Fully Fuzzy Linear Programming Models with Intuitionistic Fuzzy Numbers

  • 勞 愛媛

Student thesis: Doctoral Thesis

Abstract

Linear programming involves efficient planning of all resources in which parameters and variables must be clearly defined and the best results can be obtained from various constraints However in a real environment due to incomplete and insufficient information parameters and decision variables cannot be clearly defined Scholars have discussed fuzzy linear programming as a method by which to express the uncertainty of information with the concept of fuzzy membership function When the information is insufficient fully fuzzy linear programming problems in which all of the variables and parameters are stated as fuzzy numbers consider more uncertainty than fuzzy linear programming In the past scholars studying fully intuitionistic fuzzy linear programming mostly used ranking function or lexicographic ranking methods These methods can be used to convert the fully intuitionistic fuzzy linear programming model into a general linear programming model but the results tend to vary depending on the ranking method used by the decision maker This study proposes two fully fuzzy linear programming models that directly solve the intuitionistic fuzzy numbers using the concept of -cut Mode I is divided into four steps First a basic model of fully intuitionistic fuzzy linear programming is built Second the model is converted into an interval model In the third step the model is converted into an endpoint model and finally the model is solved Model II considers the constraints in the numerical relationship on both sides to be fuzzy and risk sensitivity degree is added to allow the decision maker to adjust the value Numerical examples and application cases reveal the feasibility of the two models proposed in this study Model II can provide decision makers with their level of risk and provide different results based on their attitude toward risk The results show that Model II proposed in this study can provide solutions with a lower degree of ambiguity for risk avoiders and a higher degree of ambiguity for decision-makers who are less risk averse
Date of Award2020
Original languageEnglish
SupervisorLiang-Hsuan Chen (Supervisor)

Cite this

'