A unified algebraic structure for uncertain reasonings

Abstract

This paper identifies an axiom foundation for uncertain reasonings in rule-based expert systems: a near topological algebra (NT-algebra for short), which holds some basic notions hidden behind the uncertain reasoning models in rule-based expert systems. In according with basic ways of topological connection in an inference network, an NT-algebraic structure has five basic operators, i.e. AND, OR, NOT, Sequential combination and Parallel combination, which obey some axioms. An NT-algebraic structure is defined on a near-degree space introduced by the authors, which is a special topological space. The continuities of real functions, of fuzzy functions and the functions in other sense can be uniformly considered in the framework of a near-degree space. This paper also proves that the EMYCIN's and PROSPECTOR'S uncertain reasoning models correspond to good NT-algebras, respectively. Compared to other related works, the NT-algebra as an axiom foundation has the following characteristics: (1) various cases of assessments for uncertainties of both evidence and rules are put into a unified algebraic structure; and (2) major emphasis has been placed on the basic laws of the propagation for them in an inference network.

This research is supported by a large grant from the Australian Research Council (A49530850).