Generalized reasoning about faults based on the diagnostic matrix

This paper introduces a set of comprehensive general reasoning rules about single faults based on a diagnostic matrix. The reasoning scheme unifies inference about faults based on a conventional binary diagnostic matrix, a two- and three-valued fault isolation system as well as on their fuzzy counterparts. There are introduced and defined notions of alternative and dominant fault signatures, fuzzy fault signatures as well as a matrix of alternative signatures. This matrix is supposed to be used instead of the classic diagnostic one. It is also shown that dominant fault signatures are transformable into alternative ones. Finally, three variants of concise general reasoning rules of faults are given. Three examples illustrate key point issues of the paper. The first example refers to a medical diagnostic case. It shows an instance of dominant fault signatures and, in fact, proposes a rational approach for planning diagnostic tests. The other examples describe the fuzzy reasoning approach employing a matrix of fuzzy alternative signatures applicable for use with multi-valued fuzzy diagnostic signals. Future works are outlined in the summary section.