A study of g*-fuzzy closed set via αm in double fuzzy topological space

Document Type : Research Paper


1 Ministry of Education, Salah al-Din Education Directorate, Tikrit, Iraq

2 Department of Mathematics, University of Tikrit, Iraq


The aim of this research paper is to present and study a new class of generalized closed sets in double fuzzy topological spaces, by using the fuzzy  $\alpha^m$-closed set, that was previously presented. This new class is called the fuzzy $\alpha^m- g^*$-closed set. The relationship of the new concept with previous concepts is studied and the characteristics of this concept is investigated through important theorems that determine the position of this set in relation to sets that have been studied or that will be presented later. Also, generalizations of the functions are presented according to the concept, their properties are studied, and some necessary examples that show the properties of this concept and its relationships.


[1] S.E. Abbas, (R,S)-generalized intuitionistic fuzzy sets, J. Math. Soc. 14(2) (2006) 283–297.
[2] S.I. Abdullah, The Continuity in Double Fuzzy Topological Spaces via αm-closed Sets, Master Thesis, Tikrit
University, 2018.
[3] K.K. Azad, On fuzzy semi-continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl.
82(1) (1981) 14–32.
[4] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1) (1968) 182–190.
[5] J.G. Garcia and S.E. Rodabaugh, Order-theoretic, topological, categorical redundancies of interval-valued sets,
grey sets, vague sets, interval-valued “intuitionistic” sets, “intuitionistic” fuzzy sets and topologies, Fuzzy Sets
Syst. 156(3) (2005) 445–484.
[6] A. Ghareeb, Normality of double fuzzy topological spaces, Appl. Math. Lett. 24(4) (2011) 533–540.
[7] T.H. Jasim, S.I. Abdullah and K.S. Eke, Contra continuity on double fuzzy topological space, Int. J. Math. Comput.
Sci. 15(4) (2020) 1309–1319.
[8] A.D. Kalamain, K. Sakthivl and C.S. Gowri, Generalized alpha closed sets in intuitionistic fuzzy topological spaces,
Appl. Math. Sci. 6(94) (2012) 4691–4700.
[9] F.M. Mohammed and S.I. Abdullah, Some types of continuous function via (r0, s1) − fuzzyαm- closed sets,
Tikrit J. Pure Sci. 23(8) (2018) 101–104.
[10] F.M. Mohammed, M.S.M. Noorani and A. Ghareeb, Slightly double fuzzy continuous functions, J. Egyptian Math.
Soc. 23(1) (2015) 173–179.
[11] L.A. Zadeh, Fuzzy sets, Inf. Cont. 8(3) (1965) 338–353.
Volume 13, Issue 1
March 2022
Pages 91-95
  • Receive Date: 13 May 2021
  • Revise Date: 16 June 2021
  • Accept Date: 29 July 2021
  • First Publish Date: 07 September 2021