Abstract
The concept of picture fuzzy sets was first introduced by Cuong and Kreinovich [B. C. Cuong, V. Kreinovich, Proceedings of the Third World Congress on Information and Communication Technologies WIICT, (2013), 1--6] in 2013, which is direct extensions of the fuzzy sets and the intuitionistic fuzzy sets. In this paper, we applied the concept of picture fuzzy sets in UP-algebras to introduce the eight new concepts of picture fuzzy sets by means of a special type: special picture fuzzy UP-subalgebras, special picture fuzzy near UP-filters, special picture fuzzy UP-filters, special picture fuzzy implicative UP-filters, special picture fuzzy comparative UP-filters, special picture fuzzy shift UP-filters, special picture fuzzy UP-ideals, and special picture fuzzy strong UP-ideals. Also, we discuss the relationship between the eight new concepts of picture fuzzy sets in UP-algebras. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.
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