Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.
-measures are special fuzzy measures decomposable with respect to some fixed t-conorm . We investigate the relationship of -measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each -measure is a plausibility measure, and that each -measure is submodular whenever is 1-Lipschitz.
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