Developing a Hybrid Fuzzy Possibilistic-flexible Modelling with Fuzzy TOPSIS to Solve Financial Investment Mathematical Programming Problems

Uncertainty is inevitable in the real world; nonetheless, fuzzy logic is regarded as one of the approaches employed in modeling such uncertainty. Therefore, a new field of mathematical programming has been proposed that is called Fuzzy Mathematical programming. Following Bellman and Zadeh, the pioneers of the Fuzzy School of Mathematics, other researchers have developed various solutions to solve fuzzy problems considering various components of mathematical models in a fuzzy condition. The present study aims to develop a novel approach to resolve investment problems using fully fuzzy mathematical model.

In general, defining the degree of fuzzy numbers, which is assumed to be fixed, should be utilized to solve the full fuzzy problem. Since the given problem is fuzzy, it is better to define a fuzzy degree to solve the problem. Thus, considering that all the components are better to be seen as fuzzy components, a fully fuzzy possibilistic-flexible composite model with a degree of fuzzy definition is developed in this study.

Finally, the proposed model used to resolve an investment problem and the results were compared to the findings of previous models. Then, the results point out a significant improvement (about 250% in intial investment) in the proposed model, which is much better than previous models.

In this study, fuzzy extent value derived from Jimenez's approach has been used to solve fully fuzzy problems. Therefore, it has provided the possibility of solving problems with multiple fuzzy objective functions and fuzzy constraints.