F-transforms determined by overlap and grouping maps over a complete lattice

TL;DR

This paper explores F-transforms on complete lattices using overlap and grouping maps, analyzing their properties, duality, and inverse, with both constructive and axiomatic methods to deepen understanding of their mathematical structure.

Contribution

It introduces a comprehensive study of F-transforms based on overlap and grouping maps over complete lattices, including duality, properties, and axiomatic characterizations.

Findings

Duality and inverse properties of F-transforms are established.

Axiomatic characterizations of direct F-transforms are provided.

The study offers both constructive and axiomatic insights into F-transforms on lattices.

Abstract

This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the inverse of proposed F-transforms have been studied, and axiomatic characterizations of proposed direct F-transforms are investigated.