Research Article

On a-continuous Intuitionistic Fuzzy Multifunctions

by  S.S. Thakur, Kush Bohre, Shailendra Singh Thakur
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 29 - Issue 3
Published: September 2011
Authors: S.S. Thakur, Kush Bohre, Shailendra Singh Thakur
10.5120/3546-4862
PDF

S.S. Thakur, Kush Bohre, Shailendra Singh Thakur . On a-continuous Intuitionistic Fuzzy Multifunctions. International Journal of Computer Applications. 29, 3 (September 2011), 20-23. DOI=10.5120/3546-4862

                        @article{ 10.5120/3546-4862,
                        author  = { S.S. Thakur,Kush Bohre,Shailendra Singh Thakur },
                        title   = { On a-continuous Intuitionistic Fuzzy Multifunctions },
                        journal = { International Journal of Computer Applications },
                        year    = { 2011 },
                        volume  = { 29 },
                        number  = { 3 },
                        pages   = { 20-23 },
                        doi     = { 10.5120/3546-4862 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2011
                        %A S.S. Thakur
                        %A Kush Bohre
                        %A Shailendra Singh Thakur
                        %T On a-continuous Intuitionistic Fuzzy Multifunctions%T 
                        %J International Journal of Computer Applications
                        %V 29
                        %N 3
                        %P 20-23
                        %R 10.5120/3546-4862
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

In 1999, Ozbakir and Coker [23] introduced the concept intuitionistic fuzzy multifunctions and studied their lower and upper intuitionistic fuzzy semi continuity from a topological space to an intuitionistic fuzzy topological space. The present paper introduces the concept of α-continuous intuitionistic fuzzy multifunctions. An Intuitionistic fuzzy multifunction F from a topological spaces (X,T) to an intuitionistic fuzzy toplogical spaces (Y,Γ) is said to be Intuitionistic fuzzy α-continuous at a point if for any G ̃_1,G ̃_2∈IFO(Y) such that F(x_0)⊂G ̃_1 and F(x_0)∩G ̃_2 there exists U∈αO(X) containing x_0 such that F(u)⊂G ̃_1 and F(u)∩G ̃_2,∀ u∈U. F is called Intuitionistic fuzzy α-continuous if it has this property at each point of X. Several properties and characterizations of Intuitionistic fuzzy α-continuous

References
  • Andrijevic D. 1984, Some Propreties of the Topology of α-sets, Mat. Vesnik 36,1-10.
  • Atanassov K. 1983, Intuitionistic Fuzzy Sets, In VII ITKR’s Session, (V. Sgurev, Ed.) Sofia, Bulgaria,
  • Atanassov K. and Stoeva S. 1983, Intuitionistic Fuzzy Sets, In Polish Symposium on Interval and Fuzzy Mathematics , Poznan, 23-26
  • K. Atanassov K. 1986, Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20, 87-96.
  • Berge C. 1959, Espaces topologiques. Fonctions multivoques, Dunod. Paris.
  • Chang C. L. 1968, Fuzzy Topological Spaces, J. Math. Anal. Appl. 24, 182-190.
  • Coker D. 1997, An Introduction to Intuitionistic Fuzzy Topological Spaces, Fuzzy Sets and Systems 88, 81-89.
  • Coker D. and Demirci M. 1995, On Intuitionistic Fuzzy Points, Notes on Intuitionistic Fuzzy Sets 2(1), 78-83
  • Evert J. 1988, Fuzzy Valued Maps. Math. Nachr. 137, 79-87.
  • Gurcay H., D. Coker D. and Hayder A. Es. 1997, On Fuzzy Continuity in Intuitionistic Fuzzy Topological Spaces. The Journal of Fuzzy Mathematics 5(2),365-378.
  • Levine N. 1963, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70, 36-41.
  • Lupianez F. G. 2004, Separation axioms in intuitionistic fuzzy topological spaces, International Journal of Pure and Applied Mathematics 17(1)29-34.
  • Maheshwari S. N., Thakur S. S. 1985, On α-Compact spaces, Bull. Int. Math. Acad. Sinica 13, 341-347.
  • Maheshwari S. N., Thakur S. S. 1980, On α-irresolute mappings, Tamkang Jour. Math. 11(2)209-214.
  • Maheshwari S. N., Thakur S. S. 1985, On α-Continuous Mappings, J. Indian. Acad. Math., 7(1), 46-50.
  • Mashhour A. S., Hasanein I. A., El- Deeb S. N. 1983, α-Continuous and α-open Mapping, Acta Math. Hungar. 41, 213-218.
  • Neubrunnov A. 1973, On certain generalizations of the notions of continuity. Mathematiki Casopis 23(4),374-80.
  • Neubrunn T. 1988, Strongly quasi-continuous multivalued mapping. In General Topology and its Relations to Modern Analysis and Algebra VI(prague 1986), Heldermann, Berlin, (1988), pp. 351-359.
  • Njastad O. 1965, On some classes of nearly open sets, Pecific J. Math. 15, 961-970.
  • Noiri T. 1982, A function which preserves connected spaces, Casopis Pest. Math. 107 , 393-396.
  • Noiri T.1984, On α-Continuous functions, Casopis Pest. Math. 109, 118-126.
  • Noiri T., Di Maio G. 1988, Properties of α-compact Spaces. In: Third National conference on Topology (Trieste, 1986) (Italian), Rend. Circ. Mat. Palermo(2) Suppl. 18,359-369.
  • Ozbakir O. and Coker D. 1999, Fuzzy Multifunction’s in Intuitionistic Fuzzy Topological Spaces, Notes on Intuitionistic Fuzzy Sets 5(3)1-5.
  • Papageorgiou N. S. 1985, Fuzzy Topology and Fuzzy multifunctions. Jour. Math. Anal. Appl.,109(2),397-425.
  • Popa V. and Noiri T. 1993, On Upper and Lower α-Continuous Multifunctions.Math.Slovaca,43,no.4,477-491.
  • Saxena S. 2008, Extension of set valued mappings in fuzzy Topololgy. Ph.D. Dissertation , Rani Durgavati Vishwavidhyalaya Jabalpur (2008).
  • Thakur S. S. and Bohre Kush 2011, On intuitionistic fuzzy multifunctions , International Journal of Fuzzy Systems and Rough Systems.4(1) (2011) (accepted).
  • Thakur S. S. and Bohre Kush , On Upper and Lower α-Continuous intuitionistic fuzzy multifunctions (Submitted)
  • Zadeh L. A. 1965, Fuzzy Sets, Information and Control, 18(1965),338-353.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Intuitionistic fuzzy sets Intuitionistic fuzzy topology Intuitionistic fuzzy multifunctions lower α-continuous and upper α-continuous Intuitionistic fuzzy multifunctions

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