Group Fuzzy Languages and its Generalizations

Authors

  • Archana Vasudevan Pillai Prasanna N.S.S. College, Cherthala., Affiliated to University of Kerala, Thiruvananthapuram
  • Ramesh Kumar P University of Kerala image/svg+xml
  • Prakash G Narasimha Shenoi Maharaja's College, Ernakulam affiliated to M G University, Kottayam

DOI:

https://doi.org/10.23755/rm.v48i0.1095

Keywords:

syntactic congruence, group fuzzy language, pseudovariety

Abstract

In fuzzy language theory, every monoid is the syntactic monoid of some fuzzy language. By using this result the properties of fuzzy language can be studied by the algebraic properties of the syntactic monoids. There are so many methods for studying fuzzy languages. We adopt the above method to analyze different class of fuzzy languages and also characterize certain varieties of fuzzy languages. In this paper we give the variety description of group fuzzy languages and also provide the Eilenberg variety theorem for the class of group fuzzy languages. Moreover we described a fuzzy language whose syntactic monoid is isomorphic to the group Zn.

Author Biographies

  • Archana Vasudevan Pillai Prasanna, N.S.S. College, Cherthala., Affiliated to University of Kerala, Thiruvananthapuram
    Assistant Professor, Department of Mathematics
  • Ramesh Kumar P, University of Kerala
    Associate Professor and Head, Department of Mathematics, University of Kerala
  • Prakash G Narasimha Shenoi, Maharaja's College, Ernakulam affiliated to M G University, Kottayam
    Associate Professor, Department of Mathematics

References

K. Ajithakumari and V. P. Archana, On monoid recognizable l--fuzzy languages, International Journal of research in relevant technology, (No. 9) 9 : 2410--2413, 2018.

V. P. Archana and P. Ramesh Kumar, Full expletive fuzzy languages, International Journal of Algebra, (No. 8) 6 : 393--397, 2012.

V. P. Archana and P. Ramesh Kumar, Varieties of some fuzzy languages, Advances in Algebra, (No. 2) 5 : 119--124, 2012.

V. P. Archana, On Varieties of fuzzy languages whose syntactic monoids has commuting idempotents, Advances in Fuzzy Sets and Systems, (No. 2) 13 : 115--125, 2012.

V. P. Archana, Commutative fuzzy languages and their generalizations, Annals of Fuzzy Mathematics and Informatics, (No. 2) 9 : 355--364, 2015.

V. P. Archana, Variety of aperiodic fuzzy languages, Annals of Fuzzy Mathematics and Informatics, (No. 6) 11 : 967--972, 2016.

S. Eilenberg, Automata, Languages and Machines, B, Academic Press, London, 1976.

G. Lallement, Semigroup and Combinatorial Applications, John-Wiley, New York, 1979.

E. T. Lee, L. A. Zadeh, Note on Fuzzy Languages, Inform. sci. 1 : 421--434, 1969.

J. N. Mordeson and D. S. Malik, Fuzzy Automata and Languages; Theory and Applications, Chapman & Hall, CRC, 2002.

T. Petkovic, Varieties of fuzzy languages, Proc. 1st International Conference on Algebraic Informatics, Aristotle University of Thessaloniki, Thessaloniki, 2005.

L. A. Zadeh, Fuzzy Sets, Information and Control, 8, : 338--353, 1965.

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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