CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms

by S. S. Dhure, S. R. Chaudhari
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 84 - Number 10
Year of Publication: 2013
Authors: S. S. Dhure, S. R. Chaudhari
10.5120/14609-2864

S. S. Dhure, S. R. Chaudhari . On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms. International Journal of Computer Applications. 84, 10 ( December 2013), 1-8. DOI=10.5120/14609-2864

@article{ 10.5120/14609-2864,
author = { S. S. Dhure, S. R. Chaudhari },
title = { On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms },
journal = { International Journal of Computer Applications },
issue_date = { December 2013 },
volume = { 84 },
number = { 10 },
month = { December },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume84/number10/14609-2864/ },
doi = { 10.5120/14609-2864 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:00:31.262465+05:30
%A S. S. Dhure
%A S. R. Chaudhari
%T On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms
%J International Journal of Computer Applications
%@ 0975-8887
%V 84
%N 10
%P 1-8
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Recent studies on fuzzy automata are influenced by algebraic techniques to tackle issues like reduction, minimization and their languages. Fuzzy automaton homomorphism is one such majorally discussed technique. This paper is concerned with the group of (weak) fuzzy automaton automorphisms and constructions of all (weak) fuzzy automaton automorphisms over arbitrary fuzzy automaton. It is shown that (1) every arbitrary fuzzy automaton is decomposed into distinct primaries, (2) primaries are maximal singly generated fuzzy automata and (3) every weak fuzzy automaton homomorphism on an arbitrary fuzzy automaton is uniquely determined into weak fuzzy automaton homomorphisms on all its primaries. Therefore, the discussion begun over strongly connected fuzzy automaton and continue constructions as well as characterizations of (weak) fuzzy automaton homomorphisms, isomorphisms, endomorphisms and automorphisms sequentially over perfect fuzzy automaton, singly generated fuzzy automaton and primaries of fuzzy automaton. Finally, it is obtained that the group of weak fuzzy automaton automorphisms and its cardinality over arbitrary fuzzy automaton.

References
  1. Bavel Z. , Structure and transition-preserving functions of finite automata, J. ACM, 15(1), pp 135-158,(Jan. 1968).
  2. Cho S. J. , Kim J. G. ,Tae Kim S. , T-fuzzy semiautomata over finite group, Fuzzy Sets and Systems, 108, pp 341-351,(1999).
  3. Choubey A. , Ravi K. M. , Minimization of deterministic finite automata with vague (final) states and intutionistic fuzzy (final) states, Iranian Journal of Fuzzy Systems, 10(1), pp 75- 88,(2013).
  4. Ciric Miroslav, Aleksandar Stamenkovic, Jelena Ignjatovic, Tatjana Petkovic, Fuzzy relation equations and reduction of fuzzy automata, J. Comput. Syst. Sci. , 76(7), pp 609- 633,(2010).
  5. Das P. ,On some properties fuzzy semiautomaton over a finite group, Information Sciences, 101, pp 71-84,(1997).
  6. Fleck A. C. , Isomorphism groups of automata, J. ACM, 9(4), pp 469-476,(Oct. 1962).
  7. Fleck A. C. , On the automorphism group of an automaton, J. ACM, 12(4), pp 566-569,(Oct. 1965).
  8. Jianhua Jin, Qingguo Li, Yongming Li, Algebraic properties of L-fuzzy finite automata, Information Sciences, 234, pp 182- 202, (2013).
  9. Kim Y. H. , Kim J. G. and Cho S. J. Product of T-generalized state machines and T-generalized transformation semigroups, Int. Journal of Fuzzy Sets and Systems 93, pp 87-97,(1998).
  10. Kumbhojkar H. V. and Chaudhari S. R. , On proper fuzzificztion of finite state machine, Int. Journal of Fuzzy Mathematics, 8(4), pp 1019-1027,(December 2000).
  11. Kumbhojkar H. V. and Chaudhari S. R. , On covering of products of fuzzy finite state machines, Fuzzy Sets and Systems, 125, pp 215-222,(2002).
  12. Malik D. S. , Mordeson J. N. and Sen M. K. , Product of fuzzy finite state machines, Int. Journal of Fuzzy Sets and Systems 92, pp 95-102,(1997).
  13. Malik D. S. , Mordeson J. N. ,Sen M. K. ,On subsystems of fuzzy finite state machines, Fuzzy Sets and Systems, 68, pp 83- 92,(1994).
  14. Mo Zhi-wen, HU Hong-li, Minimization of fuzzy finite generalized automata, J. of Electronic Science and Technology of China, 4(1), pp 86-88,(2006).
  15. J. Mockor, Semigroup homomorphisms and fuzzy automata, Soft Computing, 6 (6), pp 422-427,(2002).
  16. Mordeson J. N. and Malik D. S. (2002), Fuzzy automata and languages: theory and applications , Chapman and Hall / CRC, Boca Raton, London.
  17. Tatjana Petkovic, Congruences and homomorphisms of fuzzy automata, Fuzzy Sets and Systems, 157, pp 444-458,(2006).
  18. Tiwari S. P. and Srivastava A. K. ,On a decomposition of fuzzy automata, Fuzzy Sets and Systems, 151(3), pp 503- 511,(2005).
  19. Wegg G. P. , The structure of an automaton and its operation preserving transformation group, J. ACM, 9(3), pp 345- 349,(July. 1962).
  20. Young Bae Jun, Intutionistic fuzzy finite state machines, J. Appl. Math. and Computing, 17, pp 109-120,(2005).
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy function fuzzy automaton (strongly connected perfect and singly generated) (Weak) fuzzy automaton automorphism (homomorphism isomorphism) primaries and basis of a fuzzy automaton.

Powered by PhDFocusTM