Brigitte Charnomordic

Generating an interpretable family of fuzzy partitions from data

In this paper, we propose a new method to construct fuzzy partitions from data. The procedure generates a hierarchy including best partitions of all sizes from n to two fuzzy sets. The maximum size n is determined according to the data distribution and corresponds to the finest resolution level. We use an ascending method for which a merging criterion is needed. This criterion is based on the definition of a special metric distance suitable for fuzzy partitioning, and the merging is done under semantic constraints. The distance we define does not handle the point coordinates, but directly their membership degrees to the fuzzy sets of the partition. This leads to the introduction of the notions of internal and external distances. The hierarchical fuzzy partitioning is carried independently over each dimension, and, to demonstrate the partition potential, they are used to build fuzzy inference system using a simple selection mechanism. Due to the merging technique, all the fuzzy sets in the various partitions are interpretable as linguistic labels. The tradeoff between accuracy and interpretability constitutes the most promising aspect in our approach. Well known data sets are investigated and the results are compared with those obtained by other authors using different techniques. The method is also applied to real world agricultural data, the results are analyzed and weighed against those achieved by other methods, such as fuzzy clustering or discriminant analysis.

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.

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.

Knowledge discovery for control purposes in food industry databases

Sets of experimental data describing a product at various processing steps are widely available in food industry. Decisions taken by the human operator all through the process are implicitly contained in such a database, as well as the recorded consequences on the product. The aim of this work is knowledge discovery. This knowledge must be expressed in a way that allows cooperation with the experts knowledge. The system is implemented as a self-learning fuzzy controller, with the rule conclusions being optimized by a genetic algorithm. The role of the fuzzy controller architecture is to provide a learning framework, the database being used for rule validation, thus acquiring hidden knowledge. In order to make inferred knowledge easy to understand, a rule and variable selection methodology has been developed. Data from a cheesemaking process were used to test our approach.

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.

An iterative approach to build relevant ontology-aware data-driven models

In many fields involving complex environments or living organisms, data-driven models are useful to make simulations in order to extrapolate costly experiments and to design decision-support tools. Learning methods can be used to build interpretable models from data. However, to be really useful, such models must be trusted by their users. From this perspective, the domain expert knowledge can be collected and modeled to help guiding the learning process and to increase the confidence in the resulting models, as well as their relevance. Another issue is to design relevant ontologies to formalize complex knowledge. Interpretable predictive models can help in this matter. In this paper, we propose a generic iterative approach to design ontology-aware and relevant data-driven models. It is based upon an ontology to model the domain knowledge and a learning method to build the interpretable models (decision trees in this paper). Subjective and objective evaluations are both involved in the process. A case study in the domain of Food Industry demonstrates the interest of this approach.

Two modelling approaches of winemaking: first principle and metabolic engineering

In this article, two modelling approaches are proposed for winemaking fermentations. The first one is largely based on the first principle modelling approach and considers the main yeast physiological mechanisms. The model accurately predicts the fermentation kinetics of more than 80% of a large number of experiments performed with 20 wine yeast strains, 69 musts and different fermentation conditions. Thanks to the wide domain of validity of the model, a simulator based on this model coupled to a thermal model was developed to help winemakers to optimize tank management. It predicts the end of the fermentation and changes in the rate of fermentation but furthermore includes an optimization module based on fuzzy logic which allows, via temperature profiles and nitrogen addition strategies, to decrease the duration of fermentation and the energy requirements at winery scale according to user specifications. The objective of the second modelling approach is the development of a mathematical model of the fermentation process including some minority by-products known as characteristic flavour compounds. It refers to metabolic engineering and accounts for the intracellular behaviour of the yeast Saccharomyces cerevisiae by using approaches like the metabolic flux analysis (MFA) and the elementary flux modes (EFMs). A state of the art describes the application of these methods in the restrained field of winemaking/fermentation conditions and underlines the potential of such approaches.