Fuzzy integral based fuzzy switching functions

Abstract

This paper shows many relations among fuzzy switching functions and fuzzy integrals. First, we show that monotone fuzzy switching functions with constants are extended Sugeno integrals and fuzzy switching functions are Sugeno integrals whose inputs are double inputs, that is, true and false inputs. Next, we propose a Choquet integral based fuzzy binary switching function, which is calculated by a Choquet integral of double inputs and which uses adjusted fuzzy measure of complementary sets. The functions satisfy the complementary law and monotonicity under the monotonicity on binary inputs. Finally, we propose a logical Choquet integral and we discuss its properties. © Springer-Verlag 2004.