Journal ArticleDOI
A primal-dual method for linear programming problems with fuzzy variables
TLDR
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.Abstract:
Linear programming problems with fuzzy variables have been investigated by many researchers in the recent literature. Some methods to solve these problems, such as the primal simplex method and the dual simplex method, are based on the concept of comparison of fuzzy numbers by using ranking functions. In this paper, we give 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). This algorithm will be useful for sensitivity analysis when the activity vectors change for basic columns.read more
Citations
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Journal ArticleDOI
A new method for solving fully fuzzy linear programming problems
TL;DR: A new method is proposed to find the fuzzy optimal solution of same type of fuzzy linear programming problems and it is easy to apply the proposed method compare to the existing method for solving the FFLP problems with equality constraints occurring in real life situations.
Journal ArticleDOI
A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem
TL;DR: Based on a new lexicographic ordering on triangular fuzzy numbers, a novel algorithm is proposed to solve the FFLP problem by converting it to its equivalent a multi-objective linear programming (MOLP) problem and then it is solved by the lexicography method.
Journal ArticleDOI
Using complementary slackness property to solve linear programming with fuzzy parameters
TL;DR: This paper uses the complementary slackness to solve the fuzzy dual simplex algorithm to fuzzy linear programming with fuzzy parameters without the need of a simplex tableau.
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.
References
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Book
Fuzzy Set Theory - and Its Applications
TL;DR: The book updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research.
Book
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.
Book
Linear Programming and Network Flows
TL;DR: This chapter discusses the complexity of the Simplex Algorithms and their applications in linear algebra, convex analysis, and Polyhedral Sets.
Journal ArticleDOI
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.