An Efficient Algorithm to Computing Max-Min Post-inverse Fuzzy Relation for Abductive Reasoning

This paper provides an alternative formulation to computing the max–min inverse fuzzy relation by embedding the inherent constraints of the problem into a heuristic (objective) function. The optimization of the heuristic function guarantees maximal satisfaction of the constraints, and consequently, the condition for optimality yields solution to the inverse problem. An algorithm for computing the max–min inverse fuzzy relation is proposed. An analysis of the algorithm indicates its relatively better computational accuracy and higher speed in comparison to the existing technique for inverse computation. The principle of fuzzy abduction is extended with the proposed inverse formulation, and the better relative accuracy of the said abduction over existing works is established through illustrations with respect to a predefined error norm.