Linear programming with fuzzy parameters: An interactive method resolution

By Mariano Jiménez, Mar Arenas Parra, Amelia Bilbao-Terol, Maria Victoria Rodríguez. European Journal of Operational Research, 2007

664 citations recorded by the source corpus.

This paper proposes a method for solving linear programming problems where all the coefficients are, in general, fuzzy numbers. We use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality relation on constraints. It allows us to work with the concept of feasibility degree. The bigger the feasibility degree is, the worst the objective value will be. We offer the decision-maker (DM) the optimal solution for several different degrees of feasibility. With this information the DM is able to establish a fuzzy goal. We build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal. A reasonable solution is the one that has the biggest membership degree to this fuzzy subset. Finally, to illustrate our method, we solve a numerical example.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/626adf95dc4646bd6161a4ffc9aa9a53201d5780

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Mir Saman Pishvaee
2. S. A. Torabi
3. S. Wang
4. Jafar Razmi
5. Guohe Huang
6. Javad Nematian

In Management Science and Operations Research

1. Mir Saman Pishvaee
2. S. Wang
3. S. A. Torabi
4. Jafar Razmi
5. Guohe Huang
6. Javad Nematian

In Statistics and Probability

1. S. Wang
2. S. A. Torabi
3. Jafar Razmi
4. Guohe Huang
5. Javad Nematian
6. Mir Saman Pishvaee

Citations in the corpus

• Identifying Optimal Water Resources Allocation Strategies through an Interactive Multi-Stage Stochastic Fuzzy Programming Approach (2012, methodology): “…optimization methods were developed for dealing with uncertainties and the associated complexities in the water resources management (Slowinski 1986; Wu et al. 1997; Huang 1998; Jairaj and Vedula 2000; Seifi and Hipel 2001; Luo et al. 2003; Maqsood et al. 2005; Li et al. 2007; Wang and Huang 2011).”
• Robust possibilistic programming for socially responsible supply chain network design: A new approach (2012, methodology): “Also, the extensions of Mulvey et al. [48] approach are proposed by Yu and Li [54] and Leung et al. [55].”
• An Extended Two-stage Stochastic Programming Approach for Water Resources Management under Uncertainty (2015, methodology): “Jiménez et al. (2007) proposed an interactive fuzzy resolution method for solving linear programming problems with fuzzy parameters and Nie et al. (2007) introduced a hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty.”
• A possibilistic programming approach for closed-loop supply chain network design under uncertainty (2010, methodology): “[34] method has recently been used as the defuzzification method in some relevant works in the supply chain planning area as well (e.”