Fuzzy Sets of Higher Type and Higher Order in Fuzzy Modeling

2014 ◽  
pp. 31-49
Author(s):  
Witold Pedrycz
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Modeling ◽  
Higher Order

Distance measures for higher order dual hesitant fuzzy sets

2017 ◽  
Vol 37 (2) ◽  
pp. 1784-1806 ◽  
Author(s):  
Jianjian Chen ◽  
Xianjiu Huang ◽  
Jing Tang
Keyword(s):  
Fuzzy Sets ◽  
Higher Order ◽  
Distance Measures ◽  
Hesitant Fuzzy Sets

scholarly journals Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System

2017 ◽  
Author(s):  
Chih-Jer Lin ◽  
Chun-Ying Lee ◽  
Ying Liu
Keyword(s):  
Electric Field ◽  
Vibration Control ◽  
Fuzzy Sets ◽  
Fuzzy Modeling ◽  
Smart Structure ◽  
Thin Plates ◽  
Fuzzy Controllers ◽  
Interval Type

This study presents a vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA’s is made of a sandwich hollow structure embedded with the electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable viscosity property. ERF’s apparent viscosity can be controlled in response to the electric field and the change is reversible in 10 microseconds. Therefore, the physical properties of the ERF-embedded smart structure, such as the stiffness and damping coefficients, can be changed in response to the applied electric field. A mathematical model is difficult to be obtained to describe the exact characteristics of the ERF embedded ATVA because of the nonlinearity of ERF’s viscosity. Therefore, a fuzzy modeling and experimental validations of ERF-based ATVA from stationary random vibrations of thin plates are presented in this study. Because Type-2 fuzzy sets generalize Type-1 fuzzy sets so that more modelling uncertainties can be handled, a semi-active vibration controller is proposed based on Type-2 fuzzy sets. To investigate the different performances by using different types of fuzzy controllers, the experimental measurements employing type-1 fuzzy and interval type-2 fuzzy controllers are implemented by the Compact RIO embedded system. The fuzzy modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of ATVA from stationary random vibration of thin plates.

scholarly journals Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System

2017 ◽  
Author(s):  
Chih-Jer Lin ◽  
Chun-Ying Lee ◽  
Ying Liu
Keyword(s):  
Electric Field ◽  
Vibration Control ◽  
Fuzzy Sets ◽  
Fuzzy Modeling ◽  
Smart Structure ◽  
Thin Plates ◽  
Fuzzy Controllers ◽  
Interval Type

This study presents a vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA’s is made of a sandwich hollow structure embedded with the electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable viscosity property. ERF’s apparent viscosity can be controlled in response to the electric field and the change is reversible in 10 microseconds. Therefore, the physical properties of the ERF-embedded smart structure, such as the stiffness and damping coefficients, can be changed in response to the applied electric field. A mathematical model is difficult to be obtained to describe the exact characteristics of the ERF embedded ATVA because of the nonlinearity of ERF’s viscosity. Therefore, a fuzzy modeling and experimental validations of ERF-based ATVA from stationary random vibrations of thin plates are presented in this study. Because Type-2 fuzzy sets generalize Type-1 fuzzy sets so that more modelling uncertainties can be handled, a semi-active vibration controller is proposed based on Type-2 fuzzy sets. To investigate the different performances by using different types of fuzzy controllers, the experimental measurements employing type-1 fuzzy and interval type-2 fuzzy controllers are implemented by the Compact RIO embedded system. The fuzzy modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of ATVA from stationary random vibration of thin plates.

scholarly journals Information Volume of Fuzzy Membership Function

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Jixiang Deng ◽  
Yong Deng
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Membership Function ◽  
Higher Order ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Order Information ◽  
First Order ◽  
New Information ◽  
Open Issue

Fuzzy membership function plays an important role in fuzzy set theory. However, how to measure the information volume of fuzzy membership function is still an open issue. The existing methods to determine the uncertainty of fuzzy membership function only measure the first-order information volume, but do not take higher-order information volume into consideration. To address this issue, a new information volume of fuzzy membership function is presented in this paper, which includes the first-order and the higher-order information volume. By continuously separating the hesitancy degree until convergence, the information volume of the fuzzy membership function can be calculated. In addition, when the hesitancy degree of a fuzzy membership function equals to zero, the information volume of this special fuzzy membership function is identical to Shannon entropy. Two typical fuzzy sets, namely classic fuzzy sets and intuitiontistic fuzzy sets, are studied. Several examples are illustrated to show the efficiency of the proposed information volume of fuzzy membership function.

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