IDEAL AND DOT IDEAL OF A PS ALGEBRA IN PICTURE FUZZY ENVIRONMENT

IDEAL AND DOT IDEAL OF A PS ALGEBRA IN PICTURE FUZZY ENVIRONMENT

S. Dogra, M. Pal

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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 clari ed by an example.

Keywords

Fuzzy set, fuzzy ideal, intuitionistic fuzzy set, picture fuzzy set, picture fuzzy ideal, picture fuzzy dot ideal.