TL;DR
This paper establishes necessary and sufficient conditions for extending isotone mappings from subsets of posets to entire posets, ensuring order-preserving extensions.
Contribution
It provides a complete characterization of when isotone mappings can be extended from subsets to whole posets, filling a theoretical gap.
Findings
Derived necessary and sufficient conditions for isotone extension
Characterized extension possibilities in terms of poset properties
Contributed to the theory of order-preserving mappings
Abstract
A set of necessary and sufficient conditions under which an isotone mapping from a subset of a poset X to a poset Y has an extension to an isotone mapping from X to Y are found.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Control Systems Optimization · Optimization and Variational Analysis