Using Dual Double Fuzzy Semi-Metric to Study the Convergence

Abstract

Convergence using dual double fuzzy semi-metric is studied in this paper. Two types of dual double fuzzy semi-metric are proposed in this paper, which are called the infimum type of dual double fuzzy semi-metric and the supremum type of dual double fuzzy semi-metric. Under these settings, we also propose different types of triangle inequalities that are used to investigate the convergence using dual double fuzzy semi-metric.

Special Issue “Fuzzy Decision Making and Soft Computing Applications”

“…The remarkable progress made by these approaches in various fields underlines their benefits and is stimulating further research. In particular, despite the remarkable successes in different tasks, research on these approaches is a field of increasing interest [9], with regard to theoretical aspects, which are being deepened [10][11][12], as well as aspects regarding procedures for learning fuzzy systems optimizing accuracy and/or interpretability, or for solving mathematical tasks using fuzzy numbers and soft computing [13][14][15][16][17][18]. Moreover, these approaches are prone to easily and proficiently be employed in different new fields of application [19][20][21].…”

“…Learning procedures. In [13], the authors propose two types ("infimum type" and "supremum type") of dual double fuzzy semi-metric, as well as different types of triangle inequalities, which are used to investigate the convergence. Another contribution [14] proposes an adaptive-network-based fuzzy inference system (ANFIS) model for the accurate estimation of signal propagation.…”