Attribute reduction and information granulation in Pythagorean fuzzy formal contexts

Abstract

Pythagorean fuzzy set theory is one of the significant tools to deal with real-life problems which are prone to imprecision, partial truth or uncertainty. A Pythagorean fuzzy set reports the degree of truthness as well as falsity of a statement in order to illustrate the imprecision of that statement. Motivated by the resourcefulness of this theory, this paper is aimed to explore formal concept analysis in Pythagorean fuzzy environment. It defines Pythagorean fuzzy formal concept and Pythagorean fuzzy concept lattice associated with a Pythagorean fuzzy formal context. The proposed Pythagorean fuzzy formal concept is a duple whose first argument is (crisp) extension and second argument is Pythagorean fuzzy intension. Moreover, the join of different combinations of object concepts of a Pythagorean fuzzy formal context returns different Pythagorean fuzzy formal concepts. We also studied the knowledge reduction in Pythagorean fuzzy formal contexts in association with Pythagorean fuzzy concept lattice. The key ideas of attribute reduct, core and discernibility matrix for a Pythagorean fuzzy formal context are illustrated. Further, we merged the notions of information granulation and attribute reduction with Pythagorean fuzzy formal context. Various results of formal concepts and concept lattices are extended in Pythagorean fuzzy set theory. At last, an algorithm is developed which discovers non-redundant Pythagorean fuzzy formal concepts for a given Pythagorean fuzzy formal context. Eventually, an example is presented which elaborates the procedure of this algorithm.