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

•Singh and Yadav’s method cannot yield solutions with unique optimal values.•A lexicographic criterion for ranking LR-type intuitionistic fuzzy numbers is given.•A method to find solutions of FIFLP problems with unique optimal values is proposed.•Intuitionistic fuzzy inequality constraints are defin...

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Bibliographic Details
Published in:Expert systems with applications 2019-08, Vol.128, p.246-255
Main Authors: Pérez-Cañedo, Boris, Concepción-Morales, Eduardo René
Format: Article
Language:English
Subjects:
Fully intuitionistic fuzzy linear programming
Inequality
Lexicographic ranking criterion
Linear programming
LR-type Intuitionistic fuzzy number
Nonlinear programming
Optimization
Production planning
Unique optimal intuitionistic fuzzy value
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Summary:•Singh and Yadav’s method cannot yield solutions with unique optimal values.•A lexicographic criterion for ranking LR-type intuitionistic fuzzy numbers is given.•A method to find solutions of FIFLP problems with unique optimal values is proposed.•Intuitionistic fuzzy inequality constraints are defined lexicographically.•A fully intuitionistic fuzzy production planning problem is solved as illustration. 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.
ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2019.03.035