Robustness of Higher-Order Fuzzy Sets

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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Higher Type, Higher Order Fuzzy Sets and Hybrid Fuzzy Sets

An Introduction to Computing with Fuzzy Sets - Intelligent Systems Reference Library ◽

10.1007/978-3-030-52800-3_7 ◽

2020 ◽

pp. 95-108

Author(s):

Witold Pedrycz

Keyword(s):

Fuzzy Sets ◽

Higher Order

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Higher order fuzzy logic in controlling selective catalytic reduction systems

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.2478/bpasts-2014-0080 ◽

2014 ◽

Vol 62 (4) ◽

pp. 743-750 ◽

Cited By ~ 1

Author(s):

A. Niewiadomski ◽

M. Kacprowicz

Keyword(s):

Fuzzy Logic ◽

Fuzzy Sets ◽

Selective Catalytic Reduction ◽

Catalytic Reduction ◽

Higher Order ◽

Fuzzy Logic Systems ◽

Air Filter ◽

Logic Systems ◽

Scr System

Abstract This paper presents research on applications of fuzzy logic and higher-order fuzzy logic systems to control filters reducing air pollution [1]. The filters use Selective Catalytic Reduction (SCR) method and, as for now, this process is controlled manually by a human expert. The goal of the research is to control an SCR system responsible for emission of nitrogen oxide (NO) and nitrogen dioxide (NO2) to the air, using SCR with ammonia (NH3). There are two higher-order fuzzy logic systems presented, applying interval-valued fuzzy sets and type-2 fuzzy sets, respectively. Fuzzy sets and higher order fuzzy sets describe linguistically levels of nitrogen oxides as the input, and settings of ammonia valve in the air filter as the output. The obtained results are consistent with data provided by experts. Besides, we show that the type-2 fuzzy logic controllers allows us to obtain results much closer to desired parameters of the ammonia valve, than traditional FLS.

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A Tensor Based Stacked Fuzzy Networks for Efficient Data Regression

10.21203/rs.3.rs-1035440/v1 ◽

2021 ◽

Author(s):

Jie Li ◽

Jiale Hu ◽

Guoliang Zhao ◽

Sharina Huang ◽

Yang Liu

Keyword(s):

Neural Network ◽

Fuzzy Sets ◽

Extreme Learning Machine ◽

Random Vector ◽

Fuzzy Neural Network ◽

Higher Order ◽

Functional Link ◽

Fuzzy Neural ◽

Learning Machine

Abstract Random vector functional link and extreme learning machine have been extended by the type-2 fuzzy sets with vector stacked methods, this extension leads to a new way to use tensor to construct learning structure for the type-2 fuzzy sets-based learning framework. In this paper, type-2 fuzzy sets-based random vector functional link, type-2 fuzzy sets-based extreme learning machine and Tikhonov-regularized extreme learning machine are fused into one network, a tensor way of stacking data is used to incorporate the nonlinear mappings when using type-2 fuzzy sets. In this way, the network could learning the sub-structure by three sub-structures' algorithms, which are merged into one tensor structure via the type-2 fuzzy mapping results. To the stacked single fuzzy neural network, the consequent part parameters learning are implemented by unfolding tensor-based matrix regression. The newly proposed stacked single fuzzy neural network shows a new way to design the hybrid fuzzy neural network with the higher order fuzzy sets and higher order data structure. The effective of the proposed stacked single fuzzy neural network are verified by the classical testing benchmarks and several statistical testing methods.

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