scholarly journals Stability of multi-objective bi-level linear programming problems under fuzziness

2013 ◽  
Vol 23 (3) ◽  
pp. 343-354
Author(s):  
Mahmoud Abo-Sinna
Keyword(s):  
Linear Programming ◽  
Electronic Commerce ◽  
Partial Information ◽  
Information Service ◽  
Optimal Solution ◽  
Programming Technique ◽  
Multi Objective ◽  
Linear Programming Problems ◽  
Primary Focus ◽  
The Individual

This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC). First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i) Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii) Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

2021 ◽  
Vol 10 (12) ◽  
pp. 3699-3723
Author(s):  
L. Kané ◽  
M. Konaté ◽  
L. Diabaté ◽  
M. Diakité ◽  
H. Bado
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Interval Linear Programming ◽  
Interval Numbers ◽  
Programming Technique ◽  
Solution Approach ◽  
Interval Linear ◽  
Linear Programming Problems

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

LINEAR COORDINATION METHOD FOR FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH CONVEX POLYHEDRAL MEMBERSHIP FUNCTIONS

2004 ◽  
Vol 12 (03) ◽  
pp. 269-285 ◽  
Author(s):  
BUSABA PHRUKSAPHANRAT ◽  
ARIO OHSATO
Keyword(s):  
Linear Programming ◽  
Decision Maker ◽  
Convex Cone ◽  
Optimal Solution ◽  
Membership Functions ◽  
Convex Polyhedral ◽  
Multi Objective ◽  
Proposed Model ◽  
Optimal Solution Set ◽  
Linear Programming Problems

A fuzzy multi-objective decision-making with nonlinear membership functions is proposed in this paper by assuming that the decision maker has a fuzzy goal for each objective function. The fuzzy goals can be quantified by convex polyhedral membership functions, which are expressed by linguistic terms. The concept of the convex cone is used to formulate a normalized convex polyhedral penalty function, which can also be considered conversely as a convex polyhedral membership function. The most desirable value of membership functions are selected to be reference membership values of achievement of convex polyhedral membership functions that can be viewed as the extension of the idea of reference point method. The formulated model can be solved by existing linear programming solvers and can find the satisficing solution for the decision maker, which can be derived efficiently from among an M-Pareto optimal solution set together with the trade-off rates between the membership functions. The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker. It enriches the existing satisficing methods for fuzzy multi-objective linear programming in a more practical way with the effective method based on convex cone.

Solving Fully Fuzzy Multi-Objective Linear Programming Problems

2012 ◽  
Vol 3 (4) ◽  
pp. 1-6 ◽  
Author(s):  
M.Jayalakshmi M.Jayalakshmi ◽  
◽  
P.Pandian P.Pandian
Keyword(s):  
Linear Programming ◽  
Multi Objective ◽  
Linear Programming Problems

THE DS/AHP METHOD UNDER PARTIAL INFORMATION ABOUT CRITERIA AND ALTERNATIVES BY SEVERAL LEVELS OF CRITERIA

2012 ◽  
Vol 11 (02) ◽  
pp. 307-326 ◽  
Author(s):  
LEV V. UTKIN ◽  
NATALIA V. SIMANOVA
Keyword(s):  
Linear Programming ◽  
Incomplete Information ◽  
Decision Problem ◽  
Partial Information ◽  
Decision Makers ◽  
Ahp Method ◽  
Numerical Examples ◽  
Finite Set ◽  
Linear Programming Problems ◽  
Decision Alternatives

An extension of the DS/AHP method is proposed in the paper. It takes into account the fact that the multi-criteria decision problem might have several levels of criteria. Moreover, it is assumed that expert judgments concerning the criteria are imprecise and incomplete. The proposed extension also uses groups of experts or decision makers for comparing decision alternatives and criteria. However, it does not require assigning favorability values for groups of decision alternatives and criteria. The computation procedure for processing and aggregating the incomplete information about criteria and decision alternatives is reduced to solving a finite set of linear programming problems. Numerical examples explain in detail and illustrate the proposed approach.

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

scholarly journals Measuring the technical efficiency of local banks in UAE using rough bi-level linear programming technique

2015 ◽  
Vol 1 (1) ◽  
pp. 26
Author(s):  
Doaa Wafik ◽  
O. E. Emam
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Technical Efficiency ◽  
Auxiliary Problem ◽  
Optimal Solution ◽  
Objective Functions ◽  
Programming Technique ◽  
Decision Making Problem ◽  
Linear Objective Functions ◽  
Linear Programming Technique

The aim of this paper is to use a bi-level linear programming technique with rough parameters in the constraints, for measuring the technical efficiency of local banks in UAE and Egypt, while the proposed linear objective functions will be maximized for different goals. Based on Dauer's and Krueger's goal programmingmethod, the described approach was developed to deal with the bi-level decision-making problem. The concept of tolerance membership function together was used to generate the optimal solution for the problem under investigation. Also an auxiliary problem is discussed to illustrate the functionality of the proposed approach.

scholarly journals Assignment model with multi-objective linear programming for allocating choice ranking using recurrent neural network

2021 ◽  
Author(s):  
Zahra Sadat Mirzazadeh ◽  
Javad Banihassan ◽  
Amin Mansoori
Keyword(s):  
Neural Network ◽  
Linear Programming ◽  
Recurrent Neural Network ◽  
Absolute Priority ◽  
Multi Objective ◽  
Assignment Method ◽  
Assignment Model ◽  
Decision Attributes ◽  
Linear Programming Problems ◽  
Linear Assignment

Classic linear assignment method is a multi-criteria decision-making approach in which criteria are weighted and each rank is assigned to a choice. In this study, to abandon the requirement of calculating the weight of criteria and use decision attributes prioritizing and also to be able to assign a rank to more than one choice, a multi-objective linear programming (MOLP) method is suggested. The objective function of MOLP is defined for each attribute and MOLP is solved based on absolute priority and comprehensive criteria methods. For solving the linear programming problems we apply a recurrent neural network (RNN). Indeed, the Lyapunov stability of the model is proved. Results of comparing the proposed method with TOPSIS, VICOR, and MOORA methods which are the most common multi-criteria decision schemes show that the proposed approach is more compatible with these methods.

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