Directional monotonic fuzzy implication functions induced from directional increasing quasi-grouping functions

In this paper, first we give some basic properties of directional monotonic fuzzy implication functions proposed by Bustince et al. (Fuzzy Sets Syst 386:161-178, 2020) by relaxing the monotonicity of fuzzy implication functions to the directional monotonicity lately. And then, we propose several construction methods of directional monotonic fuzzy implication functions. Finally, we introduce the concept of (G, N)-operations on the basis of binary functions G and fuzzy negations N and investigate the conditions under which (G, N)-operations can be directional monotonic fuzzy implication functions when the binary functions G are taken as directional increasing quasi-grouping functions g proposed by Qiao recently.

Automated summary

This paper presents the basic properties of directional monotonic fuzzy implication functions and proposes construction methods. The concept of (G, N)-operations is introduced based on binary functions G and fuzzy negations N, and the conditions for (G, N)-operations to be directional monotonic fuzzy implication functions are investigated when using directional increasing quasi-grouping functions g.