BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Bull. Int. Math. Virtual Inst., Vol. 11(3)(2021), 545-553 DOI: 10.7251/BIMVI2103545G Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) NEUTROSOPHIC BIMINIMAL α-OPEN SETS Selvaraj Ganesan and Florentin Smarandache Abstract. In this article, we have introduced the notions of N j mX -α-open sets, α-interior and α-closure operators in neutrosophic biminimal structures. We investigate some basic properties and theorems of such notions. Also we have introduced the notion of N j mX -α-continuous maps and study charac- terizations of N j mX -α-continuous maps by using the α-interior and α-closure operators in neutrosophic biminimal structures. 1. Introduction Zadehs [14] Fuzzy set laid the foundation of many theories such as intuition- istic fuzzy set and neutrosophic set, rough sets etc. Later, researchers developed K. T. Atanassovs [1] intuitionistic fuzzy set theory in many fields such as differ- ential equations, topology, computer science and so on. F. Smarandache [12, 13] found that some objects have indeterminacy or neutral other than membership and non-membership. So he coined the notion of neutrosophy. Q. H. Imran et al [6] introduced and studied neutrosophic semi-α-open sets. R. Dhavaseelan et al [2] introduced and studied neutrosophic α m -continuity. C. Maheswari and S. Chan- drasekar [8] introduced and studied neutrosophic gb-closed sets and neutrosophic gb-continuity. Q. H. Imran et al [7] introduced and studied neutrosophic general- ized alpha generalized continuity. M. H. Page and Q. H. Imran [9] introduced and studied neutrosophic generalized homeomorphism. The concept of minimal struc- ture (in short, m-structure) was introduced by V. Popa and T. Noiri [10] in 2000. Also they introduced the notion of m x -open set and m x -closed set and characterize those sets using m x -closure and m x -interior operators respectively. Further they 2010 Mathematics Subject Classification. 03E72. Key words and phrases. Neutrosophic biminimal structure spaces, N j mX -open, N j mX -α-open and N j mX -α-continuous. Communicated by Daniel A. Romano. 545