TAILIEUCHUNG - Penalty method for fuzzy linear programming with trapezoidal numbers

In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. | Yugoslav Journal of Operations Research Vol 19 (2009), Number 1, 149-156 DOI: PENALTY METHOD FOR FUZZY LINEAR PROGRAMMING WITH TRAPEZOIDAL NUMBERS Bogdana STANOJEVIĆ Transilvania University of Brasov, bpop@ Milan STANOJEVIĆ Faculty of Organizational Sciences, Belgrade milans@ Received: December 2007 / Accepted: June 2009 Abstract: In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints. Keywords: Linear programming, trapezoidal fuzzy number, penalty method. 1. INTRODUCTION Concepts of fuzzy sets theory have “crowded” into a lot of research fields since 1980, because of the great success of fuzzy logic application in the control systems theory. The real advantages of the fuzzy approach to solving optimization problems can be highlighted when its comparison to the stochastic methods is made in order to deal with imprecision [4, 6]. Starting with Zimmermann [8], a lot of papers have been written covering the field of fuzzy linear programming. Buckley and Feuring dealt with the fully fuzzified linear programming problem (FFLP) by establishing all the coefficients and variables of a linear program as fuzzy quantities [1]. They transformed the fully fuzzified programming problem into a multiobjective deterministic problem (MODP) which is, in the general case treated, non-linear. In such a case, the problem is transformed into a multi-objective fuzzy problem with М. Stanojević, B. Stanojević / Penality Method for Fuzzy 150 whose help the authors explore the .

• Kỹ thuật lập trình
• Linear programming
• Trapezoidal fuzzy number
• Penalty method
• Stochastic methods
• Optimization methods
• Practice of economics
• Management science
• Linear programming applications
• Operations management
• Advanced linear programming applications
• Network models
• Integer linear programming
• An introduction to management science
• Ebook Linear optimization
• Linear optimization
• Linear extensions
• The linear programming problem
• Simplex algorithms
• Primal dual pairs
• Operations research
• Modeling with linear programming
• Advanced linear programming
• Network model
• Post optimal analysis
• Multi objective bi level linear programming problems
• Partial information of preference
• Fuzzy environment
• Parametric linear programming problems
• Parametric space
• Design and Analysis of Algorithms
• Analysis of Algorithms
• Design of Algorithms
• Data structures
• Certificate of optimality
• Linear programming duality
• Lecture Algorithms
• Bài giảng Thuật toán
• Brewer’s problem
• Linear programming formulation
• Objective function
• Ebook Linear Programming
• The Simplex Method
• Sensitivity and Parametric Analyses
• Structural Optimization
• The Affine Scaling Method
• Fuzzy linear programming
• Fuzzy number
• Modified subgradient method
• Fuzzy decisive set method
• Fuzzy technological coefficients
• Simplex type algorithms
• Primal dual exterior point algorithm
• Computational study
• Linear Programming Problem
• Object oriented programming
• Object oriented programming with Java
• Programming language
• Java programming language
• Linear search
• Binary search algorithms
• Triangular fuzzy number
• Multi choice programming
• Fuzzy programming
• Data envelopment analysis (DEA)
• Multiple objective linear programming (MOLP)
• MOLP formulation
• Measuring relative efficiency
• Fractional programming
• Centroid of triangle
• Fully fuzzified linear fractional programming
• Multilevel programming
• Indefinite quadratic programming
• Quasi concave function
• Integer programming
• Reverse logistic chain
• Electrical and electronic waste
• Linear relaxation
• Economy and environmental protection
• Resource Constraints
• project costs
• project investment
• project evaluation
• project management
• technical project management
• project management for small business
• Dynamic Programming
• Linear Time Incremental Parsing
• Liang Huang
• báo cáo khoa học
• báo cáo ngôn ngữ
• ngôn ngữ tự nhiên
• Comparative News Summarization
• Concise Integer Linear Programming Formulations
• Dependency Parsing
• F
• T
• Martins
• xử lý ngôn ngữ tự nhiên
• Recognizing Authority in Dialogue
• Integer Linear Programming Constrained Model
• Elijah Mayfield
• Grammatical Role Labeling
• Manfred Klenner
• scientific reports
• model language
• process natural language
• Linear Text Segmentation
• Dynamic Programming Algorithm
• Fragkou Pavlina