Minimum about fuzzy logic
Fuzzy generalization of AND, OR, NOT

There is infinite number of ways for generalization of the Boolean operators AND, OR, and NOT for multi-valued logic and fuzzy-logic (fuzzy generalization is suitable for multi-valued logics as well). Concerning combinations of the boundary values in the intervals (Boolean values 0 a 1), all generalized operators behave as Boolean operators AND, OR, and NOT. The logical values within the intervals [0, 1] are assigned “some” logical values again from within the interval [0, 1]. Simply said, the generalized operators perform interpolation between the Boolean values of 0 and 1. It may be discussed what operators are more suitable for the particular purpose and what provide better (smoother or less complicated) interpolation process. None of the operators described herein are unsuitable (so they can be suitable). Sometimes other symbols are used (e.g. ANF, ORF, and NOF) for distinguishing them from Boolean operators; however, traditional notation, which is used also in the standard IEC 61131-7 will be applied here and the type of the operator will be specified by an index.