A Notion of Convergence in Fuzzy Partially Ordered Sets

Abstract

The notion of sequential convergence in fuzzy partially ordered sets, under the name oF-convergence, is well known. Our aim in this paper is to introduce and study a notion of net convergence, with respect to the fuzzy order relation, named o-convergence, which generalizes the former notion and is also closer to our sense of the classic concept of "convergence". The main result of this article is that the two notions of convergence are identical in the area of complete F-lattices.

Keywords

• fuzzy order relation
• <i>o_F</i>-convergence
• <i>o</i>-convergence