<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Fuzzy logic systems, unlike black-box models, are known as transparent artificial intelligence systems that have explainable rules of reasoning. Type 2 fuzzy systems extend the field of application to tasks that require the introduction of uncertainty in the rules, e.g. for handling corrupted data. Most practical implementations use interval type-2 sets and process interval membership grades. The key role in the design of type-2 interval fuzzy logic systems is played by the type-2 inference defuzzification method. In type-2 systems this generally takes place in two steps: type-reduction first, then standard defuzzification. The only precise type-reduction method is the iterative method known as Karnik-Mendel (KM) algorithm with its enhancement modifications. The known non-iterative methods deliver only an approximation of the boundaries of a type-reduced set and, in special cases, they diminish the profits that result from the use of type-2 fuzzy logic systems. In this paper, we propose a novel type-reduction method based on a smooth approximation of maximum/minimum, and we call this method a smooth type-reduction. Replacing the iterative KM algorithm by the smooth type-reduction, we obtain a structure of an adaptive interval type-2 fuzzy logic which is non-iterative and as close to an approximation of the KM algorithm as we like.</p>
</abstract>

Fuzzy logic systems, unlike black-box models, are known as transparent artificial intelligence systems that have explainable rules of reasoning. Type 2 fuzzy systems extend the field of application to tasks that require the introduction of uncertainty in the rules, e.g. for handling corrupted data. Most practical implementations use interval type-2 sets and process interval membership grades. The key role in the design of type-2 interval fuzzy logic systems is played by the type-2 inference defuzzification method. In type-2 systems this generally takes place in two steps: type-reduction first, then standard defuzzification. The only precise type-reduction method is the iterative method known as Karnik-Mendel (KM) algorithm with its enhancement modifications. The known non-iterative methods deliver only an approximation of the boundaries of a type-reduced set and, in special cases, they diminish the profits that result from the use of type-2 fuzzy logic systems. In this paper, we propose a novel type-reduction method based on a smooth approximation of maximum/minimum, and we call this method a smooth type-reduction. Replacing the iterative KM algorithm by the smooth type-reduction, we obtain a structure of an adaptive interval type-2 fuzzy logic which is non-iterative and as close to an approximation of the KM algorithm as we like.

A Novel Approach to Type-Reduction and Design of Interval Type-2 Fuzzy Logic Systems

Department of Computer, Control and Management Engineering

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fuzzy logic systems, unlike black-box models, are known as transparent artificial intelligence systems that have explainable rules of reasoning. Type 2 fuzzy...

A Novel Approach to Type-Reduction and Design of Interval Type-2 Fuzzy Logic Systems

Publié en ligne: 23 juil. 2022

Pages: 197 - 206

Reçu: 05 janv. 2022

Accepté: 24 juin 2022

DOI: https://doi.org/10.2478/jaiscr-2022-0013

Mots clés
smooth type-reduction, interval type-2 fuzzy logic systems

© 2022 Janusz T. Starczewski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Novel Approach to Type-Reduction and Design of Interval Type-2 Fuzzy Logic Systems

Publié en ligne: 23 juil. 2022

Pages: 197 - 206

Reçu: 05 janv. 2022

Accepté: 24 juin 2022

DOI: https://doi.org/10.2478/jaiscr-2022-0013

Mots cléssmooth type-reduction, interval type-2 fuzzy logic systems

© 2022 Janusz T. Starczewski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
smooth type-reduction, interval type-2 fuzzy logic systems