S.Z. Nasseri - Department of Computer Engineering, Noshirvani University of Technology (NUT), Babolsar, Iran.
Amirhossein Nafei - Department of Industrial Engineering and Management, National Taipei University of Technology, Taipei ۱۰۶۰۸, Taiwan

The aim of this paper is to introduce a mathematical model for Linear Programming (LP) problem involving intuitionistic fuzzy variables. Here, we will focus on some fundamental concepts and results which are uselful for simplex-based algorithm to solve these problems. We classify these problems into two main different categories: Linear Programming with Intuitionistic Fuzzy Numbers (IFNLP) problems and Linear Programming with Intuitionistic Fuzzy Variables (IFVLP) problems. In methods based on the classical simplex algorithm, it is not easy to obtain a primal basic feasible solution to the minimization IFVLP problem with equality constraints and nonnegative variables. Therefore, also may investigate some improved approaches to solve these problems. Furthermore, we emphasize that according to fundamental concepts including optimality and feasibility conditions and preparing some efficient ordering approached for intuitionistic fuzzy parameters ables us to estab lished some computational procedure for dicision making tools under uncertainty environment

Dicision making, Intuitionistic fuzzy programming, Intuitionistic fuzzy number, Ordering approaches, Optimality and feasibility conditions