# Closure structures parameterized by systems of isotone Galois connections

## TL;DR

This paper explores a generalized framework for closure operators and systems parameterized by isotone Galois connections, extending fuzzy closure operators and linking to data analysis and temporal logic.

## Contribution

It introduces a new class of closure operators parameterized by isotone Galois connections, broadening the theoretical foundation and applications in data analysis and logic.

## Key findings

- Extended fuzzy closure operators with stronger properties
- Provided examples of data analysis problems using these operators
- Linked closure operators to linear temporal logic

## Abstract

We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements on idempotency and monotony conditions of closure operators. The present approach extends previous approaches to fuzzy closure operators which appeared in analysis of object-attribute data with graded attributes and reasoning with if-then rules in graded setting and is also related to analogous results developed in linear temporal logic. In the paper, we present foundations of the operators and include examples of general problems in data analysis where such operators appear.