A nonlinear modeling with linear fuzzy numbers for replicated response measures

TÜRKŞEN Ö.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, cilt.49, sa.3, ss.629-646, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1080/03610918.2019.1634813
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Computer & Applied Sciences, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.629-646
  • Anahtar Kelimeler: Linear fuzzy numbers, Fuzzy nonlinear regression, Replicated response measures, Constrained optimization, Nonparametric statistical tests, REGRESSION-ANALYSIS, LEAST-SQUARES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study, it is aimed to present a flexible modeling approach for replicated response measured data set via linear fuzzy numbers (LFNs), e.g. pentagonal linear fuzzy numbers (PLFNs), trapezoidal linear fuzzy numbers (TrLFNs), and triangular linear fuzzy numbers (TLFNs). For this purpose, a fuzzification formula of replicated measures was proposed with calculating quartile based descriptive statistics. The model parameters were also assumed as LFNs whereas the input variable was crisp. In order to obtain the predicted fuzzy nonlinear regression model, least squares (LS) approach and hybrid optimization algorithm, hybrid of Genetic Algorithm and Quasi-Newton algorithm (GA-QN), were used as estimation and optimization methods, respectively. Two data sets were chosen from the literature for application purpose. It is seen from the obtained results that the predicted fuzzy nonlinear functions, obtained with PLFNs, TrLFNs, TLFNs, have equal performance according to the nonparametric statistical tests. However, it is seen from the medians of prediction errors that the predicted fuzzy nonlinear model with PLFNs is the most preferable one.