
—Gwendolyn Brooks (b. 1917)
“I hear America singing, the varied carols I hear,
Those of mechanics, each one singing his as it should be blithe and
strong,
The carpenter singing his as he measures his plank or beam,
The mason singing his as he makes ready for work, or leaves off
work,”
—Walt Whitman (1819–1892)