Serge Guillaume

Fuzzy inference systems

Highlights? We show how fuzzy inference systems can be used in system modelling when human interaction is important. ? FIS are able to integrate expertise and rule learning from data into a single framework. ? An open source software is presented. ? Two real world case studies illustrate the approach and the software utility. The present paper aims to demonstrate the interest of fuzzy inference systems in system modeling when human interaction is important. It discusses the originality of FIS and their capability to integrate expertise and rule learning from data into a single framework, analyzing their place relatively to concurrent approaches. An open source software implementation is presented, with a focus on the useful features for modeling. Two real world case studies are presented to illustrate the approach and the software utility.

Learning interpretable fuzzy inference systems with FisPro

Fuzzy inference systems (FIS) are likely to play a significant part in system modeling, provided that they remain interpretable following learning from data. The aim of this paper is to set up some guidelines for interpretable FIS learning, based on practical experience with fuzzy modeling in various fields. An open source software system called FisPro has been specifically designed to provide generic tools for interpretable FIS design and learning. It can then be extended with the addition of new contributions. This work presents a global approach to design data-driven FIS that satisfy certain interpretability and accuracy criteria. It includes fuzzy partition generation, rule learning, input space reduction and rule base simplification. The FisPro implementation is discussed and illustrated through several detailed case studies.

Expert guided integration of induced knowledge into a fuzzy knowledge base

This paper proposes a method for building accurate and interpretable systems by integrating expert and induced knowledge into a single knowledge base. To favor the cooperation between expert knowledge and data, the induction process is run under severe constraints to ensure the fully control of the expert. The procedure is made up of two hierarchical steps. Firstly, a common fuzzy input space is designed according to both the data and expert knowledge. The compatibility of the two types of partitions, expert and induced, is checked according to three criteria : range, granularity and semantic interpretation. Secondly, expert rules and induced rules are generated according to the previous common fuzzy input space. Then, induced and expert rules have to be merged into a new rule base. Thanks to the common universe resulting from the first step, rule comparison can be made at the linguistic level only. The possible conflict situations are managed and the most important rule base features, consistency, redundancy and completeness, are studied. The first step is thoroughly described in this paper, while the second is only introduced.

Building an interpretable fuzzy rule base from data using Orthogonal Least Squares---Application to a depollution problem

In many fields where human understanding plays a crucial role, such as bioprocesses, the capacity of extracting knowledge from data is of critical importance. Within this framework, fuzzy learning methods, if properly used, can greatly help human experts. Amongst these methods, the aim of orthogonal transformations, which have been proven to be mathematically robust, is to build rules from a set of training data and to select the most important ones by linear regression or rank revealing techniques. The OLS algorithm is a good representative of those methods. However, it was originally designed so that it only cared about numerical performance. Thus, we propose some modifications of the original method to take interpretability into account. After recalling the original algorithm, this paper presents the changes made to the original method, then discusses some results obtained from benchmark problems. Finally, the algorithm is applied to a real-world fault detection depollution problem.

Practical Inference With Systems of Gradual Implicative Rules

A general approach to practical inference with gradual implicative rules and fuzzy inputs is presented. Gradual rules represent constraints restricting outputs of a fuzzy system for each input. They are tailored for interpolative reasoning. Our approach to inference relies on the use of inferential independence. It is based on fuzzy output computation under an interval-valued input. A double decomposition of fuzzy inputs is done in terms of alpha-cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply. The case of 1-D and 2-D inputs is considered, as well as higher dimensional cases. An application to a cheese-making process illustrates the approach.

A new method for inducing a set of interpretable fuzzy partitions and fuzzy inference systems from data

To improve the interpretability of a fuzzy rule base generated from data, three conditions are necessary: semantic integrity must be respected, the number of rules should be small, and incomplete rules have to be handled. An incomplete rule is a rule defined only by a few variables. The presence of incomplete rules reflects the fact that all the variables do not have the same importance for all rules.

KBCT: a knowledge extraction and representation tool for fuzzy logic based systems

This paper presents a user-friendly portable tool designed and developed in order to make easier knowledge extraction and representation for fuzzy logic based systems. KBCT is an open source software that could be executed under Linux or Windows operating systems. Main goal of KBCT is the generation or refinement of fuzzy knowledge bases with a particular interest of obtaining interpretable partitions and rules. The use of fuzzy logic simplifies the knowledge extraction process and increase interpretability of rules because of the fuzzy rule expression is closed to expert natural language. KBCT lets the user define expert variables and rules, but also provide induction capabilities for partitions and rules. Both types of knowledge, expert and induced, are integrated under the expert control. In addition to this, the user can check consistency and quality of rule base at any moment. A simplify option is implemented in order to allow the user to reduce the size of rule base. The main objective consists of ensuring interpretability, non-redundancy and consistency of the knowledge base along the whole process.

Highly Interpretable Linguistic Knowledge Bases Optimization: Genetic Tuning versus Solis-Wetts. Looking for a good interpretability-accuracy trade-off

This work shows how to achieve a good interpretability-accuracy trade-off through keeping the strong fuzzy partition property along the whole fuzzy modeling process. First, a small compact knowledge base is built. It is highly interpretable and reasonably accurate. Second, an optimization procedure, which only affects the fuzzy partitions defining the system variables, is carried out. It improves the system accuracy while preserving the system interpretability. Two optimization strategies are compared: Solis-Wetts, a local search based strategy; and Genetic Tuning, a global search based strategy. Results obtained in a well-known benchmark medical classification problem, related to breast cancer diagnosis, show that our methodology is able to achieve knowledge bases with high interpretability and accuracy comparable to that obtained by other methodologies.

Fuzzy partitions: A way to integrate expert knowledge into distance calculations

This work proposes a new pseudo-metric based on fuzzy partitions (FPs). This pseudo-metric allows for the introduction of expert knowledge into distance computations performed on numerical data and can be used in various types of statistical clustering or other applications. The knowledge is formalized by a FP, in which each fuzzy set represents a linguistic concept. The pseudo-metric is designed to respect the FP semantics. The univariate case is first studied, and the pseudo-metric behavior is discussed using synthetic experiments. Then, a multivariate version is proposed as a Minkowski-like combination of univariate distances or semi-distances. The value of the proposal is illustrated with two real-world case studies in the fields of Biology and Precision Agriculture.

DENDIS: A new density-based sampling for clustering algorithm

As clustering algorithms become more and more sophisticated to cope with current needs, large data sets of increasing complexity, sampling is likely to provide an interesting alternative. The main objective of sampling is to select a part that behaves like the whole. DENDIS is a new algorithm that combines the best of the available techniques in such a way that tractability is actually improved with a user friendly parameter setting.