Fuzzy Measures Defined by Pan-Integral

Considering a given pan-space (X, A, mu, (R) over bar (+), circle plus, circle times) and a given nonnegative measurable function f on (X, A), the pan-integral of f w.r.t mu and (circle plus, circle times) determines a new fuzzy measure v(f) on (X, A). Such new fuzzy measure preserves some important structural characteristics of fuzzy measures, such as continuity from below, continuity from above, strong order continuity, autocontinuity, null-additivity, subadditivity and the pseudometric generating property, etc.. Since the pan-integral based on a pair of pan-operations (circle plus, circle times) covers the Sugeno integral (based on (boolean OR, boolean AND)) while the Shilkret integral (based on (boolean OR, .)), therefore, the previous related results for the Sugeno integral are covered by the results presented here, in the meantime, we obtain some special results related the Shilkret integral.