Shows that signal quantization can be conveniently captured and quantified in the language of information granules. Optimal codebooks exploited in any signal quantization (discretization) lend themselves to the underlying fundamental issues of information granulation. The paper elaborates on and contrasts between various forms of information granulation such as set theory, shadowed sets, and fuzzy sets. It is revealed that a set‐based codebook can be easily enhanced by the use of the shadowed sets. This also raises awareness about the performance of the quantization process and helps increase its quality by defining additional elements of the codebook and specifying their range of applicability. We show how different information granules contribute to the performance of signal quantification. The role of clustering techniques giving rise to information granules is also analyzed. Some pertinent theoretical results are derived. It is shown that fuzzy sets defined in terms of piecewise linear membership functions with 1 / 2 overlap between any two adjacent terms of the codebook give rise to the effect of lossless quantization. The study addresses both scalar and multivariable quantization. Numerical studies are included to help illustrate the quantization mechanisms carried out in the setting of granular computing.
We introduce and study a new concept of fuzzy computing units. This construct is is aimed at coping with "negative" (inhibitory) information and accommodating it in the language of fuzzy sets. The essential concept developed in this study deals with computing units exploiting the concept of balanced fuzzy sets. We recall how the membership notion of fuzzy sets can be extended to the [-1,1] range giving rise to balanced fuzzy sets and then summarize properties of augmented (extended) logic operations for these constructs. We show that this idea is particularly appealing in neurocomputing as the "negative" information captured through balanced fuzzy sets exhibits a straightforward correspondence with inhibitory processing mechanisms encountered in neural networks. This gives rise to interesting properties of balanced computing units when compared with fuzzy and logic neurons developed on the basis of classical logic and classical fuzzy sets. Illustrative examples concerning topologies and properties and learning of balanced fuzzy computing units are included. A number of illustrative examples concerning topologies, properties and learning of balanced fuzzy fuzzy computing units are included.
As an effective way for knowledge representation and processing, fuzzy rule-based models have been extensively studied and widely used in practice. In many circumstances, a very limited amount of data or insufficient computational resources make the construction of accurate models a genuine challenge. In this study, a granular augmentation of fuzzy rule-based models is proposed with intent to realize knowledge transfer in system modeling. This research mainly focuses on how to effectively exploit the existing fuzzy model, which has been constructed on extensive previously acquired experimental evidence and could be regarded as source of knowledge, in a new environment where only very limited experimental evidence is available. Rather than constructing a new model from scratch, knowledge conveyed by the existing model could be retained and reused in the target domain. The originality and innovation of this study lies in the adaption of the existing model to the new environment through optimal allocation of information granularity to produce granular fuzzy models, which are more abstract and general than the original numeric constructs. The granular fuzzy models yield results in a granular form whose quality is evaluated using the coverage and specificity criteria.
In this study, we elaborate on an important issue of membership function determination. The main point is that any membership estimation procedure should reconcile the semantics of a fuzzy set (regarded as an information granule arising at some level of information abstraction) with the experimental evidence conveyed by numeric data. This, in the sequel, calls for the development of the hybrid two-phase approach that starts from a rough specification of the support of the fuzzy set that is followed by detailed computations involving a specific type of membership function and an estimation of its parameters. The role of robust statistics in this setting is also raised. A number of experimental results are discussed.
In automated test pattern generation (ATPG), test patterns are automatically generated and tested against all specific modeled faults. In this work, three optimization algorithms, namely: genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE), were studied for the purpose of generating optimized test sequence sets. Furthermore, this paper investigated the broad use of evolutionary algorithms and swarm intelligence in automated test pattern generation to expand the analysis of the subject. The obtained experimental results demonstrated the improvement in terms of testing time, number of test vectors, and fault coverage compared with previous optimization-based test generators. In addition, the experiments highlight the weakness of each optimization algorithm in the test pattern generation (TPG) and offer some constructive methods of improvement. We present several recommendations and guidelines regarding the use of optimization algorithms as test pattern generators to improve the performance and increase their efficiency.
