Least Square Method with Quasi Linearly Interactive Fuzzy Data: Fitting an HIV Dataset

In this manuscript we propose a method to fit a dataset with uncertainty. These data are described by interactive fuzzy numbers. The relationship of interactivity is associated with the notion of joint possibility distribution. We focus on a specific type of interactivity namely linear interactivity. We use this concept to introduce a class of fuzzy numbers called quasi linearly interactive fuzzy numbers. We provide an application to fit a dataset of the HIV disease to illustrate the proposed method.

[1]  A. Celmins.  Least squares model fitting to fuzzy vector data , 1987 .

[2]  Hung T. Nguyen,et al.  Fundamentals of Statistics with Fuzzy Data , 2006, Studies in Fuzziness and Soft Computing.

[3]  Christer Carlsson,et al.  Additions of completely correlated fuzzy numbers , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[4]  Rodney Carlos Bassanezi,et al.  Study of the dynamics of HIV under treatment considering fuzzy delay , 2014 .

[5]  Iraj Mahdavi,et al.  Fuzzy Least-Squares Linear Regression Approach to Ascertain Stochastic Demand in the Vehicle Routing Problem , 2011 .

[6]  Robert Fullér,et al.  On Interactive Fuzzy Numbers , 2003, Fuzzy Sets Syst..

[7]  Berlin Wu,et al.  A new approach to fuzzy regression models with application to business cycle analysis , 2002, Fuzzy Sets Syst..

[8]  Kazuhisa Takemura,et al.  Fuzzy Least Squares Regression Analysis for Social Judgment Study , 2005, J. Adv. Comput. Intell. Intell. Informatics.

[9]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[10]  Phil Diamond,et al.  Fuzzy least squares , 1988, Inf. Sci..

[11]  Estevão Laureano Esmi,et al.  Least Squares Method with Interactive Fuzzy Coefficient: Application on Longitudinal Data , 2018, NAFIPS.

[12]  Paolo Vicini,et al.  Fuzzy Least Squares for Identification of Individual Pharmacokinetic Parameters , 2009, IEEE Transactions on Biomedical Engineering.

[13]  Laécio C. Barros,et al.  A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics - Theory and Applications , 2016, Studies in Fuzziness and Soft Computing.

[14]  D. Dubois,et al.  Additions of interactive fuzzy numbers , 1981 .

[15]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .