Fuzzy rule base assessment models: Theoretical analyses and a case study

An assessment model is usually a mathematical model that produces a measuring index, in the form of a numerical score to a situation/object, with respect to the subject of measure. To allow a valid and useful comparison among various situations/objects according to their associated numerical scores to be made, two important properties, i.e., the monotone output property and output resolution properties, are essential in fuzzy inference-based assessment problems. In this paper, the conditions for a fuzzy assessment model to fulfill the monotone output property is investigated using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to the input, whereby the derivative should be greater than a minimum resolution. Based on the derivative, improvements to the output resolution property by refining the fuzzy production rules are suggested. A case study on the Bowles fuzzy RPN model to demonstrate the effectiveness of the properties is also included.