Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method

Summary Since isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied various fuzzy approximate reasoning [10], [13], [14]. The centroids of mentioned in this article [16], [9] formalized [11] [12]. Some propositions the composition mapping ( f + · g , or +* using Mizar formalism, where a ne mappings), proved following [3], [15]. Then different notations for same function formalized. We agreement expressed with parameters those parameters. In addition, properties on intervals endpoints domain fixed general [1], [2]. Our formal development contains also some numerical results which can be potentially useful encode either numbers [7], even implications [5], [6] extends possibility building hybrid rough-fuzzy approach future [8].