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This paper introduces new modifications of modal topological structures in intuitionistic fuzzy sets, highlighting novel insights.
The paper is a continuation of the series of papers devoted to the concept of a Modal Topological Structure (MTS) and its modification and extension. Here we introduce two new modifications of MTSs – the Level Topological Structures (LTSs, when the level operators play the role of the modal ones) and Modal Level (Topological) Structures (ML(T)Ss, when the level operators play the role of the topological ones). In addition, three extended MTSs are discussed, too – the Modal LTSs (MLTSs, when they contain simultaneously modal, level and topological operators), Modal Level Temporal Topological Structures (MLTTSs, when they contain simultaneously modal, level, temporal and topological operators) and multi-LTSs (mLTSs, when the number of their level operators is higher than 1). All these structures are illustrated with examples from intuitionistic fuzzy sets theory.
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Krassimir Atanassov (2025) studied this question.
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