New construction methods for uninorms via functions with q and uninorms on bounded lattices

TL;DR

This paper introduces new methods for constructing uninorms on bounded lattices using functions with specific properties, expanding the theoretical framework and providing illustrative examples.

Contribution

It develops novel construction techniques for uninorms on bounded lattices based on functions with particular q and p parameters, with detailed conditions and examples.

Findings

Established conditions for uninorm construction on bounded lattices.

Provided illustrative examples and figures demonstrating the methods.

Extended the theoretical understanding of uninorms in lattice structures.

Abstract

In this paper, we study the construction methods for uninorms on bounded lattices via functions with the given uninorms and $q\in \mathbb{L_{B}}$ (or $p\in \mathbb{L_{B}}$). Specifically, we investigate the conditions under which these functions can be uninorms on bounded lattices when $q\in (0,\mathfrak{e})\cup I_{\mathfrak{e}}^{\varrho}$ and $q\in I_{\varrho}^{\mathfrak{e}}$ (or $p\in (\mathfrak{e},1)\cup I_{\mathfrak{e}}^{\sigma}$ and $p\in I_{\sigma}^{\mathfrak{e}}$), respectively. Moreover, some illustrative examples and figures are provided.