mathematics Article A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers Saeid Jafarzadeh Ghoushchi 1 , Elnaz Osgooei 2, * , Gholamreza Haseli 3 and Hana Tomaskova 4, *   Citation: Ghoushchi, S.J.; Osgooei, E.; Haseli, G.; Tomaskova, H. A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers. Mathematics 2021, 9, 2937. https:// doi.org/10.3390/math9222937 Academic Editor: Aleksandr Rakhmangulov Received: 12 October 2021 Accepted: 15 November 2021 Published: 18 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Faculty of Industrial Engineering, Urmia University of Technology, Urmia 57166, Iran; s.jafarzadeh@uut.ac.ir 2 Faculty of Science, Urmia University of Technology, Urmia 57166, Iran 3 Department of Management, Faculty of Economic, Management and Social Science, Shiraz University, Shiraz 71345, Iran; ghr.haseli@gmail.com 4 Faculty of Informatics and Management, University of Hradec Kralove, 500 06 Hradec Kralove, Czech Republic * Correspondence: e.osgooei@uut.ac.ir (E.O.); hana.tomaskova@uhk.cz (H.T.) Abstract: Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method. Keywords: modified triangular fuzzy numbers; fuzzy decision variables; fully fuzzy linear program- ming; alpha-cut theory 1. Introduction In the modern and competitive world, making the right, scientific-based, and timely decisions plays a very important and decisive role in the success or failure of organiza- tions [1,2]. Uncertainty conditions and complexities of the decision-making processes have made decision makers use fuzzy theory, which is a suitable tool for management under uncertain conditions and making optimal decisions [3,4]. This theory was first proposed by Lotfi A. Zadeh [5] in 1965. Linear programming is an operational research tool that has been widely used for many years. Determining the parameters of fuzzy programming requires the opinions of decision makers; however, it cannot be determined accurately and definitively in most cases, because there is always ambiguity and uncertainty in the opinion of experts and decision makers. Fuzzy linear programming can also be explained as a fully fuzzy issue by considering all the decision parameters and variables of the problem in the fuzzy phase [6,7]. Therefore, various solution methods have been recommended to obtain the optimal solution of fuzzy linear programming. In the first method, Lotfi et al. [8] solved the problems by approximating the parameters to be as close as possible to symmetric triangular fuzzy numbers and the approximate optimal fuzzy solution. For this purpose, they solved a multiobjective linear programming model. Kumar et al. [9] used a linear ranking function to convert a fuzzy objective function to a certain state and, finally, ob- tained a certain optimal solution to solve fully fuzzy problems. Elsewhere, Ezzati et al. [10] solved problems using a new algorithm to convert the problem to multiobjective linear programming along with the lexicography method. This study examines a new approach to solve FFLP problems through fuzzy decision parameters and variables using triangular fuzzy numbers. The technique, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world Mathematics 2021, 9, 2937. https://doi.org/10.3390/math9222937 https://www.mdpi.com/journal/mathematics