Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method

IF 1 Q1 MATHEMATICS
Takashi Mitsuishi
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引用次数: 0

Abstract

Summary 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 a ne 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].
使用质心法的等腰三角形和等腰梯形隶属函数
由于等腰三角形和梯形隶属函数[4]易于管理,因此将其应用于各种模糊近似推理[10],[13],[14]。本文[16]、[9]提到了等腰三角形和梯形隶属函数的质心,并在[11]、[12]中进行了形式化。本文证明了复合映射(f +·g,或使用Mizar形式的f +* g,其中f, g是一个新映射)的一些命题[3],[15]。然后对相同的等腰三角形和梯形隶属函数进行了不同的形式化表示。证明了用不同参数表示的同一函数的一致性,并将这些质心用参数形式化。此外,Mizar[1],[2]形式化了域端点固定区间和一般区间上隶属函数的各种性质。我们的正式开发还包含一些数值结果,这些结果可能对编码模糊数[7],甚至模糊含义[5],[6]有用,并扩展了将来构建混合粗糙模糊方法的可能性[8]。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Formalized Mathematics
Formalized Mathematics MATHEMATICS-
自引率
0.00%
发文量
0
审稿时长
10 weeks
期刊介绍: Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.
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