Random Sets pp 209-242 | Cite as

Extension of Relational and Conditional Event Algebra to Random Sets with Applications to Data Fusion

  • I. R. Goodman
  • G. F. Kramer
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 97)


Conditional event algebra (CEA) was developed in order to represent conditional probabilities with differing antecedents by the probability evaluation of well-defined individual “conditional” events in a single larger space extending the original unconditional one. These conditional events can then be combined logically before being evaluated. A major application of CEA is to data fusion problems, especially the testing of hypotheses concerning the similarity or redundancy among inference rules through use of probabilistic distance functions which critically require probabilistic conjunctions of conditional events. Relational event algebra (REA) is a further extension of CEA, whereby functions of probabilities formally representing single event probabilities — not just divisions as in the case of CEA — are shown to represent actual “relational” events relative to appropriately determined larger probability spaces. Analogously, utilizing the logical combinations of such relational events allows for testing of hypotheses of similarity between data fusion models represented by functions of probabilities. Independent of, and prior to this work, it was proven that a major portion of fuzzy logic — a basic tool for treating natural language descriptions — can be directly related to probability theory via the use of one point random set coverage functions. In this paper, it is demonstrated that a natural extension of the one point coverage link between fuzzy logic and random set theory can be used in conjunction with CEA and REA to test for similarity of natural language descriptions.

Key words

Conditional Event Algebra Conditional Probability Data Fusion Functions of Probabilities Fuzzy Logic One Point Coverage Functions Probabilistic Distances Random Sets Relational Event Algebra 


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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • I. R. Goodman
  • G. F. Kramer
    • 1

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