Ideal and dot ideal of a PS algebra in picture fuzzy environment

Abstract

In this paper, the notion of picture fuzzy ideal of a PS algebra is introduced as a generalization of fuzzy ideal of a PS algebra and some important results are explored in this regard. It is highlighted that the intersection of two picture fuzzy ideals is a picture fuzzy ideal and Cartesian product of two picture fuzzy ideals is a picture fuzzy ideal. Also, it is shown by two examples that union of two picture fuzzy ideals is not necessarily a picture fuzzy ideal. The concept of picture fuzzy dot ideal is initiated here as a generalization of fuzzy dot ideal and some elementary results are investigated. A relation between picture fuzzy ideal and picture fuzzy dot ideal is developed here. It is shown that a picture fuzzy ideal is a picture fuzzy dot ideal. But the converse of this proposition is not true in general which has been clarified by an example.