Representation of interrelationships among binary variables under dempster-shafer theory of belief functions

Abstract

This paper presents an algorithm for developing models under Dempster-Shafer theory of belief functions for categorical and "uncertain" logical relationships among binary variables. We illustrate the use of the algorithm by developing belief-function representations of the following categorical relationships: "AND," "OR," "exclusive OR (EOR)" and "not exclusive OR (NEOR)," and "AND-NEOR" and of the following uncertain relationships: "discounted AND," "conditional OR," and "weighted average." Such representations are needed to fully model and analyze a problem with a network of interrelated variables under Dempster-Shafer theory of belief functions. In addition, we compare our belief-function representation of the "weighted average" relationship with the "weighted average" representation developed and used by Shenoy and Shenoy (in Belief Functions in Business Decisions, edited by R. P. Srivastava and T. Mock; Heidelberg, Germany: Physica-Verlag; pp 316-332). We find that Shenoy and Shenoy representation of the weighted average relationship is an approximation and yields significantly different values under certain conditions. C 2009 Wiley Periodicals, Inc.

Using Belief Functions in Software Agents to Test the Strength of Application Controls

“…The above conditions are defined by the following belief mass for the interrelationship among the three agents which is the relationship R diagramed above (see Srivastava et al 2009)…”

D-CFPR: D numbers extended consistent fuzzy preference relations

“…It has extended the Dempster-Shafer theory [35,36]. DempsterShafer theory is with advantages to handle uncertain information [37,38,39,40,41,42,43,44], and is extensively used in many fields, such as risk assessment [45,46], expert systems [47,48], classification and clustering [49,50], parameter estimation [51], decision making [52,53,54], and so forth [55,56,57,58,59,60,61]. However, there are some weaknesses in DempsterShafer theory.…”

D-CFPR: D numbers extended consistent fuzzy preference relations

“…It has extended the Dempster-Shafer theory [35,36]. Dempster-Shafer theory is with advantages to handle uncertain information [37,38,39,40,41,42,43,44], and is extensively used in many fields, such as risk assessment [45,46], expert systems [47,48], classification and clustering [49,50], parameter estimation [51], decision making [52,53,54], and so forth [55,56,57,58,59,60,61]. However, there are some weaknesses in Dempster-Shafer theory.…”