An extension of rule base evidential reasoning in the interval-valued intuitionistic fuzzy setting applied to the type 2 diabetes diagnostic

This paper presents an interval-valued intuitionistic fuzzy extension of rule base evidential reasoning which generally is a synthesis of fuzzy logic, the Dempster–Shafer theory of evidence (DST) and Atanassov’s intuitionistic fuzzy sets (A-IFS) theory redefined in the framework of DST. A lot of attention is paid to situations when in the solution of decision making problem the competing fuzzy classes with intersecting membership functions in antecedent parts of fuzzy rules, e.g., such as Low and Moderate play an important role in the problem formulation. As a result, a new mathematical object “belief interval bounded belief interval” (BIBBI) is obtained. The properties of BIBBI make it possible to use it as a more reliable representation of interval-valued intuitionistic fuzzy value than that formulated in terms of A-IFS. Using the introduced DST based definition of interval-valued A-IFS, the corresponding operations with BIBBIs and the DST representation of rule base evidential reasoning in the intuitionistic fuzzy setting, a new approach to the interval-valued intuitionistic fuzzy extension of rule base evidential reasoning is developed. To prove the correctness and applicability of this approach to the solution of decision making problems, a case study of its use for the type 2 diabetes diagnostics is analyzed.