Vassilis G. Kaburlasos

Fuzzy lattice neural network (FLNN): a hybrid model for learning

This paper proposes two hierarchical schemes for learning, one for clustering and the other for classification problems. Both schemes can be implemented on a fuzzy lattice neural network (FLNN) architecture, to be introduced herein. The corresponding two learning models draw on adaptive resonance theory (ART) and min-max neurocomputing principles but their application domain is a mathematical lattice. Therefore they can handle more general types of data in addition to N-dimensional vectors. The FLNN neural model stems from a cross-fertilization of lattice theory and fuzzy set theory. Hence a novel theoretical foundation is introduced in this paper, that is the framework of fuzzy lattices or FL-framework, based on the concepts fuzzy lattice and inclusion measure. Sufficient conditions for the existence of an inclusion measure in a mathematical lattice are shown. The performance of the two FLNN schemes, that is for clustering and for classification, compares quite well with other methods and it is demonstrated by examples on various data sets including several benchmark data sets.

Fuzzy lattice reasoning (FLR) classifier and its application for ambient ozone estimation

The fuzzy lattice reasoning (FLR) classifier is presented for inducing descriptive, decision-making knowledge (rules) in a mathematical lattice data domain including space R^N. Tunable generalization is possible based on non-linear (sigmoid) positive valuation functions; moreover, the FLR classifier can deal with missing data. Learning is carried out both incrementally and fast by computing disjunctions of join-lattice interval conjunctions, where a join-lattice interval conjunction corresponds to a hyperbox in R^N. Our testbed in this work concerns the problem of estimating ambient ozone concentration from both meteorological and air-pollutant measurements. The results compare favorably with results obtained by C4.5 decision trees, fuzzy-ART as well as back-propagation neural networks. Novelties and advantages of classifier FLR are detailed extensively and in comparison with related work from the literature.

Computational Intelligence Based on Lattice Theory

The emergence of lattice theory within the field of computational intelligence (CI) is partially due to its proven effectiveness in neural computation. Moreover, lattice theory has the potential to unify a number of diverse concepts and aid in the cross-fertilization of both tools and ideas within the numerous subfields of CI. The compilation of this eighteen-chapter book is an initiative towards proliferating established knowledge in the hope to further expand it. This edited book is a balanced synthesis of four parts emphasizing, in turn, neural computation, mathematical morphology, machine learning, and (fuzzy) inference/logic. The articles here demonstrate how lattice theory may suggest viable alternatives in practical clustering, classification, pattern analysis, and regression applications.

Learning in the framework of fuzzy lattices

A basis for rigorous versatile learning is introduced theoretically, that is the framework of fuzzy lattices or FL-framework for short, which proposes a synergetic combination of fuzzy set theory and lattice theory. A fuzzy lattice emanates from a conventional mathematical lattice by fuzzifying the inclusion order relation. Learning in the FL-framework can be effected by handling families of intervals, where an interval is treated as a single entity/block the way explained here. Illustrations are provided in a lattice defined on the unit-hypercube where a lattice interval corresponds to a conventional hyperbox. A specific scheme for learning by clustering is presented, namely /spl sigma/-fuzzy lattice learning scheme or /spl sigma/-FLL (scheme) for short, inspired from adaptive resonance theory (ART). Learning by the /spl sigma/-FLL is driven by an inclusion measure /spl sigma/ of the corresponding Cartesian product to be introduced here. We delineate a comparison of the /spl sigma/-FLL scheme with various neural-fuzzy and other models. Applications are shown to one medical data set and two benchmark data sets, where /spl sigma/-FLLs capacity for treating efficiently real numbers as well as lattice-ordered symbols separately or jointly is demonstrated. Due to its efficiency and wide scope of applicability the /spl sigma/-FLL scheme emerges as a promising learning scheme.

Clustering and classification in structured data domains using Fuzzy Lattice Neurocomputing (FLN)

A connectionist scheme, namely, /spl sigma/-Fuzzy Lattice Neurocomputing scheme or /spl sigma/-FLN for short, which has been introduced in the literature lately for clustering in a lattice data domain, is employed for computing clusters of directed graphs in a master-graph. New tools are presented and used, including a convenient inclusion measure function for clustering graphs. A directed graph is treated by /spl sigma/-FLN as a single datum in the mathematical lattice of subgraphs stemming from a master-graph. A series of experiments is detailed where the master-graph emanates from a thesaurus of spoken language synonyms. The words of the thesaurus are fed to /spl sigma/-FLN in order to compute clusters of semantically related words, namely hyperwords. The arithmetic parameters of /spl sigma/-FLN can be adjusted so as to calibrate the total number of hyperwords computed in a specific application. It is demonstrated how the employment of hyperwords implies a reduction, based on the a priori knowledge of semantics contained in the thesaurus, in the number of features to be used for document classification. In a series of comparative experiments for document classification, it appears that the proposed method favorably improves classification accuracy in problems involving longer documents, whereas performance deteriorates in problems involving short documents.

A granular extension of the fuzzy-ARTMAP (FAM) neural classifier based on fuzzy lattice reasoning (FLR)

The fuzzy lattice reasoning (FLR) classifier was introduced lately as an advantageous enhancement of the fuzzy-ARTMAP (FAM) neural classifier in the Euclidean space R^N. This work extends FLR to space F^N, where F is the granular data domain of fuzzy interval numbers (FINs) including (fuzzy) numbers, intervals, and cumulative distribution functions. Based on a fundamentally improved mathematical notation this work proposes novel techniques for dealing, rigorously, with imprecision in practice. We demonstrate a favorable comparison of our proposed techniques with alternative techniques from the literature in an industrial prediction application involving digital images represented by histograms. Additional advantages of our techniques include a capacity to represent statistics of all orders by a FIN, an introduction of tunable (sigmoid) nonlinearities, a capacity for effective data processing without any data normalization, an induction of descriptive decision-making knowledge (rules) from the training data, and the potential for input variable selection.

FINs: lattice theoretic tools for improving prediction of sugar production from populations of measurements

This paper presents novel mathematical tools developed during a study of an industrial-yield prediction problem. The set F of fuzzy interval numbers, or FINs for short, is studied in the framework of lattice theory. A FIN is defined as a mapping to a metric lattice of generalized intervals, moreover it is shown analytically that the set F of FINs is a metric lattice. A FIN can be interpreted as a convex fuzzy set, moreover a statistical interpretation is proposed here. Algorithm CALFIN is presented for constructing a FIN from a population of samples. An underlying positive valuation function implies both a metric distance and an inclusion measure function in the set F of FINs. Substantial advantages, both theoretical and practical, are shown. Several examples illustrate geometrically on the plane both the utility and the effectiveness of novel tools. It is outlined comparatively how some of the proposed tools have been employed for improving prediction of sugar production from populations of measurements for Hellenic Sugar Industry, Greece.

Novel Fuzzy Inference System (FIS) Analysis and Design Based on Lattice Theory

We introduce novel (set- and lattice-theoretic) perspectives and tools for the analysis and design of fuzzy inference systems (FISs). We present an FIS, including both fuzzification and defuzzification, as a device for implementing a function f: RNrarr RM. The family of FIS functions has cardinality aleph2=2aleph1, where aleph1 is the cardinality of the set R of real numbers. Hence the FIS family is much larger than polynomials, neural networks, etc.; furthermore a FIS has a capacity for local generalization. A formulation in the context of lattice theory allows us to define the set F* of fuzzy interval numbers (FINs), which includes both (fuzzy) numbers and intervals. We present a metric dK on F*, which can introduce tunable nonlinearities. FIS design based on dK has advantages such as: an alleviation of the curse of dimensionality problem and a potential for improved computer memory utilization. We present a new FIS classifier, namely granular self-organizing map (grSOM), which we apply to an industrial fertilizer modeling application

A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems

A novel distance measure between two intuitionistic fuzzy sets (IFSs) is proposed in this paper. The introduced measure formulates the information of each set in matrix structure, where matrix norms in conjunction with fuzzy implications can be applied to measure the distance between the IFSs. The advantage of this novel distance measure is its flexibility, which permits different fuzzy implications to be incorporated by extending its applicability to several applications where the most appropriate implication is used. Moreover, the proposed distance might be expressed equivalently by using either intuitionistic fuzzy sets or interval‐valued fuzzy sets. Appropriate experimental configurations have taken place to compare the proposed distance measure with similar distance measures from the literature, by applying them to several pattern recognition problems. The results are very promising because the performance of the new distance measure outperforms the corresponding performance of well‐known IFSs measures, by recognizing the patterns correctly and with high degree of confidence.

A lattice computing approach to Alzheimer's disease computer assisted diagnosis based on MRI data

We present a Computer Assisted Diagnosis (CAD) system for Alzheimers disease (AD). The proposed CAD system employs MRI data features and applies a Lattice Computing (LC) scheme. To this end feature extraction methods are adopted from the literature, toward distinguishing healthy people from Alzheimer diseased ones. Computer assisted diagnosis is pursued by a k-NN classifier in the LC context by handling this task from two different perspectives. First, it performs dimensionality reduction over the high dimensional feature vectors and, second it classifies the subjects inside the lattice space by generating adaptively class boundaries. Computational experiments using a benchmark MRI dataset regarding AD patients demonstrate that the proposed classifier performs well comparatively to state-of-the-art classification models.