On LB-Valued GFA: An LB-Valued Operator Oriented View with t-Norm/t-Conorm and Implicators

Kh. Abolpour
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Kh. Abolpour: Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 03, 573-592

Abstract: This study aims at investigating LB-valued general fuzzy automata, for simplicity, LB-valued GFA, with respect to their algebraic properties and based on t-norm/t-conorm and general implicators, where L stands for residuated lattice and B is a set of propositions about the GFA, in which its underlying structure is a complete infinitely distributive lattice. Specifically, we introduce the concepts of LB-valued operators with t-norm and LB-valued operators with t-conorm. We also examine the relationships between the LB-valued operators with t-norm and LB-valued operators with t-conorm. Finally, we introduce the concepts of LB-valued operators with implicator and study the relationships between the LB-valued operators with the implicator and the LB-valued operators with t-norm/t-conorm. To clarify the notions and the results obtained in this study, some examples are submitted as well.

Keywords: LB-valued general fuzzy automata; operator; t-norm; t-conorm; implicator; dynamically; subproposition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500296

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