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Fuzzy multiset finite automata and their languages

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Abstract

Inspired by the generalizations from grammars and finite automata to fuzzy grammars and fuzzy finite automata, respectively, we introduce the concepts of fuzzy multiset grammars and fuzzy multiset finite automata (FMFAs), as the generalizations of multiset grammars and multiset finite automata, respectively. The relationship between fuzzy multiset regular grammars and FMFAs is discussed. Furthermore, we define some operations on fuzzy multiset languages, and prove that the family of FMFA languages is closed under the operations.

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Notes

  1. \(\widetilde{\delta }(A, 0_{\Sigma }, q_{F})=\mu _{\widetilde{G}}(A\rightarrow 0_{V}),\;{\text{where}} \;A\in V_{\rm N}.\)

  2. \({\mu _{\widetilde{G}}(\langle A\rangle \rightarrow 0_{V})=\max \nolimits _{B\in Q}\{\widetilde{\delta }(A, 0_{\Sigma },B)\wedge \sigma _{1}(B)\}, \;{\text{where}}\;A, B\in Q.}\)

  3. \(\mu _{\widetilde{G}}(\langle S\rangle \rightarrow 0_{V})=\max \nolimits _{A, B\in Q}\{\sigma _{0}(A)\wedge \widetilde{\delta }(A, 0_{\Sigma },B)\wedge \sigma _{1}(B)\},\; {\text{where}}\;A, B\in Q.\)

  4. The case for \(m=1\) is that the sequence of states is empty.

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Acknowledgments

The work was fully supported by the National Natural Science Foundation of China under Grant Nos. 60803102, 61070084, National Key Basic Research Program of China (973 Program) under Grant No. 2012CB326403, Guangxi “Bagui Scholar” Teams for Innovation and Research, Natural Science Foundation of Jilin Province under Grant No.201215006, the Fundamental Research Funds for the Central Universities under Grant No. 11CXPY010, and Opening Fund of Top Key Discipline of Computer Software and Theory in Zhejiang Provincial Colleges at Zhejiang Normal University of China under Grant No.ZSDZZZZXK37.

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  1. School of Computer Science and Information Technology, Guangxi Normal University, Guilin, 130024, China

    Jinyan Wang

  2. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117, China

    Minghao Yin & Wenxiang Gu

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  1. Jinyan Wang
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  2. Minghao Yin
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  3. Wenxiang Gu
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Correspondence to Minghao Yin.

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Wang, J., Yin, M. & Gu, W. Fuzzy multiset finite automata and their languages. Soft Comput 17, 381–390 (2013). https://doi.org/10.1007/s00500-012-0913-6

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