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Isomorphism between two BL-general fuzzy automata

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Abstract

In this note first we develop the notion of general fuzzy automata (GFA) to a new one which is called “BL-general fuzzy automata” and for simplicity, we write BL-GFA, instead of BL-general fuzzy automata. Then we focus on derivation, active state set, membership assignment, output mappings, and concept of belonging to an output label according to the entrance input strings \( X \, (X \in \Upsigma^{ * } ) \) for BL-general fuzzy automata. Therefore, we define the concepts of run map and behavior of BL-GFA. After that we present the morphism with threshold \( \tfrac{{\tau_{1} }}{{\tau_{2} }} \) between two BL-general fuzzy automata. Moreover we give some examples, to clarify these notions. Finally, we prove some theorems. In particular, we show that the isomorphic BL-general fuzzy automata have the same behavior.

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Kazerun Branch, Kazerun, Iran

    Kh. Abolpour

  2. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    M. M. Zahedi

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  1. Kh. Abolpour
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  2. M. M. Zahedi
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Correspondence to Kh. Abolpour.

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Abolpour, K., Zahedi, M.M. Isomorphism between two BL-general fuzzy automata. Soft Comput 16, 729–736 (2012). https://doi.org/10.1007/s00500-011-0782-4

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