Application of self-organising maps for data mining with incomplete data sets

Self-organising maps (SOM) have become a commonly-used cluster analysis technique in data mining. However, SOM are not able to process incomplete data. To build more capability of data mining for SOM, this study proposes an SOM-based fuzzy map model for data mining with incomplete data sets. Using this model, incomplete data are translated into fuzzy data, and are used to generate fuzzy observations. These fuzzy observations, along with observations without missing values, are then used to train the SOM to generate fuzzy maps. Compared with the standard SOM approach, fuzzy maps generated by the proposed method can provide more information for knowledge discovery.     

User profiles and fuzzy logic for web retrieval issues

 We present a study of the role of user profiles using fuzzy logic in web retrieval processes. Flexibility for user interaction and for adaptation in profile construction becomes an important issue. We focus our study on user profiles, including creation, modification, storage, clustering and interpretation. We also consider the role of fuzzy logic and other soft computing techniques to improve user profiles. Extended profiles contain additional information related to the user that can be used to personalize and customize the retrieval process as well as the web site. Web mining processes can be carried out by means of fuzzy clustering of these extended profiles and fuzzy rule construction. Fuzzy inference can be used in order to modify queries and extract knowledge from profiles with marketing purposes within a web framework. An architecture of a portal that could support web mining technology is also presented.     

On fuzzy equality and approximation in fuzzy logic

The paper is a contribution to the theory of fuzzy logic in narrow sense with evaluated syntax (FLn). We show that the concepts of fuzzy equality and the provability degree enable to generalize the concept of fuzzy approximation. In the second part of the paper we return to the Mamdani-Assilian formula, which is formed on the basis of the so called totally bounded fuzzy equality and using which we can approximate any function with the prescribed accuracy.This paper has been supported by Grant A1187901/99 of the GA AV R and the project VS96037 of MMT of the Czech Republic.     

Formulation of qualitative models using fuzzy logic

Formulation of qualitative models for complex decision problems exhibiting less structure, more imprecision and uncertainty is not adequately addressed in DSS research. Typical characteristics and requirements of such problems prohibit the development of DSS using knowledge based system development methodologies. This paper presents a methodology for formulation of qualitative models using fuzzy logic to handle the imprecision and uncertainty in the problem domain. The problem domain, in this methodology, is represented using problem-solving knowledge, environmental knowledge, and control knowledge components. A high level non-procedural language for representing these components of knowledge is illustrated using a project selection and resource allocation problem. The paper also describes the implementation of a prototype decision support environment based on this methodology.     

Determination of travertine provenance from ancient buildings using self-organizing maps and fuzzy logic

This work is focused on determining provenance of travertine stones employed in the construction of some important monuments in Umbria (Italy) using two systems that use concepts and algorithms inherent to Artificial Intelligence: Kohonen self-organizing maps and fuzzy logic. The two systems have been applied to travertine samples belonging to quarries known to be sites of excavation from ancient times and monuments. Tests on quarry samples show a good discriminative power of both methods to recognize the exact provenance of most samples. The application of the systems to monument samples show that most of employed travertine stones were quarried from outcrops occurring in areas close to the towns where monuments have been erected. Results are in good agreement with historical data.     

Assessing airborne transmission of foot and mouth disease using fuzzy logic

In case of an outbreak of foot and mouth disease, the prediction of airborne spread is an important tool for decision-makers to assess the potential risk of secondary infections. Modelling approaches such as the Gaussian dispersion or Lagrangian particle model have been established but are complex to use and the structure of the models is fixed rather than adjustable to emerging disease situations. The aim of the present study was to evaluate the application of fuzzy logic as a modelling technique based on linguistic variables. Fuzzy logic models are easy to use and to modify. Adaptations to emerging outbreaks seem feasible. Using the Gaussian dispersion model as a reference, livestock-specific fuzzy logic models were developed. In a stepwise modelling process, the input parameters of the Gaussian model were added one-by-one into the fuzzy models. On the basis of weather data and randomly allocated farms, a validation dataset with 10,000 observations was generated and used in a 10-fold cross validation to compare the two modelling approaches. A good agreement between the Gaussian dispersion and the fuzzy logic models concerning the main directions of virus spread were found. The measure of agreement ranged between 87.0% and 99.9%. Falsely classified observations occurred mostly in proximity to the boundary of virus transmission based on the Gaussian dispersion model. In conclusion, fuzzy logic determined the same risk of infection for secondary cases than the Gaussian dispersion model. Limitations to certain livestock were not observed. The inclusion of up to four input variables did not influence the results in a mentionable amount. Including additional input variables into the fuzzy models could improve its application in assessing the risk of airborne foot and mouth disease transmission furthermore.     

A note on congruence permutability and fuzzy logic

We study congruence permutability of algebras with fuzzy equalities. The notion of degree of congruence permutability naturally arises in this context. We present a Mal'cev-like characterization of congruence permutable varieties of algebras with fuzzy equalities. Our note presents a way to generalize various congruence conditions from the point of view of fuzzy logic.     

An efficient posture recognition method using fuzzy logic

Computer-human interaction plays an important role in virtual reality. Glove-based input devices have many desirable features which make direct interactions between the user and the virtual world possible. However, due to the complexity of the human hand, recognising hand functions precisely and efficiently is not an easy task. Existing algorithms are either imprecise or computationally expensive, making them impractical to integrate with VR applications, which are usually very CPU intensive.In the problem of posture and gesture recognition, both the sample patterns stored in the database and the ones to be recognised may be imprecise. This kind of imprecise knowledge can be best dealt with using fuzzy logic. A fast and simple posture recognition method using fuzzy logic is presented in this paper. Our model consists of three components: the posture database, the classifier and the identifier. The classifier roughly classifies the sample postures before they are put into the posture database. The identifier compares an input posture with the records in the identified class and finds the right match efficiently. Fuzzy logic is applied in both the classification and identification processes to cope with imprecise data. The main goal of this method is to recognise hand functions in an accurate and efficient manner. The accuracy, efficiency and the noise tolerance of the model have been examined through a number of experiments.     

Simplifying the automatic design of a fuzzy logic controller using evolutionary programming

With the availability of a wide range of Evolutionary Algorithms such as Genetic Algorithms, Evolutionary Programming, Evolutionary Strategies and Differential Evolution, every conceivable aspect of the design of a fuzzy logic controller has been optimized and automated. Although there is no doubt that these automated techniques can produce an optimal fuzzy logic controller, the structure of such a controller is often obscure and in many cases these optimizations are simply not needed. We believe that the automatic design of a fuzzy logic controller can be simplified by using a generic rule base such as the MacVicar-Whelan rule base and using an evolutionary algorithm to optimize only the membership functions of the fuzzy sets. Furthermore, by restricting the overlapping of fuzzy sets, using triangular membership functions and singletons, and reducing the number of parameters to represent the membership functions, the design can be further simplified. This paper describes this method of simplifying the design and some experiments performed to ascertain its validity.     

Smoothly distributed fuzzy c-means: a new self-organizing map

This paper presents a new self-organizing map algorithm. Unlike the well-known method of Kohonen, the new algorithm corresponds to the optimization of an unambiguously defined cost function. It consists of a modified version of the widely used fuzzy c-means functional, where the code vectors are distributed on a regular low-dimensional grid, and a penalization term is added in order to guarantee a smooth distribution for the values of the code vectors on the grid. The mapping properties of the new method, similar to those of Kohonen's algorithm, are illustrated with several data sets. Computer programs (source code and executables) and data are available upon request to the authors.     

About axiomatic systems of product fuzzy logic

 This short paper has two goals. The first is to show a new axiomatic system of product fuzzy logic with only one non-BL axiom which has only two variables. The second goal is to prove that there cannot be any axiomatic system of the product fuzzy logic with single non-BL axiom with only one variable.     

Content-based image collection summarization and comparison using self-organizing maps

Progresses made on content-based image retrieval have reactivated the research on image analysis and a number of similarity-based methods have been established to assess the similarity between images. In this paper, the content-based approach is extended towards the problem of image collection summarization and comparison. For these purposes we propose to carry out clustering analysis on visual features using self-organizing maps, and then evaluate their similarity using a few dissimilarity measures implemented on the feature maps. The effectiveness of these dissimilarity measures is then examined with an empirical study.     

Fuzzy operator logic and fuzzy resolution

There have been only few attempts to extend fuzzy logic to automated theorem proving. In particular, the applicability of the resolution principle to fuzzy logic has been little examined. The approaches that have been suggested in the literature, however, have made some semantic assumptions which resulted in limitations and inflexibilities of the inference mechanism. In this paper we present a new approach to fuzzy logic and reasoning under uncertainty using the resolution principle based on a new operator, the fuzzy operator. We present the fuzzy resolution principle for this logic and show its completeness as an inference rule.     

Extracting linguistic rules from data sets using fuzzy logic and genetic algorithms

Linguistic rules in natural language are useful and consistent with human way of thinking. They are very important in multi-criteria decision making due to their interpretability. In this paper, our discussions concentrate on extracting linguistic rules from data sets. In the end, we firstly analyze how to extract complex linguistic data summaries based on fuzzy logic. Then, we formalize linguistic rules based on complex linguistic data summaries, in which, the degree of confidence of linguistic rules from a data set can be explained by linguistic quantifiers and its linguistic truth from the fuzzy logical point of view. In order to obtain a linguistic rule with a higher degree of linguistic truth, a genetic algorithm is used to optimize the number and parameters of membership functions of linguistic values. Computational results show that the proposed method is an alternative method for extracting linguistic rules with linguistic truth from data sets.     

Infrared and visible image fusion using fuzzy logic and population-based optimization

This paper presents a new wavelet-based algorithm for the fusion of spatially registered infrared and visible images. Wavelet-based image fusion is the most common fusion method, which fuses the information from the source images in the wavelet transform domain according to some fusion rules. We specifically propose new fusion rules for fusion of low and high frequency wavelet coefficients of the source images in the second step of the wavelet-based image fusion algorithm. First, the source images are decomposed using dual-tree discrete wavelet transform (DT-DWT). Then, a fuzzy-based approach is used to fuse high frequency wavelet coefficients of the IR and visible images. Particularly, fuzzy logic is used to integrate the outputs of three different fusion rules (weighted averaging, selection using pixel-based decision map (PDM), and selection using region-based decision map (RDM)), based on a dissimilarity measure of the source images. The objective is to utilize the advantages of previous pixel- and region-based methods in a single scheme. The PDM is obtained based on local activity measurement in the DT-DWT domain of the source images. A new segmentation-based algorithm is also proposed to generate the RDM using the PDM. In addition, a new optimization-based approach using population-based optimization is proposed for the low frequency fusion rule instead of simple averaging. After fusing low and high frequency wavelet coefficients of the source images, the final fused image is obtained using the inverse DT-DWT. This new method provides improved subjective and objectives results as compared to previous image fusion methods.     

Robust adaptive fuzzy logic power system stabilizer

This paper introduces a robust adaptive fuzzy controller as a power system stabilizer (RFPSS) used to damp inter-area modes of oscillation following disturbances in power systems. In contrast to the IEEE standard multi-band power system stabilizer (MB-PSS), robust adaptive fuzzy-based stabilizers are more efficient because they cope with oscillations at different operating points. The proposed controller adopts a dynamic inversion approach. Since feedback linearization is practically imperfect, components that ensure robust and adaptive performance are included in the control law to compensate for modelling errors and achieve acceptable tracking errors. Two fuzzy systems are implemented. The first system models the nominal values of the system’s nonlinearities. The second system is an adaptive one that compensates for modelling errors. A feedback linearization-based control law is implemented using the identified model. The gains of the controller are tuned via a particle swarm optimization routine to ensure system stability and minimum sum of the squares of the speed deviations. A bench-mark problem of a 4-machine 2-area power system is used to demonstrate the performance of the proposed controller and to show its superiority over other conventional stabilizers used in the literature.     

Decision making support system for house purchase by using fuzzy logic

In this paper, we suggest a decision making support system for house purchasers, using fuzzy inference and hierarchic structure of evaluation. Main part of this system consist of macro and micro evaluation. Essential factors are taken into account in macro evaluation, and unessential detailed factors are considered later in micro evaluation. By adopting this structure, many decision makers could get their most suitable result.     

Heuristic on-line tuning for nonlinear model predictive controllers using fuzzy logic

In this paper a systematic mechanism for on-line tuning of the non-linear model predictive controllers is presented. The proposed method automatically adjusts the prediction horizon P, the diagonal elements of the input weight matrix Λ, and the diagonal elements of the output weight matrix Γ for the sake of good performance. The desired good performance is cast as a time-domain specification. The control horizon (M) is left constant because of the importance of its relative value with respect to P. The concepts from fuzzy logic are used in designing the tuning algorithm. In the mechanism considered here, predefined fuzzy rules represent available tuning guidelines and the performance violation measure in the form of fuzzy sets determine the new tuning parameter values Therefore, the tuning algorithm is formulated as a simple and straightforward mechanism, which makes it more appealing for on-line implementation. The effectiveness of the proposed tuning method is tested through simulated implementation on three non-linear process examples. Two of these examples possess open-loop unstable dynamics. The result of the simulations shows that this method is successful and promising.     

Microcalcification detection using fuzzy logic and scale space approaches

Breast cancer is one of the leading causes of women mortality in the world. Since the causes are unknown, breast cancer cannot be prevented. It is difficult for radiologists to provide both accurate and uniform evaluation over the enormous number of mammograms generated in widespread screening. Computer-aided mammography diagnosis is an important and challenging task. Microcalcifications and masses are the early signs of breast carcinomas and their detection is one of the key issues for breast cancer control. In this study, a novel approach to microcalcification detection based on fuzzy logic and scale space techniques is presented. First, we employ fuzzy entropy principal and fuzzy set theory to fuzzify the images. Then, we enhance the fuzzified image. Finally, scale-space and Laplacian-of-Gaussian filter techniques are used to detect the sizes and locations of microcalcifications. A free-response operating characteristic curve is used to evaluate the performance. The major advantage of the proposed method is its ability to detect microcalcifications even in the mammograms of very dense breasts. A data set of 40 mammograms (Nijmegen database) containing 105 clusters of microcalcifications is studied. Experimental results demonstrate that the microcalcifications can be accurately and efficiently detected using the proposed approach. It can produce lower false positives and false negatives than the existing methods.