Design Methodology for the Implementation of Fuzzy Inference Systems Based on Boolean Relations

This paper proposes a methodology for the design of fuzzy inference systems based on Boolean relations. The approach using Boolean sets presents limited performance due to the abrupt transitions that occur during its functioning, therefore, fuzzy sets can be used aiming the improvement of the performance. In this approach, firstly, the design of a Boolean controller is performed, which is later extended into fuzzy under design guidelines proposed in this paper. The methodology uses Kleene algebra via truth tables for the fuzzy system design, allowing the simplification of the equations that implement the fuzzy system.

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Air Quality Modeling by Fuzzy Sets and IF-Sets

Advances in Environmental Engineering and Green Technologies - Environmental Modeling for Sustainable Regional Development ◽

10.4018/978-1-60960-156-0.ch006 ◽

2011 ◽

pp. 118-143 ◽

Cited By ~ 1

Author(s):

Vladimír Olej ◽

Petr Hájek

Keyword(s):

Air Quality ◽

Fuzzy Sets ◽

Fuzzy Inference ◽

Air Quality Modeling ◽

Membership Functions ◽

Fuzzy Inference Systems ◽

Feature Maps ◽

Quality Classification ◽

Quality Modeling ◽

Inference Systems

The chapter presents a design of parameters for air quality classification of districts into classes according to their pollution. Therefore, the chapter presents basic notions of fuzzy sets introduced by L. A. Zadeh for design hierarchical fuzzy inference systems Mamdani type and IF-sets introduced by K. T. Atanassov for design of hierarchical IF-inference systems Mamdani type. In the next part of the chapter the authors describe air quality modeling by hierarchical fuzzy inference systems, hierarchical IF-inference systems and we analyze the results. Moreover, the chapter describes air quality modeling, the design of membership functions and non-membership functions, if-then rules of individual subsystems and inference mechanism. Further, the authors present basic notions of IF-relations and their determination by Kohonen’s Self-organizing Feature Maps and K-means algorithms and process air quality classification.

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FUZZY EXTREME LEARNING MACHINE FOR A CLASS OF FUZZY INFERENCE SYSTEMS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488513400151 ◽

2013 ◽

Vol 21 (supp02) ◽

pp. 51-61 ◽

Cited By ~ 9

Author(s):

HAI-JUN RONG ◽

GUANG-BIN HUANG ◽

YONG-QI LIANG

Keyword(s):

Fuzzy System ◽

Fuzzy Inference ◽

Performance Comparison ◽

Learning Ability ◽

Benchmark Problems ◽

Fuzzy Inference Systems ◽

Inference System ◽

Training Time ◽

Rbf Network ◽

Inference Systems

Recently an Online Sequential Fuzzy Extreme Learning (OS-Fuzzy-ELM) algorithm has been developed by Rong et al. for the RBF-like fuzzy neural systems where a fuzzy inference system is equivalent to a RBF network under some conditions. In the paper the learning ability of the batch version of OS-Fuzzy-ELM, called as Fuzzy-ELM is further evaluated to train a class of fuzzy inference systems which can not be represented by the RBF networks. The equivalence between the output of the fuzzy system and that of a generalized Single-Hidden Layer Feedforward Network as presented in Huang et al. is shown first, which is then used to prove the validity of the Fuzzy-ELM algorithm. In Fuzzy-ELM, the parameters of the fuzzy membership functions are randomly assigned and then the corresponding consequent parameters are determined analytically. Besides an input variable selection method based on the correlation measure is proposed to select the relevant inputs as the inputs of the fuzzy system. This can avoid the exponential increase of number of fuzzy rules with the increase of dimension of input variables while maintaining the testing performance and reducing the computation burden. Performance comparison of Fuzzy-ELM with other existing algorithms is presented using some real-world regression benchmark problems. The results show that the proposed Fuzzy-ELM produces similar or better accuracies with a significantly lower training time.

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Properties of interval type-2 fuzzy sets in decision support systems

Bulletin of the National Technical University «KhPI» Series New solutions in modern technologies ◽

10.20998/2413-4295.2021.04.10 ◽

2021 ◽

pp. 75-81

Author(s):

Alexander Zakovorotniy ◽

Artem Kharchenko

Keyword(s):

Fuzzy Sets ◽

Fuzzy Inference ◽

Systems Design ◽

Membership Functions ◽

Fuzzy Inference Systems ◽

Footprint Of Uncertainty ◽

Expert Assessments ◽

Interval Type ◽

Inference Systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

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