In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function H and a scale transformation φ is given. Consequences for T-(S-)evaluators are established.
Non-riumerical fuzzy and possibilistic measures taking their values in
partially ordered sets, semilattices or lattices are introduced. Using the operations of supremurn and infimum in these structures, the inner and outer (lower and upper) extensions of the original measures are investigated and defined. The conditions under which the resulting functions -extend conservatively the original ones and possess the properties of fuzzy or possibilistic measures, are explicitly stated and relevant assertions are proved.
S-measures are special fuzzy measures decomposable with respect to some fixed t-conorm S. We investigate the relationship of S-measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each SP-measure is a plausibility measure, and that each S-measure is submodular whenever S is 1-Lipschitz.