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Öğe A new method to solve linear programming problems in the environment of picture fuzzy sets(University of Sistan and Baluchestan, 2022) Akram, Muhammad Saeed; Ullah, Inayat; Allahviranloo, TofighPicture 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. © 2022, University of Sistan and Baluchestan. All rights reserved.Öğe An interactive method for the solution of fully Z-number linear programming models(Springernature, 2023) Akram, Muhammad; Ullah, Inayat; Allahviranloo, TofighLinear programming is a technique widely used in decision-making nowadays. Linear programming in a fuzzy environment makes it even more interesting due to the vagueness and uncertainty of the available resources and variables. Since the market price and profit of certain goods are not known exactly, considering fuzzy variables and parameters in the linear programming makes it more closer to the real-life situation; therefore, it becomes more attractive for the decision-makers. In a fuzzy environment, there is only one information and that is the possibility of the variable. In many real-world problems, we need the reliability of the information along with its possibility. Zadeh suggested a Z-number Z = (A; B) with two components, A carrying the information of possibility of the variable, and B carrying the information about reliability of the first component A. Linear programming with its parameters and variables carrying the information in the form of Z number is even more exciting for the decision-makers. Because every decision-maker demands information that is more reliable, linear programming in a Z-number environment with both its components taken as fuzzy numbers is a very attractive problem. In this paper, we present linear programming problems with the parameters and variables taken as Z number having triangular fuzzy numbers as possibility and reliability. We also suggest an interactive method to solve Z number linear programming problems by converting Z-numbers into conventional fuzzy numbers and then using the ranking of fuzzy numbers. We also present applications of the proposed models by solving numerical examples. We also test the authenticity of the proposed method by comparing the results with the existing techniques.Öğe Multi-criteria decision making with Hamacher aggregation operators based on multi-polar fuzzy Z-numbers(Elsevier Inc., 2025) Ullah, Inayat; Akram, Muhammad; Allahviranloo, TofighMulti-polar fuzzy sets are crucial for capturing and representing diverse opinions or conflicting criteria in decision-making processes with greater flexibility and precision. While, Z-numbers are important for effectively modeling uncertainty by incorporating both the reliability of information and its degree of fuzziness, enhancing decision-making in uncertain environments. To date, no model in the literature exhibits the properties of multi-polar fuzzy sets and Z-numbers. In this article, we introduce a new concept of multi-polar fuzzy Z-number and Hamacher operations for multi-polar fuzzy Z-numbers. Based on the Hamacher operations, we propose aggregation operators for multi-polar fuzzy Z-numbers, namely, multi-polar fuzzy Z-number Hamacher weighted averaging operator, multi-polar fuzzy Z-number Hamacher ordered weighted averaging operator, multi-polar fuzzy Z-number Hamacher weighted geometric operator and multi-polar fuzzy Z-number Hamacher ordered weighted geometric operator. Additionally, we develop a decision-making model based on the proposed Hamacher aggregation operators. Further, we apply the proposed technique to a couple of case studies to check the validity and authenticity of the proposed methodology. Finally, we compare the outcomes of the study with several existing techniques to assess the accuracy of the proposed model. © 2024 Elsevier Inc.Öğe A new method for the solution of fully fuzzy linear programming models(Springer Science and Business Media Deutschland GmbH, 2022) Akram, Muhammad; Ullah, Inayat; Allahviranloo, TofighIn this study, we first show that the existing arithmetic operations of trapezoidal fuzzy numbers do not satisfy the basic properties. Then, for trapezoidal fuzzy numbers, we define new arithmetic operations. Furthermore, we demonstrate that the existing Simplex method for addressing fully fuzzy linear programming problems has some drawbacks. Finally, we provide a new strategy for solving fully fuzzy linear programming problems and compare our results with the existing methods. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
