On LR-type fully intuitionistic fuzzy linear programming with inequality constraints: Solutions with unique optimal values

Abstract

Singh and Yadav (2017) defined the product of unrestricted LR-type Intuitionistic Fuzzy Numbers (IFNs), and making use of the new product operation, the authors proposed a method to solve Fully Intuitionistic Fuzzy Linear Programming (FIFLP) problems. However, their method cannot be used to find the unique optimal value of FIFLP problems with inequality constraints. Recently, Pérez-Cañedo and Concepciõn-Morales (2019) presented a method to find the unique optimal fuzzy value of Fully Fuzzy Linear Programming (FFLP) problems with equality and inequality constraints based on the optimisation of a lexicographic criterion for ranking LR fuzzy numbers. The authors suggested that their method could be extended to find the unique optimal intuitionistic fuzzy value of FIFLP problems with inequality constraints as well. In this paper, we analyse Singh and Yadav’s method and modify it to find the unique optimal intuitionistic fuzzy value of FIFLP problems with equality and inequality constraints. Thus, a new method is obtained and is demonstrated by means of a fully intuitionistic fuzzy production planning problem. Results are compared with those obtained by using Singh and Yadav’s method and show that the proposed method overcomes the shortcomings and limitations of their method.