Fuzzy relations between Dempster–Shafer belief structures

Relationships between attribute values can involve concepts such as similar or greater then. We first discuss the mathematical structure of relationships. We consider both crisp and fuzzy relationships. We introduce some important examples of mathematical relationships and describe their formal properties. We then turn to the problem of calculating the degree of relationship between attributes whose values are uncertain. We first consider the case when the uncertainties in the attribute values are expressed in terms of possibility distributions. We next look at the case when the uncertainties are in the form of a standard Dempster–Shafer belief structure. We finally consider the situation when the uncertain information associated with the attribute values are expressed in terms of Dempster-Shafer belief structures whose focal elements are fuzzy sets.