Extended Tsukamoto's inference method for solving multi-objective linguistic optimization problems

Abstract

Multi-objective linguistic optimization problems (MOLOPs) are quite useful in modeling a number of real life problems. The decision variables used to define the problem constraints and the objective functions take linguistic values in MOLOPs. In those MOLOPs, where the values of objective functions are unknown at all the points of the variable space, the link between the values of decision variables and objective functions is defined using if-then rules. MOLOPs formulated in this way were often solved using the Tsukamoto's inference method. However, the Tsukamoto's method can solve MOLOPs if the consequents in the if-then rules are defined as monotonic functions. Also, the solution obtained from Tsukamoto's method is a precise number. So in the present work, we propose a novel extension of Tsukamoto's inference method. The extended Tsukamoto's inference method can overcome both the above limitations. That is, it can solve MOLOPs where the consequents are defined as non-monotonic functions as well as monotonic functions. Also the extended Tsukamoto's method generates intervals instead of unique numbers, in the solution. From these intervals, we then generate type-1 fuzzy set membership functions and compare them using two of their fuzzy set uncertainty measures viz. centroid and fuzziness. Furthermore, we generate linguistic recommendations for these generated type-1 fuzzy set membership functions, as humans understand linguistic information naturally. We have also demonstrated the applicability of the proposed extended Tsukamoto's inference method to the case study for student's performance evaluation. We strongly believe that our proposed method is a novel one and will provide directions to future research.