44496446
THE GENETIC DESIGN OF HYBRID FUZZY CONTROLLERS
In this study, we introduce a comprehensive design methodology of hybrid fuzzy controllers (HFCs). The hybrid facet of the proposed architecture of the controller manifests in the form of a convex combination of a standard proportional integral derivative (PID) controller and a fuzzy controller. The design procedure dwells on the use of evolutionary computing (genetic algorithms) and an autotuning algorithm based on estimation modes. The tuning of the scaling factors of the HFC is an essential component of the entire optimization process. Numerical studies are presented and a detailed comparative analysis is included as well.
31716066
The genetic development of ordinal sums
Abstract The aim of this study is to develop an operational model of an ordinal sum of triangular norms. The essence of this construct lies in the use of different t-norms (and/or t-conorms) defined over disjoint subintervals of the unit interval. The result of such aggregation is a highly versatile logic operator that can be easily adapted to the existing experimental evidence. We propose a genetic optimisation environment (Genetic Algorithms, GAs, in particular) to construct ordinal sums and show how the GA mechanism helps optimize subintervals and to allocate individual local t-norms. The application of the genetically designed ordinal sums is shown in case of Zimmermann–Zysno logic operator data. We also demonstrate the use of the ordinal sum to the construction of neuro-fuzzy systems; in this case we quantify the performance of ordinal sums to “standard” logic operators used in such models.
20379804
Hybrid Fuzzy Polynomial Neural Networks
We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x)" where A is a fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data.
2982088
Fuzzy Aggregation Method Using Fisherface and Wavelet Decomposition for Face Recognition
19471846
Fuzzy clustering with a knowledge-based guidance
Fuzzy clustering becomes a broadly accepted synonym of fundamental endeavors aimed at finding structures in multidimensional data. In essence, these methods operate in unsupervised mode. This means that they act upon data while being directed by some predefined objective function (criterion) for which they "discover" a structure (clusters) that yields a minimal value of this criterion. In this study, we discuss an issue of exploiting and effectively incorporating auxiliary problem dependent hints being available as a part of the domain knowledge associated with the pattern recognition problem at hand. As such hints are usually expressed by experts/data analysts at the level of clusters (information granules) rather than individual data (patterns), we refer to them as knowledge-based indicators and allude to a set of them as a knowledge-based guidance available to fuzzy clustering. The proposed paradigm shift in which fuzzy clustering incorporates this type of knowledge-based supervision is discussed and contrasted with the "pure" (that is data-driven) version of fuzzy clustering. Several fundamental categories of the guidance mechanisms are introduced and discussed, namely partial supervision, proximity-based guidance and uncertainty driven knowledge hints. The details on how the guidance machinery translates into updates of the partition matrices are presented. We also present a number of practical scenarios in which the role of knowledge hints becomes evident and highly justifiable. This concerns Web exploration, exploitation of labeled patterns, issues of incomplete feature spaces, and constraints of typicality of patterns, to name a few representative applications.
34168275
Fuzzy clustering with supervision
This study is concerned with clustering carried out in presence of labeled patterns. An objective of this optimization is to reconcile between the structure residing in data (and being primarily discovered by the underlying clustering mechanism) and the labels of the patterns forming such structure. In this sense, one can consider the supervised fuzzy clustering to be a framework of preliminary data analysis providing with a thorough insight into the structure of the data and supporting the ensuing design of detailed classifiers. The proposed method augments the standard fuzzy C-means algorithm by extending the original objective function by the supervision component (labeled patterns). Experimental results illustrate the approach and discuss the use of this type of clustering in vector quantization.
5269666
Conditional Fuzzy C-Means
A Fuzzy C-Means-based clustering method guided by an auxiliary (conditional) variable is introduced. The method reveals a structure within a family of patterns by considering their vicinity in a feature space along with the similarity of the values assumed by a certain conditional variable. The usefulness of the algorithm is exemplified in the problems of data mining.
34867589
Modeling temporal functions with granular regression and fuzzy rules
Modeling of temporal functions has been studied extensively in last few decades. Temporal functions or time series are found practically in the gamut of applications, ranging from engineering analysis to financial and commercial transactions.Numerous time series models been proposed, and they can be found in the relevant time series literature. Deterministic and stochastic models have dominated much of the research in this area. Nonetheless, these models have their limitations, and particularly specific models solve specific problem domains. Therefore, there is no general mechanism that can address the issues of modeling of temporal functions.Granular information is now being used to address a few of the problems in the theory of time series. This paper proposes two models that use the concepts of regression and interleaved information granules-intervals and fuzzy sets to identify the structure existing in a given time series. In brevity, we are attempting to combine regression and fuzzy rules to model temporal systems.