| There are two things that are referred to as "fuzzy logic". The first, is the true fuzzy logic, which consists of Fuzzy Set theory and Fuzzy Measure theory. The two are distinct but interrelated, and heavily mathematical in nature. In particular, Fuzzy Measure theory completely subsumes Probability theory (i.e. probability theory is a strict subset of fuzzy measure theory, and therefore anything that can be expressed in probabilistic terms can be expressed in equivalent fuzzy measure theory terms, with leeway for added generality). The second, is a class of techniques, based on Fuzzy Set / Fuzzy Measure theory, which implement some very simple behaviours which allow you to solve a particular class of problems. This is the standard Sugeno/Mamdani logic, fuzzy inference as the application of a few straightforward rules for conducting conjunction/disjunction among fuzzy rules. The first is still thriving, but largely in the theoretical realm. The second is shunned, on the basis that it feels like a bunch of interpolation heuristics, and a Bayesian approach is usually "better", even if not as intuitive of straightforward. Unfortunately this has had a self-prophetic impact, in the sense that any literature which would have been better described as fuzzy, is labelled as probabilistic, even if strictly speaking the concepts involved are not strictly-speaking probabilities, but should more correctly have been addressed as fuzzy measures. Personally I have published papers where I had to "disguise" fuzziness as probability just to get it considered for publication, or where I had to "apologize" for the term, or making it explicit that fuzziness in this context is unrelated to this set of tools that is typically thought of as "the fuzzy approach". Having said that, one area that is thriving is the use of Fuzzy methods in the context of more general AI / NeuralNetwork methods, particularly in the context of explainability. Type 2 Fuzzy methods in particular (which introduce one or more layers/dimensions of fuzziness/uncertainty over the membership function itself) are quite an active area of research. Finally, there are some frameworks that borrow heavily from fuzzy theory, but strictly speaking are independent. The one that interested me the most in recent years was "Subjective Logic", proposed by a guy called Audun Jøsang; this sounded like a very interesting logic framework and I was very keen to use it in my work, but in the end I just didn't have the time to justify that investment ... It's worth looking up though. The basic idea is that you have a framework where you have rules that have a built-in way of carrying uncertainty with them, with a one-to-one mapping with beta probabilities over your fuzzy-like rules, and a set of logical operations (which map to the usual logical operators) that are adapted to carry the uncertainty with them. This means that you can reduce your problem into a set of simple logical statements, and the framework would then take care of the uncertainty calculations for you seamlessly. |