A new method to solve linear programming problems in the environment of picture fuzzy sets

Document Type : Research Paper


1 Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan

2 Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey


Picture fuzzy set is characterized by neutral membership function along with the membership and non-membership functions, and is, therefore, more general than the intuitionistic fuzzy set which is only characterized by membership and non-membership functions. In this paper, first, we are going to point out a drawback and try to fix it by the existing trapezoidal picture fuzzy number. Furthermore, we define an $LR$ flat picture fuzzy number, which is a generalization of trapezoidal picture fuzzy numbers. We also discuss a linear programming model with $LR$ flat picture fuzzy numbers as parameters and variables and present a method to solve these type of problems using a generalized ranking function.


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