Fuzzy monotone functions and applications

Lee, Edward T.; Chou, Te‐Shun

doi:10.1108/03684920110363923

Cited by 5 publications

(5 citation statements)

References 10 publications

(10 reference statements)

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“…Other ways for realization of fuzzy controllers' structural optimization (Kondratenko and Al Zu'bi, 2009;Lee and Chou, 2001) are related:…”

Section: Structural Optimizationmentioning

confidence: 99%

“…A number of methods of fuzzy controllers's synthesis (Arkhangelsky et al, 1997;Buckley, 1993;Kondratenko and Al Zu'bi, 2009;Mizumoto, 1995) have been developed to date. They provide the desired quality control in fuzzy systems by optimizing parameters of membership functions (Lee and Chou, 2001) of linguistic terms and by using different aggregation models (Piegat, 2001;Werners, 1988;Zimmermann and Zysno, 1980). As an objective function in the implementation of these methods an integral quadratic criterion or standard deviation of the real transition from desirable are usually used.…”

Section: Introductionmentioning

confidence: 99%

“…Other ways for realization of fuzzy controllers' structural optimization (Kondratenko and Al Zu'bi, 2009;Lee and Chou, 2001) Before each following step of fuzzy controllers' structural optimization it is expedient to carry out parametrical optimization for the parameters of membership functions and also by g parameter of fuzzy information processing algorithms on the aggregation stage.…”

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confidence: 99%

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Structural optimization of fuzzy systems' rules base and aggregation models

2013

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Purpose -The purpose of this paper is to propose a general method to simplify the structure of fuzzy controllers' rule base using integrated methodology for reducing the number of fuzzy rules based on modelling and simulation. Design/methodology/approach -The paper considers the problem of developing effective methods and algorithms for optimization of fuzzy rules bases of Sugeno-type fuzzy controllers that can be applied to control of dynamic objects, including objects with non-stationary parameters. The proposed approach based on calculating the impact of each of the rule on the formation of control signals for different types of input signals provides optimization of a linguistic rules database by using exclusion mechanism for rules with negligible influence. The effectiveness of the proposed approach is investigated using a fuzzy PID controller for control of a non-stationary object of second order. Findings -In this paper, the authors argued that different aggregation models can be used for structural optimization of fuzzy controllers and not all the rules are actually required in the fuzzy controllers' rule base. Eliminating some of the rules does not necessarily lead to a significant change in the fuzzy controller's output. The proposed integrated approach based on combination of different kinds of reference input signals for fuzzy controllers modelling and simulation is able to provide guidelines to the users which rules are required and which can be eliminated. The results obtained from the case studies demonstrate that the proposed integrated approach is able to reduce the number of rules required and, at the same time, to have the desired values of quality control indices.Research limitations/implications -In order to demonstrate the feasibility of the proposed approach, only control object of second order with PID fuzzy controller of Sugeno-type is chosen. Future studies can advance this research by applying the proposed approach in different types of fuzzy systems. Practical implications -The proposed integrated approach is able to simplify the structural optimization methodology and make it possible to be implemented in real processes of the fuzzy controllers' design. Originality/value -The value of the current paper is on the proposal of an integrated approach for rule reduction to enhance the practical use of modelling and simulation in a design of fuzzy controllers.

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“…Other ways for realization of fuzzy controllers' structural optimization (Kondratenko and Al Zu'bi, 2009;Lee and Chou, 2001) are related:…”

Section: Structural Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Structural optimization of fuzzy systems' rules base and aggregation models

2013

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“…The fuzzy and monotone technologies are sometimes combined together in some applications. Edward [7] introduced the fuzzy monotone function, together with logic control applications. Many papers [8]- [21] have discussed the monotonicity property in the fuzzy inference system (FIS) including Mamdiani, TSK and etc.…”

Section: Introductionmentioning

confidence: 99%

A Novel Fuzzy Monotone Relationship Method With its Application on Inclusion Degree

Liang

Zhang

2022

IEEE Access

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This paper introduces a new fuzzy monotone relationship and its associated method, which are applied to feature selection and correlation analysis. Specifically, after the concept of a fuzzy monotone is introduced, this paper first defines a new fuzzy monotone relationship between inputs and output. Second, a fuzzy inclusive monotone model is constructed on inclusion degree through several proved propositions, together with presenting a fuzzy inclusive monotone decision membership function. Third, a new algorithm is developed according to the proposed model for feature selection or correlation analysis. Compared with several methods, the proposed algorithm has been validated on several data sets. The results indicate that the proposed algorithm is effective for the selection of numeric attributes, and the correlation analysis. The novel fuzzy monotone relationship and the method are validated through theoretic proof and experimental results.

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“…Fuzzy logic functions (Dickerson and Kosko, 1993a, b, 1996; Lee, 1993; Lee and Chou, 1995, 2001) have attracted growing attention as promising avenues in fuzzy engineering (Kosko, 1997) and other related areas. More specifically, fuzzy monotone functions (Lee and Chou, 2001), fuzzy threshold functions (Lee and Chou, 1995) fuzzy symmetric functions (Lee, 1993) have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy symmetric threshold functions and applications

Lee

2003

Kybernetes

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A fuzzy symmetric threshold (ST) function is defined to be a fuzzy set over the set of functions. All ST functions have full memberships in this fuzzy set. For n variables, there are (2n+2) ST functions. A distance measure between a nonsymmetric threshold function and the set of all ST functions is defined and investigated. An explicit expression for the membership function of a fuzzy ST function is defined through the use of this distance measure. An algorithm for obtaining this distance measure is presented with illustrative examples. It is also shown that any function and its complement always have the same grade of membership in the class of fuzzy ST functions. Applications to concise function representation and simple function implementation are also presented with examples. In addition, most inseparable unsymmetric functions are defined and investigated. Fuzzy ST functions are relevant to the development of practical applications of fuzzy methods and might contribute to the state of the art in the implementations of fuzzy methods in the areas requiring utilization of ST functions.

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Fuzzy monotone functions and applications

Cited by 5 publications

References 10 publications

Structural optimization of fuzzy systems' rules base and aggregation models

Structural optimization of fuzzy systems' rules base and aggregation models

A Novel Fuzzy Monotone Relationship Method With its Application on Inclusion Degree

Fuzzy symmetric threshold functions and applications

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