A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

This article presents a fuzzy multi-objective linear fractional programming (FMOLFP) problem. The goal programming (GP) approach is used to solve the proposed problem. The LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$LR$$\end{document} (Left and Right) possibilistic variables are addressed to the suggested the fuzzy multi-objective linear fractional programming (FMOLFP) model to deal the uncertainty of the model parameters. An auxiliary model in which objective function is the distance between the p-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p -$$\end{document} ary α-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha -$$\end{document} optimal value restriction and p-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p -$$\end{document} ary fuzzy objective function is proposed. In the last, one solved example is given to illustrate and to support the validity of the suggested approach.