# A General Theory of Concept Lattice (I): Emergence of General Concept Lattice

## TL;DR

This paper introduces a general concept lattice framework that unifies and extends traditional lattices like formal concept and rough set lattices, ensuring invariance of information content across different variable presentations.

## Contribution

It develops the first part of a comprehensive theory for a general concept lattice that can encompass various categorization methods and guarantees invariance of information content.

## Key findings

- Existence of a general concept lattice compatible with traditional lattices
- The general lattice is invariant under different variable presentations
- Formal concept and rough set lattices are special cases of the general lattice

## Abstract

As the first part of the treatise on A General Theory of Concept Lattice (I-V), this work develops the general concept lattice for the problem concerning categorization of objects according to their properties. Unlike the conventional approaches, such as the formal concept lattice and the rough set lattice, the general concept lattice is designed to adhere to the general principle that the information content should be invariant regardless how the variables/parameters are presented. Here, one will explicitly demonstrate the existence of such a construction by a sequence of fulfillment compatible with the conventional lattice structure. The general concept lattice promises to be a comprehensive categorization for all the distinctive object classes according to whatever properties they are equipped with. It will be shown that one can always regain the formal concept lattice and rough set lattice from the general concept lattice.