Interior Operators over Bipolar Intuitionistic M- Fuzzy Prime Group and Anti M- Fuzzy Prime Group

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-42 Number-1
Year of Publication : 2017
Authors : K. Gunasekaran, D. Gunaseelan
  10.14445/22315373/IJMTT-V42P501

MLA

K. Gunasekaran, D. Gunaseelan "Interior Operators over Bipolar Intuitionistic M- Fuzzy Prime Group and Anti M- Fuzzy Prime Group ", International Journal of Mathematics Trends and Technology (IJMTT). V42(1):1-9 February 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper the concept of a bipolar intuitionistic M fuzzy prime group and anti M fuzzy prime group is a new algebraic structure of a bipolar intuitionistic M fuzzy prime subgroup of a M fuzzy prime group and anti M fuzzy prime group are defined, related operators and interior operators are investigated. The purpose of the study is to implement the fuzzy set theory and group theory of bipolar intuitionistic M fuzzy prime subgroup of a M fuzzy prime group and anti M fuzzy prime group. The relation between operation of operators and interior operators of bipolar intuitionistic M fuzzy prime group and bipolar intuitionistic anti M fuzzy prime group are established.

References
[1]. Atanassov .K.T, Intuitionistic fuzzy sets, Fuzzy sets and systems,pp: 207-296, 1986.
[2]. Atanassov .K.T, New operations defined over intuitionistic fuzzy sets, Fuzzy sets and Systems , vol. 61( 2), pp: 137-142.
[3]. Atanassov .K.T, Inutitionistic fuzzy sets, Fuzzy sets and systems, vol 20(1), pp: 87-96. 1986.
[4]. Atanassov .K.T, Operators over interval valued intuitionistic fuzzy sets, Fuzzy sets and systems , vol: 64( 2), pp: 159-174, 1994.
[5]. Atanassov .K.T, Intuitionistic fuzzy sets: Theory and Applications, Springer – verlag, 1999.
[6]. Atanassov. K.T, Level operators on intuitionistic fuzzy sets, BUSEFAL, Vol-54, pp: 4-8.
[7]. ATANASSOV .K.T, Four new operators on intuitionistic fuzzy sets, preprint IM-MFAIS sofia ,pp: 4-89, 1989.
[8]. Coker .D, On topological structure using intuitionistic fuzzy sets, Notes on Intuitionistic fuzzy sets ,vol-3( 5),pp: 138-142, 1997.
[9]. Eclund .P, Gahler .W, Basic notations for fuzzy topology I, Fuzzy sets and Systems, vol- 27(3),pp: 333-356, 1998.
[10]. Lee .K.M, Bipolar valued fuzzy sets and their operations, Proc. int. con. on intelligent and technologies, Bangkok - Thailand.
[11]. Muthuraj .R, Sridharan .M, Bipolar anti fuzzy HX groups and its lower level sub HX subgroups, Journal of physical sciene,vol- 16,pp: 157-169,2012.
[12]. Palaniappan .N, Muthuraj .R, Anti fuzzy group and lower level subgroups, Antarctica Journal of Mathematics ,vol-1(1),pp: 71-76, 2004.
[13]. Palanivelrajan .M, Nandakumar .S, Some properties of intuitionistic fuzzy primary and fuzzy semi primary ideals. Notes on intuitionistic fuzzy sets. Vol-18( 3), pp: 68-74, 2012.
[14]. Palanivelrajan .M, Nandakumar .S, Some operations of intuitionistic fuzzy primary and semi primary ideal, Asian journal of Algebra,vol- 5(2),pp: 44-49, 2012.
[15]. Rosenfeld .A, Fuzzy groups J. math. anal. Application,vol- 35,pp: 512-517, 1971.
[16] Zadeh .L.A, Fuzzy sets, Information and control ,vol- 8,pp: 338-365.
[17]. Zhang .W.R, Bipolar Fuzzy sets, Proc. of fuzz –IEEE, pp: 835-840,1998.

Keywords
Bipolar fuzzy set, bipolar M fuzzy prime group, bipolar anti M fuzzy prime group, bipolar intuitionistic M fuzzy prime group, bipolar intuitionistic anti M fuzzy prime group.