Interval-Valued Neutrosophic Ideals of Hilbert Algebras

Aiyared Iampan1 ∗, P. Jayaraman2, S. D. Sudha3, N. Rajesh4

1Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of

Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand

2,3Department of Mathematics, Bharathiyar University, Coimbatore 641046, Tamilnadu, India

4Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India

Emails: aiyared.ia@up.ac.th1;jrmsathya@gmail.com2;

sudhaa88@gmail.com3;nrajesh topology@yahoo.co.in4

Abstract

The concept of interval-valued neutrosophic sets (IVNSs) was first introduced by Wang et al. (Wang, H.;

Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. Interval neutrosophic sets and logic: Theory and applications

in computing. Hexis, Phoenix, Ariz, USA, 2005.). In this paper, the concept of IVNSs to ideals of Hilbert

algebras is introduced. The homomorphic inverse image of interval-valued neutrosophic ideals (IVN ideals)

in Hilbert algebras is also studied and some related properties are investigated.

Keywords: Hilbert algebra; ideal; interval-valued neutrosophic ideal; level cut