MORE ON PICTURE FUZZY SETS AND THEIR PROPERTIES

MORE ON PICTURE FUZZY SETS AND THEIR PROPERTIES

D. Saadi, A. Amroune

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Abstract

In this paper, some basic properties of the set of a picture fuzzy set truth values D  are studied. Also, using an adequate order   of D , some picture fuzzy sets operations are introduced by meaning a punctual order (point by point). As well as the order of D  is used to show some characteristic sets of a picture fuzzy set, such as support, kernel,  -cut, strong  -cut and picture fuzzy line of degree   of a picture fuzzy set, where   2 D ; have been de ned, some properties of them have been established and some decomposition theorems of picture fuzzy sets have been proved. Finally, some of Atanassov's modal operators are extended to the picture fuzzy case.

Keywords

Picture fuzzy set, picture fuzzy sets operations,  -cuts, picture fuzzy line of degree  , modal operators.