Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions

In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $b$-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $(\alpha ,\beta )$-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.