General belief functions usually bear some internal conflict which comes mainly from disjoint focal elements, analogously there is often some conflict between two (or more) belief functions.
This theoretical contribution introduces a new approach to conflicts of belief functions. Conflicts (of belief functions) are considered independently of any combination rule and of any distance measure. Consonant conflicts are based on consonant approximations of belief functions in general; two special cases of the consonant approach based on inverse pignistic and inverse plausibility transformations are discussed. Their idea is based on our previous study of conflicts of belief functions, where internal conflicts of individual belief functions are distinguished from a conflict between belief functions.
Basic properties of these newly defined conflicts are presented, analyzed and briefly compared with our previous approaches to conflict (combinational conflict, plausibility conflict and comparative conflict) as well as with Liu's degree of conflict and Harmanec's measure of conflict.

Keywords:
Belief functions, Dempster-Shafer theory, uncertainty, internal conflict of a belief function, conflict between belief functions, consonant approximation.