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http://hdl.handle.net/11320/15406
Tytuł: | Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method |
Autorzy: | Mitsuishi, Takashi |
Słowa kluczowe: | defuzzification centroid method isosceles triangular function isosceles trapezoidal function |
Data wydania: | 2023 |
Data dodania: | 9-paź-2023 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 31, Issue 1, Pages 59-66 |
Abstrakt: | Since isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied to various fuzzy approximate reasoning [10], [13], [14]. The centroids of isosceles triangular and trapezoidal membership functions are mentioned in this article [16], [9] and formalized in [11] and [12]. Some propositions of the composition mapping (f +· g, or f +* g using Mizar formalism, where f, g are affine mappings), are proved following [3], [15]. Then different notations for the same isosceles triangular and trapezoidal membership function are formalized. We proved the agreement of the same function expressed with different parameters and formalized those centroids with parameters. In addition, various properties of membership functions on intervals where the endpoints of the domain are fixed and on general intervals are formalized in Mizar [1], [2]. Our formal development contains also some numerical results which can be potentially useful to encode either fuzzy numbers [7], or even fuzzy implications [5], [6] and extends the possibility of building hybrid rough-fuzzy approach in the future [8]. |
Afiliacja: | Faculty of Business and Informatics, Nagano University, Japan |
URI: | http://hdl.handle.net/11320/15406 |
DOI: | 10.2478/forma-2023-0006 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
Typ Dokumentu: | Article |
metadata.dc.rights.uri: | https://creativecommons.org/licenses/by-sa/3.0/ |
Właściciel praw: | © 2023 The Author(s) CC BY-SA 3.0 license |
Występuje w kolekcji(ach): | Formalized Mathematics, 2023, Volume 31, Issue 1 |
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