Research Article

Fuzzy Medial Ideals of BCI-Algebras with Interval-Valued Membership Function

by  S. M.Mostafa, A. E. Radwan, A. M. Menshawy, R. Ghanem
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 109 - Issue 2
Published: January 2015
Authors: S. M.Mostafa, A. E. Radwan, A. M. Menshawy, R. Ghanem
10.5120/19162-0611
PDF

S. M.Mostafa, A. E. Radwan, A. M. Menshawy, R. Ghanem . Fuzzy Medial Ideals of BCI-Algebras with Interval-Valued Membership Function. International Journal of Computer Applications. 109, 2 (January 2015), 24-31. DOI=10.5120/19162-0611

                        @article{ 10.5120/19162-0611,
                        author  = { S. M.Mostafa,A. E. Radwan,A. M. Menshawy,R. Ghanem },
                        title   = { Fuzzy Medial Ideals of BCI-Algebras with Interval-Valued Membership Function },
                        journal = { International Journal of Computer Applications },
                        year    = { 2015 },
                        volume  = { 109 },
                        number  = { 2 },
                        pages   = { 24-31 },
                        doi     = { 10.5120/19162-0611 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2015
                        %A S. M.Mostafa
                        %A A. E. Radwan
                        %A A. M. Menshawy
                        %A R. Ghanem
                        %T Fuzzy Medial Ideals of BCI-Algebras with Interval-Valued Membership Function%T 
                        %J International Journal of Computer Applications
                        %V 109
                        %N 2
                        %P 24-31
                        %R 10.5120/19162-0611
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper the notion of interval–valued Fuzzy medial-ideals (briefly i-v fuzzy medial -ideal) in BCI-algebras is introduced. Several theorems are stated and proved. The image and pre-image of interval–valued fuzzy medial -ideals are defined and how the homomorphic images and pre-images of interval–valued fuzzy medial -ideals become interval–valued fuzzy medial -ideals in BCI-algebras is studied as well.

References
  • R. Biswas, Rosenfeld's fuzz subgroups with interval valued membership function, Fuzzy Sets and Systems 63 (1994), No. 1 87-90.
  • M. Abe and K. Iseki, A survey on BCK and BCI algebras, Congresso de Logica Aplicada Techologia, LAPTEC 2000, 431-443. Festschrift in Hornor of Gabriel Thierrin, World Sci. (2001), 231-238.
  • K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23(1978), 1-26.
  • K. Iseki, On BCI-algebras, Math. Sem. Notes 8 (1980) 125-130.
  • Y. Imai and K. Iseki: On axiom systems of Propositional calculi, XIV, Proc. Japan Acad. Ser A, Math Sci. , 42(1966),19-22.
  • Y. Bae Jun , VALUED FUZZY SUBALGEBRAS/IDEALS IN BCK-ALGEBRAS . Scientiae Mathematicae Vol. 3, No. 3(2000), 435{444
  • J. Meng and Y. B. Jun, Notes on medial BCI-algebras, Comm. Korean Math. Soc. 8(1) (1993),33-37.
  • S. M. Mostafa, Y. B. Jun and A. El-menshawy, Fuzzy medial ideals in BCI-algebras, fuzzy math. , vol. 7, no. 2,1999, pp445-457.
  • O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36(5) (1991), 935-942.
  • L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.
  • L. A. Zadeh The concept of a linguistic variable and its application to approximate reasoning. I, Information Sci. 8 (1975), 199–249. MR 52#7225a. Zbl 397. 68071.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Fuzzy medial-ideals- interval valued fuzzy medial-ideals- images and pre- images of interval valued fuzzy medial-ideals

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