Development of the method of general interpolation for Z-number-valued if-then rules

Abstract

Rule interpolation-based methods are used when the rule base is sparse. This frequently being the case, as information relevant to real-world problems is not usually comprehensive. At the same time, relevant information is often characterized by both fuzziness and partial reliability. To deal with such kind of information, the concept of Z-number was introduced by Zadeh. This paper is devoted to an extension of the general interpolation method for fuzzy rules to the case of if-then rules with Z-number-valued antecedents and consequents. The proposed approach relies on the determination of the distance between the current observation vector and vectors of rules antecedents. By determining the distance between the current vector and the antecedents of the rules, decisions can be made based on the nearest antecedents. In this context, rule antecedents are vectors that represent certain conditions. The resulting output is computed as a weighted sum of rules consequents. Weighting factors are used to account for the importance of each rule in the interpolation. Weights of interpolations are found on the basis of mentioned distance values. The results of this study are aimed at developing an approach to decision-making in terms of Z-valued information. The method is characterized by relatively low computational complexith. Regarding the application of the proposed approach, the job satisfaction evaluation problem is considered. Consequently, the obtained results confirm the efficiency of the proposed approach. The proposed method can be a useful tool for decision-making in various applications, especially where high computational complexity is unacceptable or impractical