Modeling vague beliefs using fuzzy-valued belief structures

This paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory. We adopt as a starting point the non probabilistic interpretation of belief functions provided by Smets’ Transferable Belief Model, as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions. We then introduce the concepts of interval-valued and fuzzy-valued belief structures, defined, respectively, as crisp and fuzzy sets of belief structures verifying hard or elastic constraints. We then proceed with a generalization of various concepts of Dempster-Shafer theory including those of belief and plausibility functions, combination rules and normalization procedures. Most calculations implied by the manipulation of these concepts are based on simple forms of linear programming problems for which analytical solutions exist, making the whole scheme computationally tractable. We discuss the application of this framework in the areas of decision making under uncertainty and classification of fuzzy data.