scholarly journals A Minimax Criterion Approach to Treat the Inexactness in Feasible Set of a Linear Programming Problem

2021 ◽  
Author(s):  
Zhenzhong Gao ◽  
Masahiro Inuiguchi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Minimax Criterion ◽  
Feasible Set ◽  
Criterion Approach

scholarly journals A slight modification of the first phase of the simplex algorithm

2012 ◽  
Vol 22 (1) ◽  
pp. 107-114
Author(s):  
Tomica Divnic ◽  
Ljiljana Pavlovic
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Canonical Form ◽  
Linear Programming Problem ◽  
Standard Form ◽  
Main Idea ◽  
Slight Modification ◽  
Simplex Algorithm ◽  
Feasible Set ◽  
Standard Simplex

In this paper we give a modification of the first phase procedure for transforming the linear programming problem, given in the standard form min{cTx Ax=b, x?0}, to the canonical form, i.e., to the form with one feasible primal basis where standard simplex algorithm can be applied directly. The main idea of the paper is to avoid adding m artificial variables in the first phase. Instead, Step 2 of the proposed algorithm transforms the problem into the form with m?1 basic columns. Step 3 is then iterated until the m?th basic column is obtained, or it is concluded that the feasible set of LP problem is empty.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

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