ON FUZZY MEASURES DEFINED BY SEMINORMED FUZZY INTEGRALS AND SEMICONORMED FUZZY INTEGRALS

In this paper, we show that for the continuous t-seminorms inverted perpendicular and continuous t-semiconorms perpendicular-to , the properties of null-additivity, pseudo-null-additivity, autocontinuity and pseudo-autocontinuity of fuzzy measures g can be preserved by the fuzzy measures sigma(inverted perpendicular,g,h) and sigma(perpendicular-to,g,h) defined by semiconormed fuzzy integrals and semiconormed fuzzy integrals, respectively, at most under the conditions that inverted perpendicular(x, y) > 0, for-all x,y > 0 and perpendicular-to (x, y) < 1, for-all x,y < 1. We also show that for the continuous t-seminorms inverted perpendicular, the property of uniform autocontinuity of fuzzy measures g can be preserved by the fuzzy measures sigma(inverted perpendicular,g,h) under the condition that inverted perpendicular(x, y) > 0, for-all x,y > 0.