A hybrid fuzzy method for performance evaluation of fusion algorithms for integrated navigation system

Abstract

Aiming at the problem that traditional evaluation methods based on analytic hierarchy process (AHP) are influenced by subjectivity, this paper proposes an efficacious evaluation method which combines fuzzy logarithmic least square AHP method (fuzzy LLSM) with fuzzy comprehensive evaluation (FCE) method. Fuzzy LLSM is applied to derive the weights and FCE method is for comprehensive evaluation. Then FCE method would provide evaluation results through synthesizing the derived weight vector and membership matrix by a fuzzy operator based upon weighted average. Considering that the membership matrix requires a crisp weight vector to implement synthesis, but the derived weights have the problems of non-uniqueness and fuzziness, so we deduce the constraints to ensure the uniqueness of weights. And defuzzification of fuzzy weights is realized by using the CFCS (Converting Fuzzy numbers into Crisp Scores) method. As a result, the unique and defuzzificated weights are available to synthesis for FCE method directly. Taking the performance evaluation of SINS/Land-based/GPS integrated navigation system for a numerical example, some simulations have been carried out and we draw the conclusion that, the proposed fuzzy LLSM AHP-FCE method is superior to the existing and representative methods when applied to performance evaluation of fusion algorithm for integrated navigation system.