Simulation of Random LR Fuzzy Intervals

TL;DR

This paper develops theoretical results and efficient algorithms for simulating LR fuzzy numbers with interval-valued cores, enhancing the modeling of imprecise and random data in statistical applications.

Contribution

It introduces a new family of fuzzy numbers with interval cores and provides simulation algorithms and analysis of their limiting behavior.

Findings

Established theoretical properties of LR fuzzy numbers with interval cores.

Developed a numerically efficient simulation algorithm.

Analyzed the limiting behavior of the fuzzy number simulations.

Abstract

Random fuzzy variables join the modeling of the impreciseness (due to their ``fuzzy part'') and randomness. Statistical samples of such objects are widely used, and their direct, numerically effective generation is therefore necessary. Usually, these samples consist of triangular or trapezoidal fuzzy numbers. In this paper, we describe theoretical results and simulation algorithms for another family of fuzzy numbers -- LR fuzzy numbers with interval-valued cores. Starting from a simulation perspective on the piecewise linear LR fuzzy numbers with the interval-valued cores, their limiting behavior is then considered. This leads us to the numerically efficient algorithm for simulating a sample consisting of such fuzzy values.