Fuzzy logic and the calculi of fuzzy rules, fuzzy graphs, and fuzzy probabilities

The past few years have witnessed a rapid growth in the number and variety of applications of fuzzy logic, ranging from consumer products and industrial process control to medical instrumentation, information systems, and decision analysis. The foundations of fuzzy logic have become firmer and its impact within the basic sciences – and especially in mathematical and physical sciences – has become more visible and more substantive. And yet, there are still many misconceptions about the aims of fuzzy logic and misjudgments of its strengths and limitations. In the final analysis, the principal aim of these methodologies is to exploit the tolerance for imprecision and uncertainty to achieve tractability, robustness, and low solution cost.