Accuracy-interpretability Trade-off Research Articles

Hybrid learning models to get the interpretability–accuracy trade-off in fuzzy modeling

One of the problems associated to linguistic fuzzy modeling is its lack of accuracy when modeling some complex systems. To overcome this problem, many different possibilities of improving the accuracy of linguistic fuzzy modeling have been considered in the specialized literature. We will call these approaches as basic refinement approaches. In this work, we present a short study of how these basic approaches can be combined to obtain new hybrid approaches presenting a better trade-off between interpretability and accuracy. As an example of application of these kinds of systems, we analyze seven hybrid approaches to develop accurate and still interpretable fuzzy rule-based systems, which will be tested considering two real-world problems.

Identification of Numerically Accurate First-Order Takagi-Sugeno Systems with Interpretable Local Models from Data

The paper deals with the interpretability problem of 1st order Takagi-Sugeno systems and interpolation issues in particular. Interpolation is improved by a corrective secondary model – essentially a black box – complementing the primary (interpretable) model. Optimization technique for this two-model configuration is developed. Experimental results indicate that the approach achieves a better accuracy-interpretability tradeoff than methodologies currently in use.

Learning cooperative linguistic fuzzy rules using the best-worst ant system algorithm

Within the field of linguistic fuzzy modeling with fuzzy rule-based systems, the automatic derivation of the linguistic fuzzy rules from numerical data is an important task. In the last few years, a large number of contributions based on techniques such as neural networks and genetic algorithms have been proposed to face this problem. In this article, we introduce a novel approach to the fuzzy rule learning problem with ant colony optimization (ACO) algorithms. To do so, this learning task is formulated as a combinatorial optimization problem. Our learning process is based on the COR methodology proposed in previous works, which provides a search space that allows us to obtain fuzzy models with a good interpretability–accuracy trade-off. A specific ACO-based algorithm, the Best–Worst Ant System, is used for this purpose due to the good performance shown when solving other optimization problems. We analyze the behavior of the proposed method and compare it to other learning methods and search techniques when solving two real-world applications. The obtained results lead us to remark the good performance of our proposal in terms of interpretability, accuracy, and efficiency. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 433–452, 2005.

Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction

Tuning fuzzy rule-based systems for linguistic fuzzy modeling is an interesting and widely developed task. It involves adjusting some of the components of the knowledge base without completely redefining it. This contribution introduces a genetic tuning process for jointly fitting the fuzzy rule symbolic representations and the meaning of the involved membership functions. To adjust the former component, we propose the use of linguistic hedges to perform slight modifications keeping a good interpretability. To alter the latter component, two different approaches changing their basic parameters and using nonlinear scaling factors are proposed. As the accomplished experimental study shows, the good performance of our proposal mainly lies in the consideration of this tuning approach performed at two different levels of significance. The paper also analyzes the interaction of the proposed tuning method with a fuzzy rule set reduction process. A good interpretability-accuracy tradeoff is obtained combining both processes with a sequential scheme: first reducing the rule set and subsequently tuning the model.

Oxidation of propylene to acrolein over Cu-on-Al 2O 3 catalysts modified by molybdenum oxides

Adaptive neuro-fuzzy inference system (ANFIS) is a well-known neuro-fuzzy model for approximating highly complex non-linear systems. ANFIS uses precise fuzzy modelling concept that aims at accuracy of a fuzzy model being designed than on interpretability. But interpretability of a fuzzy system is an equally important aspect of fuzzy modelling as accuracy. So far the research based on ANFIS has been mostly application based due to which the various issues related to the interpretability of ANFIS have not been dealt with. The rule base of ANFIS is typically obtained using data driven clustering algorithms. But this process introduces redundancy in the system in terms of similar fuzzy sets and redundant fuzzy rules which unnecessarily increases system complexity. This in turn reduces both the interpretability as well as generalization capability of ANFIS. Additionally in case of ANFIS, unconstrained gradient descent based learning algorithms are used to fine-tune the membership function parameters which usually result in a rule base with inconsistent, excessively overlapping and indistinguishable membership functions for input variables and thus the interpretability of the final optimized system is not guaranteed. This paper is based on addressing the issue of rule base redundancy in ANFIS to reduce complexity and enforcing constraints during learning phase to ensure interpretability of the final optimized system. Rule base redundancy is removed using similarity analysis based rule base simplification in which similar fuzzy sets are merged and subsequently resulting fuzzy rules with equal premises are combined. Hybrid learning technique which is an efficient parameter tuning method for ANFIS is constrained to prevent inconsistency, excessive overlapping and inclusion of membership functions so that the final fuzzy partitions of inputs stay interpretable. The empirical analysis of the impact of rule base simplification and constrained learning on ANFIS is done by application to two well-known benchmark problems and a real world stock price prediction problem. The introduction of rule base simplification and constrained learning in ANFIS modeling has shown better results in terms of obtaining a desired accuracy-interpretability tradeoff than conventional ANFIS.