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Representation of interrelationships among binary variables under dempster–shafer theory of belief functions
Author(s) -
Srivastava Rajendra P.,
Gao Lei,
Gillett Peter R.
Publication year - 2009
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20347
Subject(s) - categorical variable , dempster–shafer theory , representation (politics) , mathematics , function (biology) , artificial intelligence , binary number , computer science , statistics , arithmetic , politics , political science , law , evolutionary biology , biology
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; 2002; 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. © 2009 Wiley Periodicals, Inc.