We introduce and investigate a class of neural architectures of polynomial neural networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose topology is developed through learning; it is a self-organizing network. PNN has two kinds of networks, polynomial neuron-based and fuzzy polynomial neuron (FPN)-based networks, according to a polynomial structure. The essence of the design procedure of PN-based self-organizing polynomial neural networks(SOPNN) dwells on the group method of data handling. Each node of the SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN-based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulations involve a series of synthetic as well as experimental data used across various neuro-fuzzy systems. A detailed comparative analysis is also included.
The authors introduce and study the architecture of logic-based nets, which use two computational nodes realizing AND and OR logic operations. The resulting three-layer structure called the logic processor makes it possible to realize or approximate any scalar multivalued logic function. The variety of nonlinear characteristics computed for diverse norms made the logical concepts of the network attractive in studies on sensitivity (fault tolerance) and generalization capabilities. The three-layer structure is studied in problems of approximation of many-input one-output nonlinear functions. Learning schemes are developed and analyzed. A collection of logic processors can be used in knowledge acquisition schemes leading to a series of rules induced from empirical data sets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
The paper presents a model for hierarchical fuzzy controllers, which is a form of fuzzy gain scheduling. The underlying strategy in designing hierarchical fuzzy control systems is a selection of a global policy (global nonlinear control) based on a collection of local controllers that are solely developed with respect to "locally" linearized models of the system. A sample hierarchical fuzzy attitude control system for a specific class of small satellites is given.
The study is concerned with the fundamentals of granular computing. Granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (that embrace a number of individual entities) and their ensuing processing. We elaborate on the rationale behind granular computing. Next, a number of formal frameworks of information granulation are discussed including several alternatives such as fuzzy sets, interval analysis, rough sets, and probability. The notion of granularity itself is defined and quantified. A design agenda of granular computing is formulated and the key design problems are raised. A number of granular architectures are also discussed with an objective of delineating the fundamental algorithmic, and conceptual challenges. It is shown that the use of information granules of different size (granularity) lends itself to general pyramid architectures of information processing. The role of encoding and decoding mechanisms visible in this setting is also discussed in detail, along with some particular solutions. We raise an issue of interoperability of granular environments. The intent of the paper is to elaborate on the fundamentals and put the entire area in a certain perspective while not moving into specific algorithmic details.
In evolutionary computation, balancing the diversity and convergence of the population for multiobjective evolutionary algorithms (MOEAs) is one of the most challenging topics. Decomposition-based MOEAs are efficient for population diversity, especially when the branch partitions the objective space of multiobjective optimization problem (MOP) into a series of subspaces, and each subspace retains a set of solutions. However, a persisting challenge is how to strengthen the population convergence while maintaining diversity for decomposition-based MOEAs. To address this issue, we first define a novel metric to measure the contributions of subspaces to the population convergence. Then, we develop an adaptive strategy that allocates computational resources to each subspace according to their contributions to the population. Based on the above two strategies, we design an objective space partition-based adaptive MOEA, called OPE-MOEA, to improve population convergence, while maintaining population diversity. Finally, 41 widely used MOP benchmarks are used to compare the performance of the proposed OPE-MOEA with other five representative algorithms. For the 41 MOP benchmarks, the OPE-MOEA significantly outperforms the five algorithms on 28 MOP benchmarks in terms of the metric hypervolume.
We introduce a new architecture of Information granulation based genetically optimized hybrid self-organizing fuzzy polynomial neural networks (IG_gHSOFPNN) that is based on a genetically optimized multi-layer perceptron and develop their comprehensive design methodology involving mechanisms of genetic optimization, especially information granulation and genetic algorithms. The architecture of the resulting IG_gHSOFPNN results from a synergistic usage of the hybrid system generated by combining fuzzy polynomial neurons (FPNs)-based self-organizing fuzzy polynomial neural networks(SOFPNN) with polynomial neurons (PNs)-based self-organizing polynomial neural networks (SOPNN). The augmented IG_gHSOFPNN results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HSOFPNN. The GA-based design procedure being applied at each layer of IG_gHSOFPNN leads to the selection of preferred nodes (FPNs or PNs) available within the HSOFPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The obtained results demonstrate superiority of the proposed networks over the existing fuzzy and neural models.
