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

<p>In this study, using the Mizar system [1], [2], we reuse formalization e orts in fuzzy sets described in [5] and [6]. This time the centroid method which is one of the fuzzy inference processes is formulated [10]. It is the most popular of all defuzzied methods ([11], [13], [7]) – here, defuzzified crisp value is obtained from domain of membership function as weighted average [8]. Since the integral is used in centroid method, the integrability and bounded properties of membership functions are also mentioned to fill the formalization gaps present in the Mizar Mathematical Library, as in the case of another fuzzy operators [4]. In this paper, the properties of piecewise linear functions consisting of two straight lines are mainly described.</p>
</abstract>

In this study, using the Mizar system [1], [2], we reuse formalization e orts in fuzzy sets described in [5] and [6]. This time the centroid method which is one of the fuzzy inference processes is formulated [10]. It is the most popular of all defuzzied methods ([11], [13], [7]) – here, defuzzified crisp value is obtained from domain of membership function as weighted average [8]. Since the integral is used in centroid method, the integrability and bounded properties of membership functions are also mentioned to fill the formalization gaps present in the Mizar Mathematical Library, as in the case of another fuzzy operators [4]. In this paper, the properties of piecewise linear functions consisting of two straight lines are mainly described.

Definition of Centroid Method as Defuzzification

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Definition of Centroid Method as Defuzzification"}

In this study, using the Mizar system [1], [2], we reuse formalization e orts in fuzzy sets described in [5] and [6]. This time the centroid method which is...

Definition of Centroid Method as Defuzzification

Published Online: Dec 24, 2022

Page range: 125 - 134

Accepted: Jul 23, 2022

DOI: https://doi.org/10.2478/forma-2022-0010

Keywords
defuzzification, centroid, piecewise linear function

© 2022 Takashi Mitsuishi, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Definition of Centroid Method as Defuzzification

Published Online: Dec 24, 2022

Page range: 125 - 134

Accepted: Jul 23, 2022

DOI: https://doi.org/10.2478/forma-2022-0010

Keywordsdefuzzification, centroid, piecewise linear function

© 2022 Takashi Mitsuishi, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
defuzzification, centroid, piecewise linear function