Choquet integral type fuzzy switching functions: adjustment of fuzzy measures and complementary law

We propose Choquet integral type fuzzy switching functions with constants (CI-Fuzzy/C) which satisfy the complementary law. CI-Fuzzy/C has true and false inputs for each input and fuzzy measure values are assigned by outputs of a switching function of binary inputs. So, CI-Fuzzy/Cs are taken over from binary switching functions such as the complementary law. Lastly, we discuss the properties of CI-Fuzzy/C, such as, the extension of binary logic, monotoneity conditions and linear outputs.