Triangular Fuzzy Set Composed of Two Intersecting Affine Maps

Summary In this article, various properties of triangular membership functions are formally proven, including the relationship between a triangular membership function composed of two straight lines and a MAX function, as well as a triangular membership function defined by the horizontal coordinates of the triangle’s vertices. Furthermore, we formalize defuzzified value of a triangular membership function and the integration of two connected functions.

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Publication Details

Journal
Formalized Mathematics
Published
2025-09-01
DOI
https://doi.org/10.2478/forma-2025-0011
Primary Topic
Fuzzy Systems and Optimization
Type
article
Field-Weighted Citation Impact
0.00
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article

Triangular Fuzzy Set Composed of Two Intersecting Affine Maps

Takashi Mitsuishi
Formalized Mathematics
Fuzzy Systems and Optimization
article

Triangular Fuzzy Set Composed of Two Intersecting Affine Maps

Takashi Mitsuishi
article en

Abstract

Summary In this article, various properties of triangular membership functions are formally proven, including the relationship between a triangular membership function composed of two straight lines and a MAX function, as well as a triangular membership function defined by the horizontal coordinates of the triangle’s vertices. Furthermore, we formalize defuzzified value of a triangular membership function and the integration of two connected functions.

Formalized MathematicsVol. 33(1)
Nagano University (JP)
Reduced inequalities
Openalex Percentile: Top 21%
Fuzzy Systems and Optimization
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Triangular Fuzzy Set Composed of Two Intersecting Affine Maps — Takashi Mitsuishi · Formalized Mathematics (2025) | TGRS Research Map | TGRS