Incorporating Uncertainty into the Formal Development of the Fusion Operator

This paper uses a formal approach to incorporating uncertainty of input information into the fusion process and decision making. Fuzzy set theory (fuzzy numbers, and fuzzy operators) is used to characterize and then manipulate (reason about) uncertainty. A library of speci cations of fuzzy set theory is developed using category theory and Specware, a tool that supports category theory based algebraic speci cation of software. The library is then used to construct speci cations of fuzzy information processing systems. The main construction in this process is composition. Category theory operators of limits and colimits are used for composition. As an example, a fuzzy edge detection algorithm is shown, which uses fuzzy operations in its processing. One of the advantages of this approach is that every aspect of the fusion process is speci ed formally, which allows us to reason about the uncertainty associated with the sensors and the