Stochastic Triangular Fuzzy Number (S-TFN) Normalization: A New Approach for Nonmonotonic Normalization

Abstract

Data normalization is essential in many fields, such as speech recognition, deep learning, machine learning, and optimization. Many researchers focus on developing various normalization techniques, such as min-max, score-based, maximum, vector, or sum, on processing data efficiently. However, classical normalization methods may need to be improved in Multi-Criteria Decision-Analysis (MCDA), where criteria are often non-monotonic. This paper proposes a new approach for identifying and normalizing nonmonotonic criteria in MCDA. The method combines a stochastic optimization technique - a genetic algorithm - with normalization based on triangular fuzzy numbers. This paper compares the proposed approach with classical normalization techniques, such as min-max, maximum, vector, or non-linear, using the classical MCDA method - the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS). The study results showed that the proposed approach to normalizing non-monotonic criteria yields a better match between decision preferences and the actual reference model than traditional normalization methods. Optimization using the genetic algorithm helps identify the means of triangular fuzzy numbers, which generate more accurate results. Analysis of the R2 coefficient confirms a very good fit of the proposed model. Therefore, the new non-linear normalization approach in MCDA presented in this work has great potential in adjusting decision preferences to non-monotonic criteria. Future research should continue on the accuracy of this approach in identifying non-linear decision models and apply it to other MCDA methods and real-world decision problems.