Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2017
  • Volume: 36e
  • Issue: 2

T-Intuitionistic fuzzy H-Ideals of BCK-Algebras

1Department of Mathematics, D.H.S.K. College, Dibrugarh-786001, Assam, India. E-mail: akdutta28@gmail.com

2Department of Mathematics, Srikishan Sarda College, Hailakandi-788151, Assam, India. E-mail: saidurbarbhuiya@gmail.com

3Department of Mathematics, Assam University, Silchar-788011, Assam, India. E-mail: karabidc@gmail.com

4Department of Mathematical Sciences, Tezpur University, Tezpur, Assam-784 028, India, E-mail: dbasnet@tezu.ernet.in

*Corresponding Author: S.R. Barbhuiya, Assistant Professor and Head, Department of Mathematics, Srikishan Sarda College, Hailakandi-788151, Assam, India. E-mail: saidurbarbhuiya@gmail.com

Online published on 16 January, 2018.

Abstract

The aim of this paper is to introduce the concept of t-intuitionistic fuzzy H-ideals of BCK-algebras as a generalization of intuitionistic fuzzy H-ideals BCK-algebras and study the effect of some modal operators on t-intuitionistic fuzzy H-ideals of BCK-algebras.

The method adapted to study the objectives is analytic/logical method. Some examples and counter examples are provided in support of theorem and remarks etc. We observe that if t=1 the t-intuitionistic fuzzy H-ideal of BCK-algebra becomes a intuitionistic fuzzy H-ideal of BCKalgebra.

Here we define t-intuitionistic fuzzy H-ideals of BCK-algebras. Some noble properties of t-intuitionistic fuzzy H-ideals are stated and proved. We observe that t-intuitionistic fuzzy Hideal of BCK-algebras is invariant under modal operators and homomorphic mappings. We proved that the intersection and cartesian product of two or more t-intuitionistic fuzzy H-ideals of BCK-algebras is again a t-intuitionistic fuzzy H-ideal.

t-intuitionistic fuzzy H-ideal of BCK-algebra can be used in medical diagnosis, image processing, artficial intelligency etc.

Keywords

BCK-algebra, t-intuitionistic fuzzy set, t-intuitionistic fuzzy H-ideal, Modal operator, Homomorphism