Myriam Regattieri Delgado

General Type-2 Fuzzy Inference Systems: Analysis, Design and Computational Aspects

The aim of this work is to handle non-interval type-2 fuzzy logic systems (NIT2 FLS) in a simple manner. We retrieve an alternative representation of Type-2 fuzzy sets (T2 FS) that we call general footprint of uncertainty. Such representation, not only lets us easily visualize T2 FS in two-dimensions but also makes the understanding of basic operations and the inference procedure easier. We introduce the concept of supremum of a T2 FS and translation and cylindric extension for vertical slices to support the adopted inference mechanism, based on the scaled inference mechanism of Type-1 FIS. Finally, we propose a new defuzzification method, the vertical slice centroid type reduction, which requires low computational effort. Some calculations are presented to illustrate that the theory and simplifications proposed in this paper make NIT2 FLS, referred here as general type-2 fuzzy inference systems, much more accessible to FIS designers.

An artificial immune system for fuzzy-rule induction in data mining

This work proposes a classification-rule discovery algorithm integrating artificial immune systems and fuzzy systems. The algorithm consists of two parts: a sequential covering procedure and a rule evolution procedure. Each antibody (candidate solution) corresponds to a classification rule. The classification of new examples (antigens) considers not only the fitness of a fuzzy rule based on the entire training set, but also the affinity between the rule and the new example. This affinity must be greater than a threshold in order for the fuzzy rule to be activated, and it is proposed an adaptive procedure for computing this threshold for each rule. This paper reports results for the proposed algorithm in several data sets. Results are analyzed with respect to both predictive accuracy and rule set simplicity, and are compared with C4.5rules, a very popular data mining algorithm.

Hierarchical genetic fuzzy systems

Abstract This paper introduces a hierarchical evolutionary approach to optimize the parameters of Takagi–Sugeno (TS) fuzzy systems. The approach includes a least-squares method to determine the parameters of nonlinear consequents. A pruning procedure is developed to avoid redundancy in each rule consequent and to achieve proper representation flexibility. The performance of the hierarchical evolutionary approach is evaluated using function approximation and classification problems. They demonstrate that the evolutionary algorithm, working together with optimization and pruning procedures, provides structurally simple fuzzy systems whose performance seems to be better than the ones produced by alternative approaches.

Coevolutionary genetic fuzzy systems: a hierarchical collaborative approach

Abstract In this paper a coevolutionary genetic approach is devised to support hierarchical, collaborative relations between individuals representing different parameters of Takagi–Sugeno fuzzy models. The coevolutionary approach assumes species to mean partial solutions of fuzzy modeling problems organized into four hierarchical levels. Individuals at each hierarchical level encode membership functions, individual rules, rule-bases and fuzzy systems, respectively. A shared fitness evaluation scheme is used to measure the performance of each individual. Constraints are observed and particular targets are defined throughout the hierarchical levels, with the purpose of promoting the occurrence of valid individuals and inducing rule compactness, rule base consistency, and partition set visibility. The performance of the approach is evaluated via an example of function approximation with noisy data, and a nonlinearly separable classification problem.

ADEMO/D: Multiobjective optimization by an adaptive differential evolution algorithm

This paper presents an approach for continuous optimization called Adaptive Differential Evolution for Multiobjective Problems (ADEMO/D). The approach incorporates concepts of Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) and mechanisms of strategies adaptation. In this work we test two methods to perform adaptive strategy selection: Probability Matching (PM) and Adaptive Pursuit (AP). PM and AP are analyzed in combination with four credit assignment techniques based on relative fitness improvements. The DE strategy is chosen from a candidate pool according to a probability that depends on its previous experience in generating promising solutions. In experiments, we evaluate certain features of the proposed approach, considering eight different versions while solving a well established set of 10 instances of Multiobjective Optimization Problems. Next the best-so-far version (ADEMO/D) is confronted with its non-adaptive counterparts. Finally ADEMO/D is compared with four important multiobjective optimization algorithms in the same application context. Pareto compliant indicators and statistical tests are applied to evaluate the algorithm performances. The preliminary results are very promising and stand ADEMO/D as a candidate to the state-of-the-art for multiobjective optimization.

Self-adapting evolutionary parameters: encoding aspects for combinatorial optimization problems

Evolutionary algorithms are powerful tools in search and optimization tasks with several applications in complex engineering problems. However, setting all associated parameters is not an easy task and the adaptation seems to be an interesting alternative. This paper aims to analyze the effect of self-adaptation of some evolutionary parameters of genetic algorithms (GAs). Here we intend to propose a flexible GA-based algorithm where only few parameters have to be defined by the user. Benchmark problems of combinatorial optimization were used to test the performance of the proposed approach.

Multi-label Hierarchical Classification of Protein Functions with Artificial Immune Systems

This work proposes two versions of an Artificial Immune System (AIS) - a relatively recent computational intelligence paradigm --- for predicting protein functions described in the Gene Ontology (GO). The GO has functional classes (GO terms) specified in the form of a directed acyclic graph, which leads to a very challenging multi-label hierarchical classification problem where a protein can be assigned multiple classes (functions, GO terms) across several levels of the GOs term hierarchy. Hence, the proposed approach, called MHC-AIS (Multi-label Hierarchical Classification with an Artificial Immune System), is a sophisticated classification algorithm tailored to both multi-label and hierarchical classification. The first version of the MHC-AIS builds a global classifier to predict all classes in the application domain, whilst the second version builds a local classifier to predict each class. In both versions of the MHC-AIS the classifier is expressed as a set of IF-THEN classification rules, which have the advantage of representing comprehensible knowledge to biologist users. The two MHC-AIS versions are evaluated on a dataset of DNA-binding and ATPase proteins.

A neuro-coevolutionary genetic fuzzy system to design soft sensors

This paper addresses a soft computing-based approach to design soft sensors for industrial applications. The goal is to identify second-order Takagi–Sugeno–Kang fuzzy models from available input/output data by means of a coevolutionary genetic algorithm and a neuro-based technique. The proposed approach does not require any prior knowledge on the data-base and rule-base structures. The soft sensor design is carried out in two steps. First, the input variables of the fuzzy model are pre-selected from the secondary variables of a dynamical process by means of correlation coefficients, Kohonen maps and Lipschitz quotients. Such selection procedure considers nonlinear relations among the input and output variables. Second, a hierarchical coevolutionary methodology is used to identify the fuzzy model itself. Membership functions, individual rules, rule-bases and fuzzy inference parameters are encoded into each hierarchical level and a shared fitness evaluation scheme is used to measure the performance of individuals in such levels. The proposed methodology is evaluated by developing soft sensors to infer the product composition in petroleum refining processes. The obtained results are compared with other benchmark approaches, and some conclusions are presented.

Land Cover Classification Based on General Type-2 Fuzzy Classifiers

This paper proposes a fuzzy classifier based on type-2 fuzzy sets to be applied in land cover classification. The classifier is built on the basis of the available data and considers the merging of information drawn from different experts. The data regard a thematic mapper representing the land cover of a real plain cultivated area. The experts are represented by different bands which classify the spectral sensor information. The new proposed method to design the classifier as well as the use of general type-2 fuzzy sets allows the modeling of input-output relations and minimizes the effects of uncertainties in the usual fuzzy rule-based classifiers. The experiments carried out attest to the efficiency of the proposed general type-2 fuzzy classifier.

ADEMO/D: Adaptive Differential Evolution for Multiobjective Problems

This paper proposes a method for continuous optimization based on Differential Evolution (DE). The approach named Adaptive Differential Evolution for Multiobjective Problems (ADEMO/D) incorporates concepts of Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) and mechanisms of mutation strategies adaptation inspired by the adaptive DE named Self-adaptive Differential Evolution (SaDE). Additionally a new mutation strategy, based on MOEA/D neighborhood concept, is proposed to be used in the strategy candidate pool. ADEMO/D is compared with three multi-objective optimization approaches using a set of benchmarks. The preliminary results are very promising and stand the proposed approach as a candidate to the State-of-art for multi-objective optimization.