⋀-Pseudo Homogeneity of Fuzzy Implications and Binary Classification based on Gödel Integrals

The study of functional equations involving fuzzy logic operations has an immense impact both on the theoretical and applicational fronts. In this work, the pseudo-homogeneity functional equation involving fuzzy implications with the minimum t-norm is studied and some complete solutions are given under reasonable assumptions on the involved operations. Noting that the Gödel implication is one such solution, we determine an equivalent formulation for the Gödel integral based binary classifier, which offers an alternative perspective, especially on the interpretation of the threshold λ employed.