Information granules are generic building blocks supporting the processing realized in granular computing and facilitating communication with the environment. In this paper, we are concerned with a fundamental problem of encoding-decoding of information granules. The essence of the problem is outlined as follows: given a finite collection of granular data X1, X2,...,XN (sets, fuzzy sets, etc.), construct an optimal codebook composed of information granules A 1, A2, ..., Ac, where typically c <;<; N, so that any Xk represented in terms of A i's and then decoded (reconstructed) with the help of this codebook leads to the lowest decoding error. A fundamental result is established, which states that in the proposed encoders and decoders, when encoding-decoding error is present, the information granule coming as a result of decoding is of a higher type than the original information granules (say, if Xk is information granule of type-1, then its decoded version becomes information granule of type-2). It would be beneficial to note that as the encoding-decoding process is not lossless (in general, with an exception of a few special cases), the lossy nature of the method is emphasized by the emergence of information granules of higher type (in comparison with the original data being processed). For instance, when realizing encoding-decoding of numeric data (viz., information granules of type-0), the losses occur and they are quantified in terms of intervals, fuzzy sets, probabilities, rough sets, etc., where, in fact, the result becomes an information granule of type-1. In light of the nature of the constructed result when Xkis an interval or a fuzzy set, an optimized performance index engages a distance between the bounds of the interval-valued membership function. We develop decoding and encoding mechanisms by engaging the theory of possibility and fuzzy relational calculus and show that the decoded information granule is either a granular interval or interval-valued fuzzy set. The optimization mechanism is realized with the aid of the particle swarm optimization (PSO). A series of experiments are reported with intent to illustrate the details of the encoding-decoding mechanisms and show that the PSO algorithm can efficiently optimize the granular codebook.
We introduce a new model of fuzzy pattern recognition where data available about class membership are given implicitly rather than explicitly. While the explicit classification training set conveys complete details about class membership, the implicit format of classification lends itself to more synthetic forms of classification outcomes (such as those expressed in terms of similarities between some pairs of patterns). The relevant architectures are proposed along with the pertinent learning schemes. >
Abstract 1 In this paper, we survey the relationship between the similarity measure and dissimilarity measure for fuzzy sets. First, we design a similarity measure using a distance measure for fuzzy sets and prove its usefulness. From this result, we assert that the similarity between two complementary fuzzy sets satisfies the fuzzy entropy definition. We also show that the summation of the similarity and dissimilarity measures between two membership functions of fuzzy sets constitute all the information of the fuzzy set itself. We then extend our results to two data group fuzzy sets. Data similarity and dissimilarity measures between two fuzzy membership functions satisfy complementary. We also verify and discuss the characteristics of the relation between the similarity measure and dissimilarity measure with illustrative example.
In this study, we elaborate on a realization of fuzzy clustering and the construction of fuzzy rule-based models on the basis of vertically partitioned datasets in a privacy-preserving federated learning approach. The main focus of the overall design process is to construct a family of information granules (clusters) and the corresponding fuzzy rules in the presence of a collection of vertically partitioned datasets without compromising data privacy. These datasets are composed of the same data but are described by different features, and due to security considerations, data cannot be shared. The vertical federated fuzzy clustering can be realized as an iterative optimization process composed of successive cycles: 1) computation (update) of the prototypes and partition matrices performed on the basis of local datasets and 2) an integration of the local sources of knowledge carried out on a central coordinator-server. The update of the partition matrices can be completed using a distance-based or gradient-based approach. The communication of findings between local clients and the coordinator-server is realized through exchanging partition matrices, which are more general than numeric data and can avoid leakage of data privacy. Fuzzy models are optimized in a similar manner through exchanging the gradients of the performance index computed with respect to the parameters between the clients and the global coordinator. The proposed mechanism exhibits significant originality since the realization of fuzzy modeling in a vertical federated learning environment has not been studied. Experimental studies show that the proposed federated clustering and fuzzy model design could effectively reveal the structure of the entire dataset and achieve high performance compared with the results obtained in a centralized manner.
The contribution of this paper is the introduction of an abstract sensor-actuator pair to the subsumption architecture of robots introduced by Brooks (1987). The perceiving side of this pair derives from Gibson's (1979) affordance, which is a form of grasping of situations involving perceived objects. This study is part of a new form of evolutionary robotics called cognitive robotics. It considers a new context for a classical form of learning, namely, habitation. The inspiration for the form of affordances described in this paper comes from Heidegger's (1982) notion of the convergence of the concurrent activities of building, dwelling and thinking. In some sense, building and dwelling are at the threshhold of thinking. A brief description of the form and functioning of abstract S-A pairs is given.
This paper introduces neurogenetic controllers designed for small satellites. We introduce two main classes of neurogenetic control topologies that clearly unveil two different approaches toward the use of neurocomputing and evolutionary computing in many tasks of control engineering. The two main neurogenetic control architectures that are elaborated in this paper are gain scheduling and matrix feedback control with genetic training of the feedback matrix. A number of experiments were carried out in the context of control environment for small satellites.
Designing machine learning models followed by their deployment in a real-world environment has been an area of recent pursuits, resulting in a large number of successful applications. In particular, these applications target environments that call for a great deal of autonomy and criticality of the developed constructs and ensuing decision processes. An efficient design, carefully structured advanced architecture, high performance, and efficient learning methods are of paramount importance. Equally desired is the confidence of any result produced by the numeric model. In this study, we advocate that the associated information granularity of the numeric models and their results inherently link with the notion of specificity of information granularity. The confidence of results can be quantified in the form of an information granule where the two associated criteria of granular outcomes, such as coverage and specificity, are crucial to the holistic evaluation of the granularity of the results. It is shown that these two characteristics are conflicting and their quality becomes evaluated and optimized. Two main approaches are studied in depth. The first one concerns a granular embedding of numeric models. In the second one, we consider a synergistic environment of Gaussian process models whose results come as probabilistic information granules and can be transformed into interval information granules. An interesting architecture of a rule-based model constructed with the use of innovative clustering takes into account the generative-discriminative aspect of the process of structure discovery, which is accomplished through the optimization of some augmented objective functions. This model is investigated with regard to the two approaches to the design of the mechanism of granular assessment of results. Some illustrative examples are covered to show the essentials of the design process.
2 University of Alberta Multiplayer perceptrons or feed-forward networks are generally trained to represent functions or many-to-one (m-o) mappings. This creates a problem if the training data exhibits the property of many-to-many or almost many-many valued-ness because the model, which generated the data, was many-to-many. Therefore in this paper a modified feed-forward network and training algorithm is considered to represent a multi-valued mappings. The solution consists of adding another input to the standard feed-forward network and of modifying the training algorithm. This additional input will generally have no training values provided and an amended training algorithm is used to find its values. The modified feed-forward network and training method has been successfully applied both in representing the mapping implied by data generated by multivalued functions and in representing the mapping implied by data obtained from benchmark databases.
