Open AccessJournal Article
Solving Fuzzy Linear Programming Problems with Linear Membership Function
TL;DR: This paper proposes the ``modified subgradient method'' and uses it for solving fuzzy programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers and compares it with well known ``fuzzy decisive set method''.
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Abstract: In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the ``modified subgradient method'' and use it for solving these problems. We also compare the new proposed method with well known ``fuzzy decisive set method''. Finally, we give illustrative examples and their numerical solutions.
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Citations
Is there a need for fuzzy logic
TL;DR: In this paper, fuzzy logic is viewed in a nonstandard perspective and the cornerstones of fuzzy logic-and its principal distinguishing features-are: graduation, granulation, precisiation and the concept of a generalized constraint.
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An evaluation of airline service quality using the fuzzy weighted SERVQUAL method
Chien-Chang Chou,Li-Jen Liu,Sue-Fen Huang,Jeng-Ming Yih,Tzeu-Chen Han +4 more
- 01 Mar 2011
TL;DR: This article attempts to fill the gap in the current literature by establishing a fuzzy weighted SERVQUAL model for evaluating the airline service quality and a case study of Taiwanese airline is conduced to demonstrate the effectiveness.
319
Is there a need for fuzzy logic
Lotfi A. Zadeh
- 19 May 2008
TL;DR: In this paper, fuzzy logic is viewed in a nonstandard perspective and the cornerstones of fuzzy logic-and its principal distinguishing features-are: graduation, granulation, precisiation and the concept of a generalized constraint.
A fuzzy programming approach for a cell formation problem with dynamic and uncertain conditions
TL;DR: A fuzzy programming-based approach is developed to solve an extended mixed-integer programming model of the dynamic CFP, in which there are piecewise fuzzy numbers as coefficients in the objective function and the technological matrix.
73
References
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Fuzzy Sets and Fuzzy Logic: Theory and Applications
George J. Klir,Bo Yuan +1 more
- 01 Jan 1995
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.
7.6K
•Book
Decision-making in a fuzzy environment
Richard Bellman,Lotfi A. Zadeh +1 more
- 01 Jan 1970
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.
On Fuzzy-Mathematical Programming
Hideo Tanaka,Tetsuji Okuda,Kiyoji Asai +2 more
- 01 Jan 1973
TL;DR: The main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh.
617
Fuzzy linear programming problems with fuzzy numbers
H. Tanaka,Kiyoji Asai +1 more
TL;DR: This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential and a reasonable solution under consideration of the ambiguity of parameters is obtained.
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