A Novel Method for Solving Multiobjective Linear Programming Problems with Triangular Neutrosophic Numbers

In the field of operation research, linear programming (LP) is the most utilized apparatus for genuine application in various scales. In our genuine circumstances, the manager/decision-makers (DM) face problems to get the optimal solutions and it even sometimes becomes impossible. To overcome these limitations, neutrosophic set theory is presented, which can handle all types of decision, that is, concur, not certain, and differ, which is common in real-world situations. By thinking about these conditions, in this work, we introduced a method for solving neutrosophic multiobjective LP (NMOLP) problems having triangular neutrosophic numbers. In the literature study, there is no method for solving NMOLP problem. Therefore, here we consider a NMOLP problem with mixed constraints, where the parameters are assumed to be triangular neutrosophic numbers (TNNs). So, we propose a method for solving NMOLP problem with the help of linear membership function. After utilizing membership function, the problem is converted into equivalent crisp LP (CrLP) problem and solved by any suitable method which is readily available. To demonstrate the efficiency and accuracy of the proposed method, we consider one classical MOLP problem and solve it. Finally, we conclude that the proposed approach also helps decision-makers to not only know and optimize the most likely situation but also realize the outcomes in the optimistic and pessimistic business situations, so that decision-makers can prepare and take necessary actions for future uncertainty.

Finding compromise solutions for fully fuzzy multi-olbjective linear programming problems by using game theory approach

Solving multiobjective linear programming (MOLP) problems and fully fuzzy multi-objective linear programming (FFMOLP) problems involves the trade-off process among several objectives. A new algorithm extended where FFMOLP problems are solved using a 2-player zero-sum game approach to deal with this case. Firstly, The FFMOLP problem is separated into a certain number of fully fuzzy linear programming (FFLP) problems and each is solved by applying any method. After forming a ratio matrix, a game theory approach is applied for finding the weights of objective functions and a weighted LP problem is constructed by these weights. Solving the weighted LP problem, a fuzzy compromise solution of the FFMOLP problem is found. Constructing different ratio matrices, it is also possible to obtain more than one compromise solution to be offered to the decision-maker(s). Some examples are given to show the applicability of the algorithm.

Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming

To study the reasons of the low academic performance of students in Spain, authorities must consider emotional dimensions, such as well-being, which directly affect their learning achievement. Furthermore, it would be interesting to compare Spanish students with students from Finland, which stand out in international rankings. We analyze how to promote students’ well-being in Spain as a mechanism to enhance their academic achievement. Using data from PISA 2018, four indicators are used to measure well-being according to variables describing the students’ context. By means of econometric techniques, interval multiobjective linear programming problems are formulated for Spain and Finland and solved through a new methodological scheme proposed in this paper, assuring the generation of possibly and necessarily efficient solutions in interval multiobjective linear programming. The purpose is to determine which aspects would allow the best possible well-being to be reached. We found several differences between the students achieving optimal compromise levels in each country, and we analyzed how the improvement of one indicator might affect the remaining aspects of well-being. Spanish students can further enhance their well-being compared to Finnish students. Furthermore, the lowest improvement rate is associated with the bullying index, especially in Finland, highlighting the need to promote anti-bullying measures.