Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 5 Sayı: 4, 24 - 39, 01.10.2017

Öz

Kaynakça

  • Y. H. Kim, J. G. Kim, S. J. Cho, Products of T-generalized state machines and T-generalized transformation semigroups, Fuzzy Sets and Systems 93 (1998) 87–97.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, On subsystems of a fuzzy finite state machine, Fuzzy Sets and Systems 68 (1994) 83–92.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, Products of fuzzy finite state machines, Fuzzy Sets and Systems 92 (1997) 95–102.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, Semigroups of fuzzy finite state machines, in: P.P. Wang (Ed.), Advances in Fuzzy Theory and Technology, Vol. II, 1994, pp. 87–98.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, Submachines of fuzzy finite state machines, J. Fuzzy Math. 4 (1994) 781–792
  • H. Bustince, E. Barrenechea, M. Pagola, J. Fernndez, Interval-valued fuzzy sets constructed from matrices: application to edge detection, Fuzzy Sets Syst. 160, (2009), 1819-1840.
  • R. Belohlavek, Determinism and fuzzy automata, Inform. Sci. 143 (1) (2002) 205–209.
  • J. Ignjatovic, M. Ciric, S. Bogdanovic, Determinations of fuzzy automata with membership values in complete residuated lattices, Inform. Sci. 178, (2008) 164–180.
  • H. X. Lei, Y. M. Li, Minimization of states in automata theory based on finite lattice-ordered monoids, Inform. Sci. 177, (6) (2007), 1413–1421.
  • Y. M. Li, W. Pedrycz, Minimization of lattice finite automata and its application to the decomposition of lattice languages, Fuzzy Sets Syst. 158, (2007), 1423–1436.
  • Ping Li, Y. M. Li, Algebraic properties of LA-languages, Inform. Sci. 176 (21) (2006) 3232–3255.
  • H. Z. Li, P. Li, Y. Y. Li, The relationships among several types of fuzzy automata, Inform. Sci. 176 (15) (2006) 2208–2226.
  • K. Peeva, Zl. Zahariev, Computing behavior of finite fuzzy machines – algorithm and its application to reduction and minimization, Inform. Sci. 178 (21), (2008), 4152–4165.
  • D. W. Qiu, Notes on automata theory based on quantum logic, Science in China Series F: Inform. Sci. 50 (2) (2007) 154–169.
  • S. P. Tiwari, Arun K. Srivastava, On a decomposition of fuzzy automata, Fuzzy Sets Syst. 151 (2005) 503–511.
  • Y. B. Jun, Intuitionistic fuzzy transformation semigroups, Inform. Sci. 179 (24) (2009) 4284–4291.
  • Y. B. Jun, Intuitionistic fuzzy finite state machines, J. Appl. Math. Comput. 17 (1–2) (2005) 109–120.
  • Y. B. Jun, Intuitionistic fuzzy finite switchboard state machines, J. Appl. Math. Comput. 20 (1–2) (2006) 315–325.
  • Y. B. Jun, Quotient structures of intuitionistic fuzzy finite state machines, Inform. Sci. 177 (2007) 4977–4986
  • W. G. Wee, On generalization of adaptive algorithm and application of fuzzy sets concept to pattern classification. PH.D Theses, Purdue University, June, 1967.
  • E. Orlowska, Semantic analysis of inductive reasoning, Theoret. Comput. Sci. 43 (1986) 81–89.
  • A. Kandal, Fuzzy Switching and Automata: Theory and Applications (Crane Russak, 1980).
  • W. M. Holcombe, Algebraic Automata Theory (Cambridge Univ. Press, Cambridge, 1982).
  • L. A. Zadeh, Fuzzy sets, Inform. Control 8, (1965), 338-353.
  • H. V. Kumbhojkar and S. R. Chaudhari, On covering of products of fuzzy finite state machines, Fuzzy Sets and Systems 125 (2002), 215–222.
  • K. Peeva, Zl. Zahariev, Computing behavior of finite fuzzy machines – algorithm and its application to reduction and minimization, Inform. Sci. 178 (21), (2008) 4152–4165.
  • D. W. Qiu, Notes on automata theory based on quantum logic, Science in China Series F: Inform. Sci. 50 (2), (2007), 154–169.
  • D. S. Malik, J. N. Mordeson, Structure of upper and lower approximation spaces of infinite sets, in: T.Y. Lin, Y.Y. Yao, L.A. Zadeh (Eds.), Data Mining,
  • Rough Sets and Granular Computing, Studies in Fuzziness and Soft Computing, vol. 95, Physica-Verlag, Heidelberg, New York, 2002, pp. 461–472.
  • Z. Pawlak, Rough Sets, Theoretical Aspects about Data, Kluwer Academic Publisher, Dordrecht, 1991.
  • N. Kuroki, J. N. Mordeson, Successor and source functions, J. Fuzzy Math. 5 (1997) 173–182
  • N. Kuroki, J. N. Mordeson, Successor and source functions, J. Fuzzy Math. 5 (1997) 173–182
  • Z. Bavel, Introduction to the Theory of Automata, Reston Publishing Company, Inc., Reston, Virginia, 1983.
  • E. S. Santos, On reduction of max–min machines, J. Math. Anal. Appl. 37 (1972) 677–686.
  • E. S. Santos, Fuzzy automata and languages, Inform. Sci. 10 (1976) 193–197.
  • Y. B. Jun, C. S. Kim, K. O. Yang, Cubic sets, Annals of fuzzy Mathematics and Informatics, 4(2012), 83-98.
  • S. Eilenberg, “Automata, Languages, and Machines,” Academic Press, New York, vol. A, B, 1974.
  • S. Kleene, “Representation of events in nerve nets and finite automata,” in: C.E. Shannon and J. McCarthy (eds.), Automata Studies, Princeton University Press, pp. 3–42, 1956.
  • S. Yu, “Regular languages,” in: G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages, Springer-Verlag, Berlin, Heidelberg, vol. 1, pp. 41–110, 1997.
  • S. P. Tiwari, Arun K. Srivastava, On a decomposition of fuzzy automata, Fuzzy Sets Syst. 151 (2005) 503–511
  • A. V. Aho and J. D. Ullman , “Foundations of Computer Science,” Computer Science Press, New York, 1994.
  • L. A. Zadeh, Fuzzy Sets, Inform. & Control 8, (1965), 338 -353.

Cubic finite state machine and cubic transformation semigroups

Yıl 2017, Cilt: 5 Sayı: 4, 24 - 39, 01.10.2017

Öz

This
paper provides a new generalization of fuzzy finite state machines, fuzzy
transformation semigroups and their relationship. Consider a cubic structure,
we introduce cubic finite state machines, cubic transformation semigroups,
cubic successor, cubic exchange properties cubic subsystems, cubic submachines,
cubic q-twins, cubic retrievable and study fundamental properties of them. We
provide relationship between cubic q-twins and a cubic q-related. We provide a characterization of a cubic retrievable. We define
cfsm homomorphism and investigated related properties. We show that the
composition of strong cfsm homomorphism is 
also strong. We also define cubic transformation semigroup and it
related properties. We define cts homomorphism and its properties.

Kaynakça

  • Y. H. Kim, J. G. Kim, S. J. Cho, Products of T-generalized state machines and T-generalized transformation semigroups, Fuzzy Sets and Systems 93 (1998) 87–97.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, On subsystems of a fuzzy finite state machine, Fuzzy Sets and Systems 68 (1994) 83–92.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, Products of fuzzy finite state machines, Fuzzy Sets and Systems 92 (1997) 95–102.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, Semigroups of fuzzy finite state machines, in: P.P. Wang (Ed.), Advances in Fuzzy Theory and Technology, Vol. II, 1994, pp. 87–98.
  • D. S. Malik, J. N. Mordeson, M. K. Sen, Submachines of fuzzy finite state machines, J. Fuzzy Math. 4 (1994) 781–792
  • H. Bustince, E. Barrenechea, M. Pagola, J. Fernndez, Interval-valued fuzzy sets constructed from matrices: application to edge detection, Fuzzy Sets Syst. 160, (2009), 1819-1840.
  • R. Belohlavek, Determinism and fuzzy automata, Inform. Sci. 143 (1) (2002) 205–209.
  • J. Ignjatovic, M. Ciric, S. Bogdanovic, Determinations of fuzzy automata with membership values in complete residuated lattices, Inform. Sci. 178, (2008) 164–180.
  • H. X. Lei, Y. M. Li, Minimization of states in automata theory based on finite lattice-ordered monoids, Inform. Sci. 177, (6) (2007), 1413–1421.
  • Y. M. Li, W. Pedrycz, Minimization of lattice finite automata and its application to the decomposition of lattice languages, Fuzzy Sets Syst. 158, (2007), 1423–1436.
  • Ping Li, Y. M. Li, Algebraic properties of LA-languages, Inform. Sci. 176 (21) (2006) 3232–3255.
  • H. Z. Li, P. Li, Y. Y. Li, The relationships among several types of fuzzy automata, Inform. Sci. 176 (15) (2006) 2208–2226.
  • K. Peeva, Zl. Zahariev, Computing behavior of finite fuzzy machines – algorithm and its application to reduction and minimization, Inform. Sci. 178 (21), (2008), 4152–4165.
  • D. W. Qiu, Notes on automata theory based on quantum logic, Science in China Series F: Inform. Sci. 50 (2) (2007) 154–169.
  • S. P. Tiwari, Arun K. Srivastava, On a decomposition of fuzzy automata, Fuzzy Sets Syst. 151 (2005) 503–511.
  • Y. B. Jun, Intuitionistic fuzzy transformation semigroups, Inform. Sci. 179 (24) (2009) 4284–4291.
  • Y. B. Jun, Intuitionistic fuzzy finite state machines, J. Appl. Math. Comput. 17 (1–2) (2005) 109–120.
  • Y. B. Jun, Intuitionistic fuzzy finite switchboard state machines, J. Appl. Math. Comput. 20 (1–2) (2006) 315–325.
  • Y. B. Jun, Quotient structures of intuitionistic fuzzy finite state machines, Inform. Sci. 177 (2007) 4977–4986
  • W. G. Wee, On generalization of adaptive algorithm and application of fuzzy sets concept to pattern classification. PH.D Theses, Purdue University, June, 1967.
  • E. Orlowska, Semantic analysis of inductive reasoning, Theoret. Comput. Sci. 43 (1986) 81–89.
  • A. Kandal, Fuzzy Switching and Automata: Theory and Applications (Crane Russak, 1980).
  • W. M. Holcombe, Algebraic Automata Theory (Cambridge Univ. Press, Cambridge, 1982).
  • L. A. Zadeh, Fuzzy sets, Inform. Control 8, (1965), 338-353.
  • H. V. Kumbhojkar and S. R. Chaudhari, On covering of products of fuzzy finite state machines, Fuzzy Sets and Systems 125 (2002), 215–222.
  • K. Peeva, Zl. Zahariev, Computing behavior of finite fuzzy machines – algorithm and its application to reduction and minimization, Inform. Sci. 178 (21), (2008) 4152–4165.
  • D. W. Qiu, Notes on automata theory based on quantum logic, Science in China Series F: Inform. Sci. 50 (2), (2007), 154–169.
  • D. S. Malik, J. N. Mordeson, Structure of upper and lower approximation spaces of infinite sets, in: T.Y. Lin, Y.Y. Yao, L.A. Zadeh (Eds.), Data Mining,
  • Rough Sets and Granular Computing, Studies in Fuzziness and Soft Computing, vol. 95, Physica-Verlag, Heidelberg, New York, 2002, pp. 461–472.
  • Z. Pawlak, Rough Sets, Theoretical Aspects about Data, Kluwer Academic Publisher, Dordrecht, 1991.
  • N. Kuroki, J. N. Mordeson, Successor and source functions, J. Fuzzy Math. 5 (1997) 173–182
  • N. Kuroki, J. N. Mordeson, Successor and source functions, J. Fuzzy Math. 5 (1997) 173–182
  • Z. Bavel, Introduction to the Theory of Automata, Reston Publishing Company, Inc., Reston, Virginia, 1983.
  • E. S. Santos, On reduction of max–min machines, J. Math. Anal. Appl. 37 (1972) 677–686.
  • E. S. Santos, Fuzzy automata and languages, Inform. Sci. 10 (1976) 193–197.
  • Y. B. Jun, C. S. Kim, K. O. Yang, Cubic sets, Annals of fuzzy Mathematics and Informatics, 4(2012), 83-98.
  • S. Eilenberg, “Automata, Languages, and Machines,” Academic Press, New York, vol. A, B, 1974.
  • S. Kleene, “Representation of events in nerve nets and finite automata,” in: C.E. Shannon and J. McCarthy (eds.), Automata Studies, Princeton University Press, pp. 3–42, 1956.
  • S. Yu, “Regular languages,” in: G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages, Springer-Verlag, Berlin, Heidelberg, vol. 1, pp. 41–110, 1997.
  • S. P. Tiwari, Arun K. Srivastava, On a decomposition of fuzzy automata, Fuzzy Sets Syst. 151 (2005) 503–511
  • A. V. Aho and J. D. Ullman , “Foundations of Computer Science,” Computer Science Press, New York, 1994.
  • L. A. Zadeh, Fuzzy Sets, Inform. & Control 8, (1965), 338 -353.
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Saleem Abdullah Bu kişi benim

Rabia Naz Bu kişi benim

Witold Pedrycz Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 4

Kaynak Göster

APA Abdullah, S., Naz, R., & Pedrycz, W. (2017). Cubic finite state machine and cubic transformation semigroups. New Trends in Mathematical Sciences, 5(4), 24-39.
AMA Abdullah S, Naz R, Pedrycz W. Cubic finite state machine and cubic transformation semigroups. New Trends in Mathematical Sciences. Ekim 2017;5(4):24-39.
Chicago Abdullah, Saleem, Rabia Naz, ve Witold Pedrycz. “Cubic Finite State Machine and Cubic Transformation Semigroups”. New Trends in Mathematical Sciences 5, sy. 4 (Ekim 2017): 24-39.
EndNote Abdullah S, Naz R, Pedrycz W (01 Ekim 2017) Cubic finite state machine and cubic transformation semigroups. New Trends in Mathematical Sciences 5 4 24–39.
IEEE S. Abdullah, R. Naz, ve W. Pedrycz, “Cubic finite state machine and cubic transformation semigroups”, New Trends in Mathematical Sciences, c. 5, sy. 4, ss. 24–39, 2017.
ISNAD Abdullah, Saleem vd. “Cubic Finite State Machine and Cubic Transformation Semigroups”. New Trends in Mathematical Sciences 5/4 (Ekim 2017), 24-39.
JAMA Abdullah S, Naz R, Pedrycz W. Cubic finite state machine and cubic transformation semigroups. New Trends in Mathematical Sciences. 2017;5:24–39.
MLA Abdullah, Saleem vd. “Cubic Finite State Machine and Cubic Transformation Semigroups”. New Trends in Mathematical Sciences, c. 5, sy. 4, 2017, ss. 24-39.
Vancouver Abdullah S, Naz R, Pedrycz W. Cubic finite state machine and cubic transformation semigroups. New Trends in Mathematical Sciences. 2017;5(4):24-39.