Antonio A. Márquez

A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systems with adaptive defuzzification

In this paper we propose a multi-objective evolutionary algorithm with a mechanism to improve the interpretability in the sense of complexity for Linguistic Fuzzy Rule based Systems with adaptive defuzzification. The use of parameters in the defuzzification operator introduces a series of values or associated weights to each rule, which improves the accuracy but increases the system complexity and therefore has an effect on the system interpretability. To this end, we use maximizing the accuracy as an usual objective for the evolutionary process, and we define objectives related with interpretability, using three metrics: minimizing the classical number of rules, the number of rules with weights associated and the average number of rules triggered by each example. The proposed method was compared in an experimental study with a single objective accuracy-guided algorithm in two real problems showing that many solutions in the Pareto front dominate those obtained by the single objective-based one.

A Mechanism to Improve the Interpretability of Linguistic Fuzzy Systems with Adaptive Defuzzification based on the use of a Multi-objective Evolutionary Algorithm

Abstract This paper proposes a mechanism that helps improve the interpretability of linguistic fuzzy ruled based systems with common adaptive defuzzification methods. Adaptive defuzzification significantly improves the system accuracy, but introduces weights associated with each rule of the rule base, decreasing the system interpretability. The suggested mechanism is based on three goals: 1) reducing the number of total rules considering that rule weight close to zero can be removed; 2) reducing the rules with weights coupled because rules with weights close to one do not need the weight, and 3) reducing rules triggered jointly, all of them by using several metrics and a proposed interpretability index. This is performed using a multi-objective evolutionary algorithm, obtaining a set of solutions with different trade-offs between accuracy and interpretability. In addition, it is important to note that adaptive defuzzification and therefore the proposal developed in this work can be used together with othe...

An efficient adaptive fuzzy inference system for complex and high dimensional regression problems in linguistic fuzzy modelling

The use of adaptive connectors as conjunction operators in adaptive fuzzy inference systems is one of the methodologies, also compatible with others, to improve the accuracy of fuzzy rule-based systems by means of local adaptation of the inference process to each rule of the rule base. However, when dealing with such currently challenging issues as high-dimensional regression problems, adapting their parameters becomes difficult due to the exponential rule explosion. In this paper, we propose to address the problem by using a new adaptive conjunction operator. This operator provides considerable advantages in efficiency while maintaining the accuracy. Moreover, it is completed with a multi-objective evolutionary algorithm as a search method due to its efficiency in achieving different balances between complexity and accuracy in the learned fuzzy systems. An in-depth experimental study is performed to show the advantages of the proposal presented, using 17 regression problems of different size and complexity, using different rule bases, analyzing the multi-objective algorithms and Pareto fronts obtained and performing statistical analyses. It confirms its effectiveness in terms of efficiency, but also in terms of accuracy and complexity of the obtained models.

Cooperation between the Inference System and the Rule Base by Using Multiobjective Genetic Algorithms

This paper presents an evolutionary Multiobjective learning model achieving positive synergy between the Inference System and the Rule Base in order to obtain simpler and still accurate linguistic fuzzy models by learning fuzzy inference operators and applying rule selection. The Fuzzy Rule Based Systems obtained in this way, have a better trade-off between interpretability and accuracy in linguistic fuzzy modeling applications.

A CSP model for simple non-reversible and parallel repair plans

This work presents a constraint satisfaction problem (CSP) model for the planning and scheduling of disassembly and assembly tasks when repairing or substituting faulty parts. The problem involves not only the ordering of assembly and disassembly tasks, but also the selection of them from a set of alternatives. The goal of the plan is the minimization of the total repairing time, and the model considers, apart from the durations and resources used for the assembly and disassembly tasks, the necessary delays due to the change of configuration in the machines, and to the transportation of intermediate subassemblies between different machines. The problem considers that sub-assemblies that do not contain the faulty part are nor further disassembled, but allows non-reversible and parallel repair plans. The set of all feasible repair plans are represented by an extended And/Or graph. This extended representation embodies all of the constraints of the problem, such as temporal and resource constraints and those related to the selection of tasks for obtaining a correct plan.

Rule base and adaptive fuzzy operators cooperative learning of Mamdani fuzzy systems with multi-objective genetic algorithms

In this paper, we present an evolutionary multi-objective learning model achieving cooperation between the rule base and the adaptive fuzzy operators of the inference system in order to obtain simpler, more compact and still accurate linguistic fuzzy models by learning fuzzy inference adaptive operators together with rules. The multi-objective evolutionary algorithm proposed generates a set of fuzzy rule based systems with different trade-offs between interpretability and accuracy, allowing the designers to select the one that involves the most suitable balance for the desired application. We develop an experimental study testing our approach with some variants on nine real-world regression datasets finding the advantages of cooperative compared to sequential models, as well as multi-objective compared with single-objective models. The study is elaborated comparing different approaches by applying non-parametric statistical tests for pair-wise. Results confirm the usefulness of the proposed approach.

On Selecting and Scheduling Assembly Plans Using Constraint Programming.

This work presents the application of Constraint Programming to the problem of selecting and sequencing assembly operations. The set of all feasible assembly plans for a single product is represented using an {it And/Or} graph. This representation embodies some of the constraints involved in the planning problem, such as precedence of tasks, and the constraints due to the completion of a correct assembly plan. The work is focused on the selection of tasks and their optimal ordering, taking into account their execution in a generic multi-robot system. In order to include all different constraints of the problem, the {it And/Or} graph representation is extended, so that links between nodes corresponding to assembly tasks are added, taking into account the resource constraints. The resultant problem is mapped to a Constraint Satisfaction Problem (CSP), and is solved using Constraint Programming, a powerful programming paradigm that is increasingly used to model and solve many hard real-life problems.

A scalable evolutionary linguistic fuzzy system with adaptive defuzzification in big data

This work deals with the design of scalable methodologies to build the Rule Bases of Linguistic Fuzzy Rule Based Systems from examples for Fuzzy Regression in Big Data environments. We propose a distributed MapReduce model based on the use of an adaptation of a classic data driven method followed by an Evolutionary Adaptive Defuzzification to increase the accuracy of the final fuzzy model.

An efficient multi-objective evolutionary adaptive conjunction for high dimensional problems in linguistic fuzzy modelling

Adaptive connectors as conjunction operators of the inference system is one of the methodologies to improve the accuracy of fuzzy rule based systems by means of local adaptation of the inference process to each rule of the rule base. They are usually implemented through the classic adaptive t-norms, but when dealing with high-dimensional problems (several variables and/or instances) the adaptation of their parameters becomes problematic. In this paper, we propose a new adaptive conjunction connector and an associated multi-objective evolutionary learning algorithm which is more efficient and thus suitable for using adaptive connectors in high dimensional problems. The proposal is compared in an experimental study with the use of a well known efficient adaptive t-norm from the literature as conjunction operator. The results obtained on five regression problems confirm the effectiveness of the presented proposal in terms of efficiency, but also in terms of simplicity and compactness of the obtained models.