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1

Higher order fuzzy logic in controlling selective catalytic reduction systems

Niewiadomski A., Kacprowicz M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2014

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Vol. 62, nr 4

743--750

EN

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.

2

On some properties of (h,e)-implications. distributivities with t-norms and t-conorms.

Massanet S., Torrens J.

Journal of Artificial Intelligence and Soft Computing Research

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2012

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Vol. 2, No. 2

109--123

EN

In this paper some basic properties of (h, e)-implications are studied. This kind of implications has been recently introduced (see [29]). They are implications generated from an additive generator of a representable uninorm in a similar way of Yager’s f- and gimplications which are generated from additive generators of continuous Archimedean t-norms and t-conorms, respectively. In addition, they satisfy a classical property of some types of implications derived from uninorms that is I(e,y) = y for all y ∈ [0,1]. Moreover they are examples of fuzzy implications satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0,1] 2 → [0,1]. On the other hand, the distributivities with conjunctions and disjunctions (t-norms and t-conorms) are also studied leading to new solutions of the corresponding functional equations. Finally, it is proved that they do not intersect with any of the most used classes of implications.

3

Implikacje rozmyte

Wojutyński J.

Problemy Eksploatacji

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2002

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nr 4

47-57

PL

Implikacja IF A THEN B, gdzie A i B sa zbiorami rozmytymi, jest podstawą systemów wnioskowania rozmytego. W artykule omówiono podstawowe własności implikacji. Przedstawiono wykorzystanie oprogramowania autorskiego do wizualizacji postaci i działania implikacji.

EN

Implication IF A THEN B where A and B are fuzzy sets is a base of fuzzy inference systems. Basic properties of implication are represented in the article. Author's softwere helps in vizualizatiom of implications and their action.

4

Implication-Based Neuro-Fuzzy Architectures

Rutkowska D., Nowicki R.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 4

675-701

EN

This paper presents connectionist multi-layer architectures of neuro-fuzzy systems based on various fuzzy implications. The well-known Mamdani approach (constructive) and the logical approach (destructive) are considered. Two kinds of architectures, a simpler and a more general one, are distinguished. Examples of application to classification and control problems are provided.

5

A Neuro-Fuzzy System Based on Logical Interpretation of If-then Rules

Łęski J., Henzel N.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 4

703-722

EN

Several important fuzzy implications and their properties are described on the basis of an axiomatic approach to the definition of the fuzzy implications. Then the idea of approximate reasoning using the generalized modus ponens and fuzzy implications is considered. The elimination of the non-informative part of the final fuzzy set before defuzzification plays the key role in this paper. After reviewing well-known fuzzy systems, a new artificial neural network based on logical interpretation of if-then rules (ANBLIR) is introduced. Moreover, this system automatically generates rules from numerical data. Applications of ANBLIR to pattern recognition on numerical examples using benchmark databases are indicated.