PARAMETRIC OPERATIONS FOR TWO 3-DIMENSIONAL TRAPEZOIDAL FUZZY SETS

초록

We extend the parametric operator for trapezoidal fuzzy sets to three dimensions. We define and calculate parametric operators between 3D trapezoidal fuzzy sets and present the results in a graph. Since the graph is defined in 3D space and drawn in 4D, it cannot be represented in 3D. The presented graph is drawn in three dimensions using a special definition of a fuzzy number in which the membership function’s value ranges from 0 to 1. The membership function’s value at each point is expressed as the color intensity at that point. If you cut the graph into a plane passing through the longest axis, you can observe that different function values on the plane are represented by colors of varying intensities. As it is a trapezoidal fuzzy set, a certain portion of the center shares the same color. By presenting this graph, the results will be cited and applied in various areas, similar to the one-dimensional and two-dimensional results. © 2024 Asia Pacific Journal of Mathematics.

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