Oscar Camacho Nieto

Generators of Fuzzy Operations for Hardware Implementation of Fuzzy Systems

The problem of effective hardware implementation of parametric operations of fuzzy systems is studied in this paper. The methods of generation of parametric classes of fuzzy conjunctions and disjunctions by means of introduced generators and basic operations are considered. Several types of generators of parametric fuzzy operations simple for hardware implementation are proposed. Examples of hardware implementation of proposed parametric operations are presented.

VLSI implementation of a module for realization of basic t-norms on fuzzy hardware

Fuzzy theory applications have been explored and analyzed on fields as pattern recognition, control, data classification, signal processing, expert systems, among others. To accomplish this, more complex calculations and faster processing speed are required, turning fuzzy hardware implementation to be the perfect choice. Fuzzy operations as t-norms and t-conorms are used in fuzzy systems as conjunction and disjunction operations respectively. Commonly used t-norms for hardware implementation are minimum and algebraic product, first one is cheaper to implement; second consumes more resources. On this work FPGA technology is used to implement basic fuzzy t-norms as minimum, Lukasiewicz and drastic product into an 8 bit single circuit that allows operation selection. Timing, resources and comparative results are presented.

Parametric Operations for Digital Hardware Implementation of Fuzzy Systems

Operations used in fuzzy systems to realize conjunction and disjunction over fuzzy sets are commonly minimum and maximum because they are easy to implement and provide good results when fuzzy system is tuned, but tuning of the system is a hard work that can result on knowledge lost. A good choice to tune the system without loss of previously stated knowledge is by using parametric classes of conjunction and disjunction operations, but these operations must be suitable to be efficiently implemented on digital hardware. In this paper, the problem of obtain effective digital hardware for parametric operations of fuzzy systems is studied. The methods for generation of parametric classes of fuzzy conjunctions and disjunctions by means of generators and basic operations are considered. Some types of generators of parametric fuzzy operations simple for hardware implementation are proposed. New hardware implementation for parametric operations with operation selection is presented.

Generalized fuzzy operations for digital hardware implementation

Hardware implementation of fuzzy systems plays important role in many industrial applications of fuzzy logic. The most popular applications of fuzzy hardware systems were found in the domain of control systems but the area of application of these systems is extending on other areas such as signal processing, pattern recognition, expert systems etc. The digital fuzzy hardware systems usually use only basic operations of fuzzy logic like min, max and some others, first, due to their popularity in traditional fuzzy control systems and, second, due to the difficulties of hardware implementation of more complicated operations, e.g. parametric classes of t-norms and t-conorms. But for extending the area of applications and flexibility of fuzzy hardware systems it is necessary to develop the methods of digital hardware implementation of wide range of fuzzy operations. The paper studies the problem of digital hardware implementation of fuzzy parametric conjunction and disjunction operations. A new class of such operations is proposed which is simple for digital hardware implementation and is flexible, due to its parametric form, for possible tuning in fuzzy models. The methods of hardware implementation of these operations in digital systems are proposed.

Wavelet Filter Adjusting for Image Lossless Compression Using Pattern Recognition

A method for image lossless compression using lifting scheme wavelet transform is presented. The proposed method adjusts wavelet filter coefficients analyzing signal spectral characteristics to obtain a higher compression ratio in comparison to the standard CDF(2,2) and CDF(4,4) filters. The proposal is based on spectral pattern recognition with 1-NN classifier. Spectral patterns of a small fixed length are formed for the entire image permitting thus the global optimization of the filter coefficients, equal for all decompositions. The proposed method was applied to a set of test images obtaining better results in entropy values in comparison to the standard wavelet lifting filters.

Discrete fuzzy systems: The aggregation operator

Knowledge-based systems have the ability to realize inferences out of pre-defined rules. As the antecedents are driven into the fuzzy system, the system infers to obtain the consequents. These consequents are used to obtain crisp output data. The aggregation operator combines these consequents to obtain a unified shape from which a unique result can be obtained. The way to handle the aggregation varies according to the type of membership functions involved. This paper presents a way of realizing aggregation operation when the membership functions are represented by means of a-levels, showing that this case is suitable for discrete fuzzy system implementations.

Soft-core implementation for centre of Slice Area Average defuzzifier

Fuzzy systems are broad used for the decision making task given its capability of extract knowledge from an expert and translate it into rules that define described system. Implementations are made according to speed requirements of the problem, for the case of critical real time systems hardware is the best choice. One important issue on fuzzy systems is the final step, defuzzifier, when computed fuzzy data is turned into crisp data. There are many different defuzzifier methods from which most used for hardware purposes are Center Of Gravity and Mean Of Maxima. This work presents hardware implementation for Center of Slice Area Average defuzzifier, for digital soft-core implementation; its main advantages are reduction on resource consumption and reduction of calculation time without loss of accuracy.

Discrete Fuzzy Inference Engine Algorithm for Digital Implementations of Approximate Reasoning

Fuzzy logic has become a very good choice to represent uncertain models of complex systems that cannot be easily represented in terms of conventional mathematics. Specifically fuzzy hardware has turned to be the choice to reach high speed inference rates. There are two forms to represent membership values universe: first one is when floating point numbers are used, second form is when integer universe is used. In the first case result of operations belongs to [0, 1], in the second case results belong to interval of integers [0, m], where m is an integer that can be represented by a different number of bits according to application resolution demands. This case is fully compatible with digital computers because floating point operations consume much more time and resources than integer operations. This paper presents an algorithm to implement fuzzy logic inference engine for discrete implementations and new method of defuzzification procedure, with the objective of reducing the number of instructions to be executed, having as consequence fewer processing time and less resources consumed. Simulation results for new methods are considered.