Jose Maria Alonso Moral,Ciro Castiello,Luis Magdalena,and Corrado Mencar,Explainable Fuzzy Systems: Paving the Way from Interpretable Fuzzy Systems to Explainable AI Systems,Springer,Cham,Switzerland,2021

The advent of deep leaning necessitates the need for explainable AI. The term Artificial Intelligence (AI) was coined in the mid 1950s to indicate logic reasoning-based approaches. For a few decades, applying AI mostly meant applying expert systems –where a computer makes decisions based on expert-provided rules. These systems were often imperfect. However, when they provided a recommendation, one could easily extract an explanation for this recommendation –the sequence of expert-provided rules that led the system to make its conclusions.

There were also researchers interested in neural networks, in fuzzy methods, etc., but these researchers were usually considered to be somewhat (or even fully) outside AI, under different names like Computational Intelligence. Some neural and fuzzy papers were accepted at AI conferences, but most papers at these conferences were still based on logical reasoning.

The situation changed drastically in the 2010s, with the invention of deep learning. Deep learning techniques led to many sensational successes –like winning over the world champion of Go, something that logic-based AI tried for a long time. Now, when a journalist talks about AI, he/she usually means deep learning. Deep learning is behind self-driving cars, deep learning helps financial institutions make decisions, etc. The resulting AI systems are much better than in the past, but there is a problem: in contrast to explanation-based expert system, systems based on deep learning simply give out recommendations, without providing any explanation at all.

It might have been tolerable if these systems were always right, but of course, they are not perfect. Human experts are not perfect either, but at least they provide an explanation: if a medical doctor recommends a certain medicine (of, if needed, a surgery), the doctor can provide an explanation for why he/she made this recommendation. If the patient is not convinced, he/she can consult with another doctor, these two doctor can discuss their arguments. In contrast, a recommendation from a system based on deep learning comes without any explanation.

What is worse, the recommendations made by a machine learning system are usually based on the prior experience, so they tend to propagate the past biases. For example, it is known that in the past, many banks where more reluctant to approve loans for females than for males. A system learning from the past experience will naturally learn this past strategy and deny loans to female applicants. In case of a personal decision, the applicant can ask for explanations and argue –but for a black-box system, there are no rules, no explanations, no way to argue.

It is therefore necessary to make recommendations explainable.

Fuzzy logic is a natural tool for this. Making recommendations –generated by a number-based machine learning algorithm –explainable means providing natural-language rules that would explain these numerical results. In other words, we need to find a relation between numerical recommendations and natural-language rules. Finding such a relation was exactly what started fuzzy logic, although at that time, the motivation was different: Lotfi Zadeh wanted to know how to translate natural-language rules into precise numerical control and decision strategies. His approach was very successful, and fuzzy controllers were (and are) successfully used in many practical applications, ranging from controlling trains and elevators to controlling rice cookers.

Since fuzzy logic has established successful relation between numerical recommendations and natural-language rules, a natural idea is to use fuzzy techniques to make AI explainable.

But the situation is not so straightforward. There are universal approximation results that show that any numerical strategy can be approximated, with any given accuracy, by natural-language rules. There are algorithms for designing such rules. At first glance, the situation is straightforward –fuzzy techniques is exactly what the doctor ordered.

However, in reality, the situation is much more complex. Yes, we can approximate any numerical strategy by fuzzy rules, but to get a good accuracy, we need many such rules. And if we replace a deep learning recommendation –that when a person has weight 150 pounds and blood pressure 160/100, we should prescribe him 120 mg of whatever medicine –with a fuzzy rule that if weight is approximately 150 and blood pressure approximately 160/100, we should prescribe approximately 120 mg –how will this help? Even if we find natural-language words for “approximately 160/100”, like “elevated but not too high”, this will not make the conclusion clearer.

To be truly explainable, the set of fuzzy rules must be clear to us. This means, e.g., that for each quantity like weight, we should have only 7 ± 2 different fuzzy degrees –in line with a known psychological law. We should have not too many conditions in each rule. For any given situation, only a few rules should be applicable. And so on.

Coming up with such human-understandable set of rules is not so easy. And this complex task is the main objective of this book.

The structure of the book. The book, by the way, is intended both for fuzzy researchers interested in explainable AI and for AI researchers interested in using fuzzy techniques. In line with this dual audience, it starts with explaining the need for explainable AI (in Chapter 1) and explaining fuzzy techniques (in Chapter 2).

The really new part starts in Chapter 3, where the authors list all the requirements that make a system of fuzzy rules helpful and human-understandable. Chapter 4 explains how to combine these criterion into a single index allowing us to gauge how interpretable is a given systems of rules. Chapter 5 explains how to design a fuzzy system which is reasonable interpretable –and Chapter 6 explains the freely available software that the authors created for this purpose.

This software is illustrated on the example of a problem that most of us will easily understand –how to classify different beers.

Remaining open problems. OK, so we describe a reasonably small set of rules –are we done? Not really. We only reached the stage that the authors call interpretable AI. To make the system really explainable, we need to be able to explain where these rules come from –and, in general, it is not clear how to do it.

Hopefully, readers of this pioneering book will be inspired by remaining open problems, and, working all together, we will finally make AI explainable.