Minimum‐cost flow problems having arc‐activation costs

2021 ◽  
Author(s):  
Robert M. Curry ◽  
J. Cole Smith
Keyword(s):  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Flow Problems ◽  
Cost Flow ◽  
Minimum Cost Flow Problems

A New Method for Solving Single- and Multi-Objective Capacitated Solid Minimum Cost Flow Problems under Uncertainty

2016 ◽  
Vol 25 (2) ◽  
pp. 159-183
Author(s):  
Manjot Kaur ◽  
Rehan Sadiq
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Multi Objective ◽  
Flow Problems ◽  
Cost Flow ◽  
Minimum Cost Flow Problems

AbstractIn real life, a person may assume that an object belongs to a set, but it is possible that he (she) is not sure about it. In other words, there may be hesitation or confusion whether an object belongs to a set or not. In fuzzy set theory, there is no means to incorporate such type of hesitation or confusion. A possible solution is to use intuitionistic fuzzy set [K. T. Atanassov, Intutionistic fuzzy sets, Fuzzy Sets Syst.20 (1986), 87–96]. In this article, the concept of unbalanced fully fuzzy multi-objective capacitated solid minimum cost flow (SMCF) problems is generalized by unbalanced intuitionistic fully fuzzy multi-objective capacitated SMCF (CSMCF) problems and new methods are proposed for solving these problems. The main advantage of the proposed methods over the existing methods is that all the unbalanced fully fuzzy single- and multi-objective CSMCF problems that can be solved by the existing methods can also be solved by the proposed method.

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