In this study, we introduce a recent multicriteria decision theory concept of a new, generalized form of Choquet integral function and its application, in particular to the problem of face classification based on the aggregation of classifiers. Such function may be constructed by a simple replacement of the product used under the Choquet integral sign by any t-norm. This idea brings forward a broad class of aggregation operators, which can be incorporated into the decision-making theory. In this context, in a series of experiments we compare the most known t-norms and thoroughly examine their performance in the process of combining individual classifiers based either on facial regions or classic face recognition methods. Such kind of generalization can successfully improve the classification process provided that the parameters of the t-norms are carefully adjusted.
Fuzzy cognitive maps (FCMs) are convenient and widely used architectures for modeling dynamic systems, which are characterized by a great deal of flexibility and adaptability. Several recent works in this area concern strategies for the development of FCMs. Although a few fully automated algorithms to learn these models from data have been introduced, the resulting FCMs are structurally considerably different than those developed by human experts. In particular, maps that were learned from data are much denser (with the density over 90% versus about 40% density of maps developed by humans). The sparseness of the maps is associated with their interpretability: the smaller the number of connections is, the higher is the transparency of the map. To this end, a novel learning approach, sparse real-coded genetic algorithms (SRCGAs), to learn FCMs is proposed. The method utilizes a density parameter to guide the learning toward a formation of maps of a certain predefined density. Comparative tests carried out for both synthetic and real-world data demonstrate that, given a suitable density estimate, the SRCGA method significantly outperforms other state-of-the-art learning methods. When the density estimate is unknown, the new method can be used in an automated fashion using a default value, and it is still able to produce models whose performance exceeds or is equal to the performance of the models generated by other methods.
Fuzzy rule-based models (FRBMs) are sound constructs to describe complex systems. However, in reality, we may encounter situations, where the user or owner of a system only owns either the input or output data of that system (the other part could be owned by another user); and due to the consideration of data privacy, he/she could not obtain all the needed data to build the FRBMs. Since this type of situation has not been fully realized (noticed) and studied before, our objective is to come up with some strategy to address this challenge to meet the specific privacy consideration during the modeling process. In this study, the concept and algorithm of the collaborative fuzzy clustering (CFC) are applied to the identification of FRBMs, describing either multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) systems. The collaboration between input and output spaces based on their structural information (conveyed in terms of the corresponding partition matrices) makes it possible to build FRBMs when input and output data could not be collected and used in unison. Surprisingly, on top of this primary pursuit, with the collaboration mechanism the input and output spaces of a system are endowed with an innovative way to comprehensively share, exchange, and utilize the structural information between each other, which results in their more relevant structures that guarantee better model performance compared with performance produced by some state-of-the-art modeling strategies. The effectiveness of the proposed approach is demonstrated by experiments on a series of synthetic and publicly available datasets.
Neurofuzzy systems are computing architectures whose main features arise as an effect of an important synergy occurring between two fundamental facets of information processing such as fuzzy computing and neurocomputing. Their underpinning is in a complementary character of fuzzy sets and neural networks. The latter is oriented toward more numeric processing of massive data. On the other hand, fuzzy sets tend to address an important aspect of processing focused on the formation of information granules and their processing. We discuss various architectures and learning paradigms concentrating of many ways in which such essential symbiotic links between fuzzy sets and neurocomputing are established and exploited.
