General Framework for Intuitionistic Values and Related Fuzzy Sets Based on Automorphisms

Matúš Ďubek; Adam Šeliga

doi:10.2478/tmmp-2026-0004

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General Framework for Intuitionistic Values and Related Fuzzy Sets Based on Automorphisms

Tatra Mountains Mathematical Publications

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By: Matúš Ďubek and Adam Šeliga

Open Access

|Apr 2026

Abstract

This paper introduces a novel framework for understanding intuitionistic values and fuzzy sets through the automorphism of the unit interval [0, 1]. By generalizing the concepts of classical intuitionistic sets using strong negations generated by these automorphisms, we define the φ-intuitionistic values and explore their arithmetic, establishing a comprehensive set of operations based mainly on additive generators of t-(co)norms and their properties. This approach provides greater flexibility to the modelling with these sets.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2026-0004 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Submitted on: Jun 23, 2025

Accepted on: Jan 5, 2026

Published on: Apr 22, 2026

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

strong negations,

intuitionistic fuzzy sets,

interval arithmetic

Related subjects:

Mathematics,

General mathematics

© 2026 Matúš Ďubek, Adam Šeliga, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

AHEAD OF PRINT