Convergence theorems for seminormed fuzzy integrals: Solutions to Hutn\`ik's open problems
Micha{\l} Boczek, Marek Kaluszka
TL;DR
This paper provides solutions to open problems related to convergence theorems for seminormed fuzzy integrals, advancing the theoretical understanding of these integrals within fuzzy set theory.
Contribution
It offers new convergence theorems for seminormed fuzzy integrals, addressing previously unresolved open problems in the field.
Findings
Solutions to Problems 9.4 and 9.5 from prior open problems
New convergence theorems established for seminormed fuzzy integrals
Advances theoretical foundations in fuzzy set theory
Abstract
In this note, we give solutions to Problems and which were presented by Mesiar and Stup\v{n}anov\'{a} [{\it Open problems from the 12th International Conference on Fuzzy Set Theory and Its Applications}, Fuzzy Sets and Systems 261 (2015)] and by Borzov\'a-Moln\'arov\'a, Hal\u{c}inov\'a and Hutn\'ik, in [{\it The smallest semicopula-based universal integrals I: properties and characterizations,} Fuzzy Sets and Systems (2014), http://dx.doi.org/ 10.1016/j.fss.2014.09.024].
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Taxonomy
TopicsFuzzy Systems and Optimization · Multi-Criteria Decision Making · Fuzzy and Soft Set Theory