Open Access
Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems
Nezam Mahdavi-Amiri,Seyed Hadi Nasseri,Alahbakhsh Yazdani +2 more
- Vol. 1, Iss: 2, pp 68-84
TLDR
This work considers two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems, and develops fuzzy primal simplex algorithms for solving these problems.Abstract:
Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. We consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.read more
Citations
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Journal ArticleDOI
A primal-dual method for linear programming problems with fuzzy variables
TL;DR: A new primal-dual algorithm for solving linear programming problems with fuzzy variables by using duality results, which was proposed by Mahdavi-Amiri and Nasseri (2007) will be useful for sensitivity analysis when the activity vectors change for basic columns.
Journal ArticleDOI
Bounded linear programs with trapezoidal fuzzy numbers
TL;DR: By a natural extension of Ganesan and Veeramani's approach to solving a kind of linear programming problems involving symmetric trapezoidal fuzzy numbers, some new results are obtained leading to a new method to overcome this shortcoming.
Journal ArticleDOI
A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems
TL;DR: This paper proposes a fuzzy primal simplex algorithm for solving the flexible linear programming problem and suggests the fuzzy primalsimplex method to solve the flexiblelinear programming problems directly without solving any auxiliary problem.
Journal ArticleDOI
Sensitivity analysis in fuzzy number linear programming problems
TL;DR: The concept of sensitivity analysis in fuzzy number linear programming (FLNP) problems is generalized by applying fuzzy simplex algorithms and using the general linear ranking functions on fuzzy numbers to determine changes in the optimal solution of FNLP problem.
Journal ArticleDOI
Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients
TL;DR: The bounded fuzzy primalsimplex algorithm starts with a primal feasible basis and moves towards attaining primal optimality while maintaining primal feasibility throughout, which will be useful for sensitivity analysis using primal simplex tableaus.
References
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Book
Fuzzy Sets and Fuzzy Logic: Theory and Applications
George J. Klir,Bo Yuan +1 more
TL;DR: Fuzzy Sets and Fuzzy Logic is a true magnum opus; it addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic.
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Decision-making in a fuzzy environment
Richard Bellman,Lotfi A. Zadeh +1 more
TL;DR: A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
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Fuzzy programming and linear programming with several objective functions
TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
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A procedure for ordering fuzzy subsets of the unit interval
TL;DR: A function to help in the ordering of fuzzy subsets of the unit interval is introduced, which is the integral of the mean of the level sets associated with the fuzzy subset.
Journal ArticleDOI
Reasonable properties for the ordering of fuzzy quantities (II)
Xuzhu Wang,Etienne Kerre +1 more
TL;DR: It is proved that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity, so a widely applicable formulation to derive a total ranking order from a fuzzy relation is given.