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

Author

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  • Kh. Abolpour

    (Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran)

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.

Suggested Citation

  • Kh. Abolpour, 2022. "On LB-Valued GFA: An LB-Valued Operator Oriented View with t-Norm/t-Conorm and Implicators," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 573-592, November.
    • Handle: RePEc:wsi:nmncxx:v:18:y:2022:i:03:n:s1793005722500296
    DOI: 10.1142/S1793005722500296
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