Fuzzy decision implication canonical basis

Yanhui Zhai, Deyu Li, Kaishe Qu

Abstract: Fuzzy decision implication (FDI) is regarded as a basic form of knowledge representation in fuzzy decision based formal concept analysis. How to reduce redundant FDIs and generate an informative and minimal set of FDIs from a given set of FDIs is the main concern in the study of FDI. This paper introduces fuzzy decision premise, constructs fuzzy decision implication canonical basis (FD canonical basis) and proves that FD canonical basis is complete, non-redundant and optimal, i.e., FD canonical basis contains the least number of FDIs among all complete sets of FDIs. Thus, from a given set of FDIs, one can generate its corresponding FD canonical basis, which turns out to be informative (complete) and minimal (optimal).