Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment
- 123 Downloads
The present paper gives a new computational algorithm for the solution of multiobjective linear programming (MOLP) problem in interval-valued intuitionistic fuzzy (IV-IF) environment. In MOLP problem which occurs in agricultural production planning, industrial planning and waste management. The parameters involved in real-life MOLP problems are impure, and several pioneer works have been done based on fuzzy or intuitionistic fuzzy sets for its compromise solutions. But many times the degree of membership and non-membership for certain element is not defined in exact numbers, so we observe another important kind of uncertainty. Thus fixed values of membership and non-membership cannot handle such uncertainty involved in real-life MOLP problem. Atanassov and Gargov first identified it and presented concept of IV-IF sets which is characterized by sub-intervals of unit interval. In this paper, we study IV-IF sets and develop a new computational method for the solution of real-life MOLP problems based on IV-IF sets. Further, the developed method has been presented in the form of a computational algorithm and implemented on a production problem, and solutions are compared with other existing methods.
KeywordsMultiobjective programming Interval-valued intuitionistic fuzzy sets Positive deal solution Pareto optimal solution
Compliance with ethical standards
Conflict of interest
Authors of this paper declare that we have no conflict of interest.
- Bharati SK, Singh SR (2015) A note on solving a fully intuitionistic fuzzy linear programming problem based on sign distance. Int J Comput Appl 119:30–35Google Scholar
- Bharati SK, Nishad AK, Singh SR (2014) Solution of multi-objective linear programming problems in intuitionistic fuzzy environment. In: Proceedings of the second international conference on soft computing for problem solving (SocProS 2012), vol 236. Advances in Intelligent Systems and Computing, pp 161–171Google Scholar
- Bharati, SK, Abhishekh, Singh SR (2017) A computational algorithm for the solution of fully fuzzy multi-objective linear programming problem. Int J Dyn Control. https://doi.org/10.1007/s40435-017-0355-1
- Dubey D, Mehra A (2011) Linear programming with triangular intuitionistic fuzzy number, EUSFLAT-LFA 2011, vol 1. Advances in Intelligent Systems Research, Atlantis Press, pp 563–569Google Scholar
- Garg A, Singh SR (2010) Optimization under uncertainty in agricultural production planning. iconcept Pocket J Comput Intell Financ Eng 1:1–12Google Scholar
- Jana, B, Roy TK (2007) Multiobjective intuitionistic fuzzy linear programming and its application in transportation model. NIFS-13-1-34-51, pp 1–18Google Scholar
- Malhotra R, Bharati SK (2016) Intuitionistic fuzzy two stage multiobjective transportation problems. Adv Theor Appl Math 11:305–316Google Scholar
- Nishad AK, Bharati SK, Singh SR (2014) A new centroid method of ranking for intuitionistic fuzzy numbers. In: Proceedings of the second international conference on soft computing for problem solving (SocProS 2012), vol 236. Advances in Intelligent Systems and Computing, pp 151–159Google Scholar