Publications

Fuzzy models are regarded as numeric constructs and as such are optimized and evaluated at the numeric level. In this study, we depart from this commonly accepted position and propose a granular evaluation of fuzzy models and present an augmentation of fuzzy models by forming information granules around numeric values of the parameters and constructions of the models. The concepts and algorithms of granular fuzzy models are discussed in the setting of Takagi-Sugeno rule-based architectures. We show how different protocols of forming and allocating information granules lead to the improvement of the granular performance of the models. Different from the standard numeric performance measure of fuzzy models coming in the form of the root mean squared error index, two performance measures are introduced that are pertinent to granular constructs, namely coverage and specificity. Furthermore, we propose a global indicator implied by these two measures, called an area under the curve, being computed for the characteristics of the granular model expressed in the coverage-specificity coordinates. A series of experimental studies is reported, which offers a comprehensive overview of the introduced performance measure criteria as well as the underlying realization of the granular fuzzy models.

Knowledge discovery through spatial and temporal aspects of data related to occurrences of events has many applications in digital forensics. Specifically, in electronic surveillance, it is helpful to construct a timeline to analyze information. The existing techniques only analyze the occurrence and co-occurrence of events; however, in general, there are three aspects of events: occurrences (and co-occurrences), nonoccurrences, and uncertainty of occurrences/non-occurrences with respect to spatial and temporal aspects of data. These three aspects of events have to be considered to better analyze periodicity and predict future events. This study focuses on the spatial and temporal aspects given in intuitionistic fuzzy (IF) datasets using the granular computing (GrC) paradigm; formal concept analysis (FCA) was used to understand the granularity of data. The originality of the proposed approach is to discover the periodicity of events data given in IF sets through FCA and the GrC paradigm that helps to predict future events. An experimental evaluation was also performed to understand the applicability of the proposed methodology.

S.294-296

The concept of fuzzy information becomes a cornerstone of processing and handling linguistic data. As opposed to processing of numeric information where there is a wealth of advanced methods, by entering the area of linguistic information processing we are immediately faced with a genuine need to revisit the fundamental concepts. We first review a notion of information granularity as a primordial concept playing a key role in human cognition. Dwelling on that, the study embarks on the concept of interacting at the level of fuzzy sets. In particular, we discuss a basic construct of a fuzzy communication channel. The ideas of communication exploiting fuzzy information call for its efficient encoding and decoding that subsequently leads to minimal losses of transmitted information. Interestingly enough, the incurred losses depend heavily on the granularity of the linguistic information involved – in this way one can take advantage of the uncertainty residing within the transmitted information granules and exploit it in the design of the corresponding channel.

Initialization of neuron weights is one of key problems in artificial neural networks (ANNs). This problem is particularly important in ANNs implemented as Application Specific Integrated Circuits (ASICs), where the number of the weights becomes large. When ANNs are implemented in software, the weights can be easily programmed. In contrast, in parallel systems of this type realized as ASICs it is necessary to provide programming and addressing lines to each weight that causes a large increase in the complexity of such designs. In this paper we present investigations that demonstrate that Self-Organizing Maps (SOMs) in many situations may be trained without the initialization (with zeroed weights). We present example results of several thousands simulations for different topologies of the SOM, for different neighborhood functions and two distance measures between the learning patterns and particular neurons in the input data space. Simulations were performed for zero initial values, for small values (up to 1 % of full scale range) and for neurons randomly distributed over the overall input data space. The results are comparable that allows to reduce the complexity of the SOM implemented in the CMOS technology.

This chapter elaborates on the connections and interdisciplinary links between knowledge discovery in databases (KDD) and neural networks and neurocomputing, in general. We identify a number of basic categories of synergistic links existing therein. We show that data mining can benefit from the learning abilities of neural networks. Similarly, there are ways in which data mining can augment the research agenda of neurocomputing by drawing attention to the issues of processing large data sets and identifying possible ways of learning enhancement through data granulation. The aspect of increased transparency of neural networks is another essential topic promoted by KDD.