Abstract: Reproducing Kernel Hilbert Space (RKHS) and Reproducing Transformation Methods for Series Summation that allow analytically obtaining alternative representations for series in the finite form are developed.

Keywords: The reproducing transformation method, Hilbert space, reproducing kernel, RKHS, Series Summation Method.

ACM Classification Keywords: G.1.10 Mathematics of Computing: Applications

Link:

RKHS-METHODS AT SERIES SUMMATION FOR SOFTWARE IMPLEMENTATION

Svetlana Chumachenko, Ludmila Kirichenko

http://www.foibg.com/ijita/vol13/ijita13-3-p05.pdf

Abstract: The task of revealing the relationship between a search algorithm and a class of functions those it solves is considered. Particularly, there was found a class of functions solvable by some adaptive search algorithm for a discrete space of low cardinality. To find an optimal algorithm exhaustive search was used. Algorithm quality criterion based on equivalence classes was also introduced.

Keywords: search algorithm, adaptive search, optimization, global extreme, no free launch theorem.

ACM Classification Keywords: G.1.6. Numerical analysis: Optimization; G.2.m. Discrete mathematics: miscellaneous.

Link:

FINDING THE RELATIONSHIP BETWEEN A SEARCH ALGORITHM AND A CLASS OF FUNCTIONS ON DISCRETE SPACE BY EXHAUSTIVE SEARCH1

Victor Nedel’ko, Svetlana Nedel’ko

http://www.foibg.com/ijita/vol14/ijita14-4-p06.pdf

Abstract: The general discussion of the data flow algorithmic models, and the linear programming problem with the variating by data flow criterion function coefficients are presented. The general problem is widely known in different names - data streams, incremental and online algorithms, etc. The more studied algorithmic models include mathematical statistics and clustering, histograms and wavelets, sorting, set cover, and others. Linear programming model is an addition to this list. Large theoretical knowledge exists in this as the simplex algorithm and as interior point methods but the flow analysis requires another interpretation of optimal plans and plan transition with variate coefficients. An approximate model is devised which predicts the boundary stability point for the current optimal plan. This is valuable preparatory information of applications, moreover when a parallel computational facility is supposed.

Keywords: data flow algorithm, linear programming, approximation

ACM Classification Keywords: G.1.6 Numerical analysis: Optimization

Link:

DATA FLOW ANALYSIS AND THE LINEAR PROGRAMMING MODEL1

Levon Aslanyan

http://www.foibg.com/ijita/vol13/ijita13-1-p08.pdf

Abstract: Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

Keywords: neural nets, dynamical systems, training.

ACM Classification Keywords: G.1.6 Optimization, G.1.2 Approximation, I.2 Artificial Intelligence

Link:

REPRESENTATION OF NEURAL NETWORKS BY DYNAMICAL SYSTEMS

Volodymyr Donchenko, Denys Serbaev

http://www.foibg.com/ijita/vol12/ijita12-4-p09.pdf

Abstract: The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

Key words: Fresnel diffraction, fractional Fourier-transform

ACM Classification Keywords: G.1.2 Fast Fourier transforms (FFT)

Link:

AN ALGORITHM FOR FRESNEL DIFFRACTION COMPUTING BASED ON FRACTIONAL FOURIER TRANSFORM

Georgi Stoilov

http://www.foibg.com/ijitk/ijitk-vol01/ijitk01-2-p14.pdf

Abstract: The task of approximation-forecasting for a function, represented by empirical data was investigated. Certain class of the functions as forecasting tools: so called RFT-transformers, – was proposed. Least Square Method and superposition are the principal composing means for the function generating. Besides, the special classes of beam dynamics with delay were introduced and investigated to get classical results regarding gradients. These results were applied to optimize the RFT-transformers. The effectiveness of the forecast was demonstrated on the empirical data from the Forex market.

Keywords: empirical functions, learning samples, beam dynamics with delay, recursive nonlinear regressive transformer, Generalized Inverse, Least Square Method.

ACM Classification Keywords: G.1.2 Approximation, G.1.3 Numerical Linear Algebra, G.1.6 Optimization

Link:

DYNAMICAL SYSTEMS IN DESCRIPTION OF NONLINEAR RECURSIVE REGRESSION TRANSFORMERS

Mykola Kirichenko, Volodymyr Donchenko, Denys Serbaev

http://www.foibg.com/ijita/vol13/ijita13-1-p07.pdf

Abstract. The present article discusses units of measure and their base units, work environments built in the Units package of the computer algebra system Maple. An analysis is drawn of the tools of the application in connection with the use of physical quantities and their features. Maple’s main commands are arranged in groups depending on the function. Some applied mathematical problems are given as examples making use of derivative, integral and differential equations.

Key words: conversion, dimension, Maple, unit, systems of quantities, systems of units, Units package.

ACM Classification Keywords: G. Mathematics of Computing, I. Computing Methodologies

Link:

USING PHYSICAL QUANTITIES IN APPLIED MATHEMATICAL PROBLEMS WITH MAPLE

Tsvetanka Kovacheva

http://www.foibg.com/ijitk/ijitk-vol02/ijitk02-5-p08.pdf

Abstract: Trillas et al. introduced in 7 and 8 the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Later, in 1 and 2 the necessity of determine not only the contradiction, but also the degree in that this property occurs, was considered. This paper takes up again these subjects, and firstly we study if there exists some connection between the two first notions. After that, taking into account that selfcontradiction of a fuzzy set could be understood as the contradiction with itself, and starting from the degrees of contradiction between two fuzzy sets proposed in 5, we obtain degrees of self-contradiction. Finally, preservation of some intuitive properties both in the use of connectives and in the obtaining of new knowledge throughout compositional rule of inference, are tested.

Keywords: fuzzy sets, t-norm, t-conorm, strong fuzzy negations, contradiction, measures of contradiction, fuzzy relation, compositional rule of inference.

ACM Classification Keywords: F.4.1 Mathematical Logic and Formal Languages: Mathematical Logic (Model theory, Set theory); I.2.3 Artificial Intelligence: Deduction and Theorem Proving (Uncertainty, “fuzzy” and probabilistic reasoning); I.2.4 Artificial Intelligence: Knowledge Representation Formalisms and Methods (Predicate logic, Representation languages).

Link:

CONTRADICTION VERSUS SELFCONTRADICTION IN FUZZY LOGIC*

Carmen Torres, Susana Cubillo, Elena Castineira

http://www.foibg.com/ijita/vol14/ijita14-4-p05.pdf

Abstract: For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in 5 and 6. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in 1 and 2, suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in 0,12. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

Keywords: fuzzy sets, t-norm, t-conorm, fuzzy strong negations, contradiction, measures of contradiction.

ACM Classification Keywords: F.4.1 Mathematical Logic and Formal Languages: Mathematical Logic (Model theory, Set theory); I.2.3 Artificial Intelligence: Deduction and Theorem Proving (Uncertainty, “fuzzy” and probabilistic reasoning); I.2.4 Artificial Intelligence: Knowledge Representation Formalisms and Methods (Predicate logic, Representation languages).

Link:

A GEOMETRICAL INTERPRETATION TO DEFINE CONTRADICTION DEGREES BETWEEN TWO FUZZY SETS

Carmen Torres, Elena Castiñeira, Susana Cubillo, Victoria Zarzosa

http://www.foibg.com/ijita/vol12/ijita12-2-p04.pdf

Abstract: Non-preemptive two-machine flow-shop scheduling problem with uncertain processing times of n jobs is studied. In an uncertain version of a scheduling problem, there may not exist a unique schedule that remains optimal for all possible realizations of the job processing times. We find necessary and sufficient conditions (Theorem 1) when there exists a dominant permutation that is optimal for all possible realizations of the job processing times. Our computational studies show the percentage of the problems solvable under these conditions for the cases of randomly generated instances with n ≤100 . We also show how to use additional information about the processing times of the completed jobs during optimal realization of a schedule (Theorems 2 – 4). Computational studies for randomly generated instances with n ≤ 50 show the percentage of the twomachine flow-shop scheduling problems solvable under the sufficient conditions given in Theorems 2 – 4.

Keywords: Scheduling, flow-shop, makespan, uncertainty.

ACM Classification Keywords: F.2.2 Non-numerical algorithms and problems: Sequencing and scheduling

Link:

REALIZATION OF AN OPTIMAL SCHEDULE FOR THE TWO-MACHINE FLOW-SHOP WITH INTERVAL JOB PROCESSING TIMES

Natalja Leshchenko, Yuri Sotskov

http://www.foibg.com/ijita/vol14/ijita14-2-p12.pdf

Abstract: Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The processing time ti of each operation i ∈V is known before solving problems SALBP-1 and SALBP-2. However, during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations V\V~ . Another subset V~ ⊆V includes manual operations, for which it is impossible to fix exact processing times during the whole life cycle of the assembly line. If j ∈V~, then operation times tj can differ for different cycles of the production process. For the optimal line balance b of the assembly line with operation times t1, t2, …, tn, we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j ∈V~.

Keywords: Scheduling, robustness and sensitivity analysis, assembly line.

ACM Classification Keywords: F.2.2 Nonnumerical algorithms and problems: Sequencing and scheduling.

Link:

RECENT RESULTS ON STABILITY ANALYSIS OF AN OPTIMAL ASSEMBLY LINE BALANCE

Yuri Sotskov

http://www.foibg.com/ijita/vol14/ijita14-2-p11.pdf

Abstract: We propose the adaptive algorithm for solving a set of similar scheduling problems using learning technology. It is devised to combine the merits of an exact algorithm based on the mixed graph model and heuristics oriented on the real-world scheduling problems. The former may ensure high quality of the solution by means of an implicit exhausting enumeration of the feasible schedules. The latter may be developed for certain type of problems using their peculiarities. The main idea of the learning technology is to produce effective (in performance measure) and efficient (in computational time) heuristics by adapting local decisions for the scheduling problems under consideration. Adaptation is realized at the stage of learning while solving a set of sample scheduling problems using a branch-and-bound algorithm and structuring knowledge using pattern recognition apparatus.

Keywords: Scheduling, mixed graph, learning, pattern recognition.

ACM Classification Keywords: F.2.2 Nonnumerical algorithms and problems: sequencing and scheduling.

Link:

LEARNING TECHNOLOGY IN SCHEDULING BASED ON THE MIXED GRAPHS

Yuri Sotskov, Nadezhda Sotskova, Leonid Rudoi

http://www.foibg.com/ijita/vol12/ijita12-4-p12.pdf

Abstract: This paper presents an analysis of different techniques that is designed to aid a researcher in determining which of the classification techniques would be most appropriate to choose the ridge, robust and linear regression methods for predicting outcomes for specific quasi-stationary process.

Keywords: classification techniques, neural network, composite classifier

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems

Link:

SELECTING CLASSIFIERS TECHNIQUES FOR OUTCOME PREDICTION USING NEURAL NETWORKS APPROACH

Tatiana Shatovskaya

http://www.foibg.com/ijita/vol14/ijita14-3-p15.pdf

Abstract: Let V be an array. The range query problem concerns the design of data structures for implementing the following operations. The operation update(j,x) has the effect v v x j j ← + , and the query operation retrieve(i,j) returns the partial sum i j v +K+ v . These tasks are to be performed on-line. We define an algebraic model – based on the use of matrices – for the study of the problem. In this paper we establish as well a lower bound for the sum of the average complexity of both kinds of operations, and demonstrate that this lower bound is near optimal – in terms of asymptotic complexity.

Keywords: zero-one matrices, lower bounds, matrix equations

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems

Link:

MATRICIAL MODEL FOR THE STUDY OF LOWER BOUNDS

Jose Joaquin Erviti, Adriana Toni

http://www.foibg.com/ijita/vol13/ijita13-1-p09.pdf

Abstract: In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in Evtushenko, 1997 and spatial central finite difference with diagonally implicit Runge-Kutta? method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Keywords: Distributed control problems, Second order parabolic heat equation, Runge-Kutta? method, CGM.

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems; G.4 Mathematical Software

Link:

OPTIMAL CONTROL OF A SECOND ORDER PARABOLIC HEAT EQUATION

Mahmoud Farag, Mainouna Al-Manthari?

http://www.foibg.com/ijita/vol13/ijita13-3-p03.pdf

Abstract: In data mining, efforts have focused on finding methods for efficient and effective cluster analysis in large databases. Active themes of research focus on the scalability of clustering methods, the effectiveness of methods for clustering complex shapes and types of data, high-dimensional clustering techniques, and methods for clustering mixed numerical and categorical data in large databases. One of the most accuracy approach based on dynamic modeling of cluster similarity is called Chameleon. In this paper we present a modified hierarchical clustering algorithm that used the main idea of Chameleon and the effectiveness of suggested approach will be demonstrated by the experimental results.

Keywords: Chameleon, clustering, hypergraph partitioning, coarsening hypergraph.

ACM Classification Keywords F.2.1 Numerical Algorithms and Problems

Link:

THE NEW SOFTWARE PACKAGE FOR DYNAMIC HIERARCHICAL CLUSTERING FOR CIRCLES TYPES OF SHAPES

Tetyana Shatovska, Tetiana Safonova, Iurii Tarasov

http://www.foibg.com/ijita/vol15/ijita15-2-p13.pdf

Abstract: Presented is webComputing – a general framework of mathematically oriented services including remote access to hardware and software resources for mathematical computations, and web interface to dynamic interactive computations and visualization in a diversity of contexts: mathematical research and engineering, computer-aided mathematical/technical education and distance learning. webComputing builds on the innovative webMathematica technology connecting technical computing system Mathematica to a web server and providing tools for building dynamic and interactive web-interface to Mathematica-based functionality. Discussed are the conception and some of the major components of webComputing service: Scientific Visualization, Domain- Specific Computations, Interactive Education, and Authoring of Interactive Pages.

Keywords: web-access, mathematical user-interfaces, web computations, mathematical active learning.

ACM Classification Keywords: F.1.2 Modes of Computation: interactive computation, online computation; G.4 Mathematical Software: user interfaces; K.3.1 Computer Use in Education: distance learning.

Link:

WEBCOMPUTING SERVICE FRAMEWORK

Evgenija Popova

http://www.foibg.com/ijita/vol13/ijita13-3-p08.pdf

Abstract: This paper is focused on a parallel JAVA implementation of a processor defined in a Network of Evolutionary Processors. Processor description is based on JDom, which provides a complete, Java-based solution for accessing, manipulating, and outputting XML data from Java code. Communication among different processor to obtain a fully functional simulation of a Network of Evolutionary Processors will be treated in future. A safe-thread model of processors performs all parallel operations such as rules and filters. A non-deterministic behavior of processors is achieved with a thread for each rule and for each filter (input and output). Different results of a processor evolution are shown.

Keywords: Networks of Evolutionary Processors, Membrane Systems, Natural Computation.

ACM Classification Keywords: F.1.2 Modes of Computation, I.6.1 Simulation Theory, H.1.1 Systems and Information Theory

Link:

NETWORKS OF EVOLUTIONARY PROCESSORS: JAVA IMPLEMENTATION OF A THREADED PROCESSOR1

Miguel Angel Díaz, Luis Fernando de Mingo López, Nuria Gómez Blas

http://www.foibg.com/ijita/vol15/ijita15-1-p06.pdf

Abstract: This paper presents the application of Networks of Evolutionary Processors to Decision Support Systems, precisely Knowledge-Driven? DSS. Symbolic information and rule-based behavior in Networks of Evolutionary Processors turn out to be a great tool to obtain decisions based on objects present in the network. The non-deterministic and massive parallel way of operation results in NP-problem solving in linear time. A working NEP example is shown.

Keywords: Natural Computing, Networks of Evolutionary Processors, Decision Support Systems.

ACM Classification Keywords: F.1.2 Modes of Computation, I.6.1 Simulation Theory, H.1.1 Systems and Information Theory.

Link:

NETWORKS OF EVOLUTIONARY PROCESSORS (NEP) AS DECISION SUPPORT SYSTEMS1

Nuria Gómez Blas, Miguel Angel Díaz, Juan Castellanos, Francisco Serradilla

http://www.foibg.com/ijita/vol15/ijita15-1-p05.pdf

Abstract: Transition P Systems are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of evolution rules. But, to establish the rules to be applied, it is required the previous calculation of useful, applicable and active rules. Hence, computation of useful evolution rules is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. This work defines usefulness states through an exhaustive analysis of the P system for every membrane and for every possible configuration of the membrane structure during the computation. Moreover, this analysis can be done in a static way; therefore membranes only have to check their usefulness states to obtain their set of useful rules during execution.

Keywords: Evolution Rules, Usefulness States, Transition P System, Sequential Machines, Static Analysis

ACM Classification Keywords: F.1.1 Computation by abstract devices – Models of computation. D.1.m Miscellaneous – Natural Computing

Link:

STATIC ANALYSIS OF USEFULNESS STATES IN TRANSITION P SYSTEMS

Juan Alberto Frutos, Luis Fernandez, Fernando Arroyo, Gines Bravo

http://www.foibg.com/ijitk/ijitk-vol02/ijitk02-1-p10.pdf

Abstract: Special generalizing for the artificial neural nets: so called RFT – FN – is under discussion in the report. Such refinement touch upon the constituent elements for the conception of artificial neural network, namely, the choice of main primary functional elements in the net, the way to connect them(topology) and the structure of the net as a whole. As to the last, the structure of the functional net proposed is determined dynamically just in the constructing the net by itself by the special recurrent procedure. The number of newly joining primary functional elements, the topology of its connecting and tuning of the primary elements is the content of the each recurrent step. The procedure is terminated under fulfilling “natural” criteria relating residuals for example. The functional proposed can be used in solving the approximation problem for the functions, represented by its observations, for classifying and clustering, pattern recognition, etc. Recurrent procedure provide for the versatile optimizing possibilities: as on the each step of the procedure and wholly: by the choice of the newly joining elements, topology, by the affine transformations if input and intermediate coordinate as well as by its nonlinear coordinate wise transformations. All considerations are essentially based, constructively and evidently represented by the means of the Generalized Inverse.

Keywords: Artificial neural network, approximating problem, beam dynamics with delay, optimization.

ACM Classification keywords:F.1.1.Models of Computation: Self modifying machines(neural networks; G.1.6. Optimization; H.1.m. Models and principles; I.2.6. Artificial Intelligence: learning, connectionism and neural nets.

Link:

GENERALIZING OF NEURAL NETS: FUNCTIONAL NETS OF SPECIAL TYPE

Volodymyr Donchenko, Mykola Kirichenko, Yuriy Krivonos

http://www.foibg.com/ijita/vol14/ijita14-3-p10.pdf

Abstract: We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

Keywords: system of the linear Diophantine equations, set of the basis solutions, outputless finite state automaton.

ACM Classification Keywords: F.1.1 Models of Computation - finite automata, systems of linear Diophantine constraints

Link:

AUTOMATA–BASED METHOD FOR SOLVING SYSTEMS OF LINEAR CONSTRAINTS IN {0,1}

Sergey Krivoi, Lyudmila Matvyeyeva, Wioletta Grzywacz

http://www.foibg.com/ijita/vol12/ijita12-4-p10.pdf

Abstract: This paper presents some connectionist models that are widely used to solve NP-problems. Most well known numeric models are Neural Networks that are able to approximate any function or classify any pattern set provided numeric information is injected into the net. Neural Nets usually have a supervised or unsupervised learning stage in order to perform desired response. Concerning symbolic information new research area has been developed, inspired by George Paun, called Membrane Systems. A step forward, in a similar Neural Network architecture, was done to obtain Networks of Evolutionary Processors (NEP). A NEP is a set of processors connected by a graph, each processor only deals with symbolic information using rules. In short, objects in processors can evolve and pass through processors until a stable configuration is reach. This paper just shows some ideas about these two models.

Keywords: Natural Computation, Membrane Systems, Neural Networks, Networks of Evolutionary Processors.

ACM Classification Keywords: F.1.1 Models of Computation: Self-modifying machines (neural networks); F.4.1 Mathematical Logic: Computational logic

Link:

FILTERED NETWORKS OF EVOLUTIONARY PROCESSORS*

Luis Fernando de Mingo López, Eugenio Santos Menéndez,Francisco Gisbert

http://www.foibg.com/ijita/vol12/ijita12-1-p01.pdf

Abstract: Signal processing is an important topic in technological research today. In the areas of nonlinear dynamics search, the endeavor to control or order chaos is an issue that has received increasing attention over the last few years. Increasing interest in neural networks composed of simple processing elements (neurons) has led to widespread use of such networks to control dynamic systems learning. This paper presents backpropagation-based neural network architecture that can be used as a controller to stabilize unsteady periodic orbits. It also presents a neural network-based method for transferring the dynamics among attractors, leading to more efficient system control. The procedure can be applied to every point of the basin, no matter how far away from the attractor they are. Finally, this paper shows how two mixed chaotic signals can be controlled using a backpropagation neural network as a filter to separate and control both signals at the same time. The neural network provides more effective control, overcoming the problems that arise with control feedback methods. Control is more effective because it can be applied to the system at any point, even if it is moving away from the target state, which prevents waiting times. Also control can be applied even if there is little information about the system and remains stable longer even in the presence of random dynamic noise.

Keywords: Neural Network, Backpropagation, Chaotic Dynamic Systems, Control Feedback Methods.

ACM Classification Keywords: F.1.1 Models of Computation: Self-modifying machines (neural networks); F.1.2 Modes of Computation: Alternation and nondeterminism; G.1.7 Ordinary Differential Equations: Chaotic systems; G.3 Probability and Statistics: Stochastic processes

Link:

NEURAL CONTROL OF CHAOS AND APLICATIONS

Cristina Hernández, Juan Castellanos, Rafael Gonzalo, Valentín Palencia

http://www.foibg.com/ijita/vol12/ijita12-2-p01.pdf

Abstract: An important task for a direct mailing company is to detect potential customers in order to avoid unnecessary and unwanted mailing. This paper describes a non-linear method to predict profiles of potential customers using dARTMAP, ARTMAP-IC, and Fuzzy ARTMAP neural networks. The paper discusses advantages of the proposed approaches over similar techniques based on MLP neural networks.

Keywords: ARTMAP, neural networks, data mining

ACM Classification Keywords: F.1.1 Models of Computation - neural networks, H.2.8 Database Applications -data mining.

Link:

SOLVING A DIRECT MARKETING PROBLEM BY THREE TYPES OF ARTMAP NEURAL NETWORKS

Anatoli Nachev

http://www.foibg.com/ijita/vol15/ijita15-1-p10.pdf