Ishita Approach to Construct an Intuitionistic Fuzzy Linear Regression Model

To the best of our knowledge, there is only two approaches for constructing an intuitionistic fuzzy linear regression model (regression model in which all the variables and coefficients are considered as intuitionistic triangular fuzzy numbers). However, after a deep study, some mathematical incorrect assumptions have been considered in these approaches. Therefore, it is scientifically incorrect to use these approaches for general real-life data. Keeping the same in mind, in this paper, a new approach (named as Ishita approach) is proposed to construct an intuitionistic fuzzy linear regression model. The proposed approach overcomes the limitations of the existing approaches. It is fit for positive, negative or mixed of positive and negative datasets represented as symmetric or asymmetric intuitionistic triangular fuzzy numbers. Moreover, the constructed models of the proposed approach guarantee the homogeneity principle such that for symmetric intuitionistic fuzzy data, the constructed model is symmetric, i.e., the estimated model’s coefficients are symmetric intuitionistic fuzzy numbers. Furthermore, the proposed approach is illustrated with the help of a numerical example.

Keywords:

Atanassov’s triangular intuitionistic fuzzy number (ATIFN) , Intuitionistic fuzzy linear regression , Least absolute deviations