An In-Depth Look at Quantitative Information Fusion Rules

This chapter may look like a glossary of the fusion rules and we also introduce new ones presenting their formulas and examples: Conjunctive, Disjunctive, Exclusive Disjunctive, Mixed Conjunctive-Disjunctive rules, Conditional rule, Dempster’s, Yager’s, Smets’ TBM rule, Dubois-Prade’s, DezertSmarandache classical and hybrid rules, Murphy’s average rule, Inagaki-LefevreColot-Vannoorenberghe Unified Combination rules [and, as particular cases: Iganaki’s parameterized rule, Weighted Average Operator, minC (M. Daniel), and newly Proportional Conflict Redistribution rules (Smarandache-Dezert) among which PCR5 is the most exact way of redistribution of the conflicting mass to non-empty sets following the path of the conjunctive rule], Zhang’s Center Combination rule, Convolutive x-Averaging, Consensus Operator (Jøsang), Cautious Rule (Smets), α-junctions rules (Smets), etc. and three new T -norm & T -conorm rules adjusted from fuzzy and neutrosophic sets to information fusion (TchamovaSmarandache). Introducing the degree of union and degree of inclusion with respect to the cardinal of sets not with the fuzzy set point of view, besides that of intersection, many fusion rules can be improved. There are corner cases where each rule might have difficulties working or may not get an expected result. As a conclusion, since no theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories extending the power and hyper-power sets from previous theories to a Boolean algebra obtained by the closures of the frame of discernment under union, intersection, and complement of sets (for non-exclusive elements one considers a fuzzy or neutrosophic complement). And, at each application, one selects the most appropriate model, rule, and algorithm of implementation. The material of this chapter has been presented at NASA Langley Research Center, Hampton, Virginia, on November 5, 2004.