FUZZY T-CONORM INTEGRAL WITH RESPECT TO FUZZY MEASURES - GENERALIZATION OF SUGENO INTEGRAL AND CHOQUET INTEGRAL

This article discusses integrals with respect to Sugeno's fuzzy measures. Sugeno integrals and Choquet integrals with respect to general fuzzy measures are generalized in the setting of a t-conorm algebraic system. First t-conorm integrals with respect to decomposable measures based on t-conorm algebraic system are defined. They are a modification of the Weber integral. Secondly they are extended to fuzzy t-conorm integrals with respect to general fuzzy measures. The extension is made in the same way as the extension of the Lebesgue integral to the Choquet integral. The class of the fuzzy t-conorm integrals includes Choquet integrals and Sugeno integrals. Properties of the integrals, especially their representation, are discussed.