<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In real-world approximation problems, precise input data are economically expensive. Therefore, fuzzy methods devoted to uncertain data are in the focus of current research. Consequently, a method based on fuzzy-rough sets for fuzzification of inputs in a rule-based fuzzy system is discussed in this paper. A triangular membership function is applied to describe the nature of imprecision in data. Firstly, triangular fuzzy partitions are introduced to approximate common antecedent fuzzy rule sets. As a consequence of the proposed method, we obtain a structure of a general (non-interval) type-2 fuzzy logic system in which secondary membership functions are cropped triangular. Then, the possibility of applying so-called regular triangular norms is discussed. Finally, an experimental system constructed on precise data, which is then transformed and verified for uncertain data, is provided to demonstrate its basic properties.</p></abstract>

In real-world approximation problems, precise input data are economically expensive. Therefore, fuzzy methods devoted to uncertain data are in the focus of current research. Consequently, a method based on fuzzy-rough sets for fuzzification of inputs in a rule-based fuzzy system is discussed in this paper. A triangular membership function is applied to describe the nature of imprecision in data. Firstly, triangular fuzzy partitions are introduced to approximate common antecedent fuzzy rule sets. As a consequence of the proposed method, we obtain a structure of a general (non-interval) type-2 fuzzy logic system in which secondary membership functions are cropped triangular. Then, the possibility of applying so-called regular triangular norms is discussed. Finally, an experimental system constructed on precise data, which is then transformed and verified for uncertain data, is provided to demonstrate its basic properties.

Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based 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.

{"article-title":"Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems"}

In real-world approximation problems, precise input data are economically expensive. Therefore, fuzzy methods devoted to uncertain data are in the focus of...

Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems

Published Online: Jun 15, 2020

Page range: 271 - 285

Received: Oct 03, 2019

Accepted: May 01, 2020

DOI: https://doi.org/10.2478/jaiscr-2020-0018

Keywords
general type-2 fuzzy logic systems, fuzzy-rough fuzzification, regular type-2 t-norms, cropped triangular secondary membership functions

© 2020 Janusz T. Starczewski et al., published by Sciendo

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

Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems

Published Online: Jun 15, 2020

Page range: 271 - 285

Received: Oct 03, 2019

Accepted: May 01, 2020

DOI: https://doi.org/10.2478/jaiscr-2020-0018

Keywordsgeneral type-2 fuzzy logic systems, fuzzy-rough fuzzification, regular type-2 t-norms, cropped triangular secondary membership functions

© 2020 Janusz T. Starczewski et al., published by Sciendo

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

Keywords
general type-2 fuzzy logic systems, fuzzy-rough fuzzification, regular type-2 t-norms, cropped triangular secondary membership functions