An Intuitionistic Fuzzy Pseudo Enlarged Ideal of a BH-Algebra

In this Work the concepts of an intuitionistic fuzzy pseudo ideal of a pseudo BH-algebra are insert. several propositions and examples are scrupulous to study properties of this idea.


Definition
Assume that I and a subset of a BH-X. Therefore I is named an ideal of X if that was achieved: , X  0 I.  I and I I.

Definition
Assume that I and a subset of a P.BH-algebra and there is no need an ideal of , a subset J of is named an Enlarged ideal of related to I, and signify by E. I if that was achieved : for every ,  I is a subset of J  0 J  I and I J.

Definition
A pseudo BH indicates P.BH is a set with a fixed 0 and dual operations , check the next conditions :

Definition
Assume that S is a subset of a P.BH-X is named a P.BH-subalgebra of X signify by P.BH-S if that was achieved : and S, , S. 2.7. Definition Assume that I and subset of a P.BH-X. Therefore I is named a pseudo ideal & signify by P. I of X if achieved : , X  0 I.  , I and I I.

Definition
Assume that I and subset of a P.BH-algebra , a subset J of is named a pseudo Enlarged ideal of related to I, and signify by P. E. I if that was achieved : ,  I is a subset of J  0 J  I, I and I J.

Definition
Assume X that is a non-empty set, fuzzy subset , in X are a formula from X into [0 , 1] of the real number.

The Main Results
In the work, is defined the concepts of intuitionistic fuzzy pseudo enlarged ideal in P.BH-algebra. for our conversation, we will study the advantages of these concepts. 3.1. Definition Assume A & B are two I. F. S of a BH-algebra X, so that A B then B is named intuitionistic fuzzy enlarged ideal of X related to A & signify by I. F. E. I if that was achieved :

3.4.Example
Assume that X = { 0, k, v, h }is a P.BH with the following cayley tables : Then B is an I. F. P. E. I of X related to A.

3.5.Theorem
Assume that { | } is a family of I. F. P. E. I of a P.BH-algebra X related to A. Then is an I. F. P. E. I of X related to A. Proof :- Assume that μ X, ,

Theorem
Assume that X is a P.BH such that ́ is an I. F. S of X so that (0) = (0) & (0) = (0), then B is an I. F. P. E. I of X related to A ́ is an I. F. P. E. I of X related to ́. Proof :-Suppose B is an I. F. P. E. I of X related to A and μ X (μ ) (μ ),