abdullah al-qudaimi

Regression models have been tremendously studying with so many applications in the presence of imprecise data. The regression coefficients are unknown i.e., they cannot be restricted. To the best of our knowledge, there is no approach except Chen and Hsueh approach (IEEE Transactions on Fuzzy Systems, vol. 17, no. 6, December 2009 pp.1259-1272) which can be used to find the regression coefficients of a fuzzy regression model without considering the non-negative restrictions on the regression coefficients. Chen and Hsueh have used some mathematical assumptions which lead to limitations in their approach. Furthermore, Chen and Hsueh approach is inefficient regarding to computational complexity. This paper proposed a simplified approach overcoming the limitations and computational complexity of Chen and Hsueh approach which can be considered by the researchers who would like to use Chen and Hsueh approach in real life applications.

Triangular Fuzzy numbers (TFNs) are vast and common representation of fuzzy data in applied sciences. Multiplication is a very indispensable operation for fuzzy numbers. It is necessary to decompose fuzzy systems such as fully triangular fuzzy regression models where the unknown and unrestricted triangular fuzzy coefficients multiplied by known TFNs as data input. Tens of research works and application of triangular fuzzy regression have dealt with degenerated existing multiplication expressions. This paper highlighted the drawbacks of such expressions and propounded a simple method (named as QKB method). The method is a straightforward method where there is no exaggeration for multiplying two or more TFNs. It respects the trinity-order condition of a TFN where the number without it cannot be considered as a TFN. Besides, it is suitable for known and unknown multiplied TFNs with conserving homogeneity principle such that the resultant of two symmetric TFNs has to be symmetric either, to prove that a proposed new membership function for a TFN (named quantified membership function) has been used. Illustrative examples have shown the soundness of the proposed method and the drawbacks of existing expressions. Furthermore, its expression of multiplication is more efficient than other expression on the needs of computation.

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.

Souza et al. (Knowledge-Based Systems, 131 (2017), pp. 149-159) pointed out that although several approaches have been proposed in the literature for fitting interval linear regression models (linear regression models its parameters are represented as intervals). However, as there are flaws in all the existing approaches, it is scientifically incorrect to use these approaches in real life problems. To resolve the flaws of the existing approaches, Souza et al. proposed a new approach for fitting interval linear regression models. After a deep study, it is observed that in the approach, proposed by Souza et al., some mathematical incorrect assumptions have been considered and hence, it is scientifically incorrect to use the Souza et al.’s approach, in real life problems. In this paper the mathematical incorrect assumption, considered by Souza et al, is pointed out and suggested modifications are provided as well as a new approach is proposed as  for fitting the interval linear regression models. The proposed model guarantee mathematical coherent such that the predicted values of the model are intervals with lower bound less than or equal upper bound. Furthermore, the proposed has been illustrated with the help of a numerical example.