Project Details
Abstract
In general, to formulate fuzzy linear programming problem with n S-shaped utility
(membership) functions, n or more extra binary variables are required in the traditional
methods because S-shaped curve is neither convex nor concave everywhere (Yang et al. 1991,
Lin and Chen 2002, Chang 2007). As shown by Keha et al. (2004), adding binary variables do
not improve the bound of the linear programming relaxation. On the contrary, the binary
variables will increase the computational burden in the solution process, if problem size gets
large. Therefore, the formulation without binary variables seems to be more efficient.
Following this, the study proposes a novel approach to formulate S-shaped membership
function without adding any extra binary variable. That is, the formulated fuzzy linear
programming problem with S-shaped membership functions represents a linear form which
can be easily solved using common linear programming packages. This improves the
efficiency of fuzzy linear programming in solving decision / management problems with
S-shaped membership function. Finally, computational experience is provided to demonstrate
the superiority of the proposed models. An illustrative example is also provided to show the
usefulness of the proposed method.
Project IDs
Project ID:PF9907-3356
External Project ID:NSC99-2410-H182-015-MY3
External Project ID:NSC99-2410-H182-015-MY3
Status | Finished |
---|---|
Effective start/end date | 01/08/10 → 31/07/11 |
Keywords
- Piecewise linear function
- Fuzzy linear programming
- Fuzzy goal programming
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