Zhian M. Mahmood1,a) and Nejmaddin A.Sulaiman1,b)
1Department of Mathematics, College of Education, Salahaddin University, Erbil, 44001, Iraq
DOI: https://doi.org/10.31972/ticma22.15
Abstract
In this paper Standard Error of Mean (SEM), as a new technique, is used for transforming multi-objective linear programming problems (MOLPPs) to the single objective linear programming problems (SOLPPs). To this end, an algorithm has been proposed and suggested to solve MOLPPs, which have been tested through numerical examples by employing Excel Solver. However, the study compares the results of other techniques like (Chandra Sen, Optimal Average of Minimax and Maximin, New Arithmetic Average, New Geometric Average, New Harmonic Average, and Advanced Transformation) with the results of this new technique SEM. The numerical results indicate that a new technique in general is promising.
Key Words: Multi-Objective Linear Programming, Geometric Average, Harmonic Average.
1) Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq.
2) Department of Mathematics, College of Education, University of Garmian, Kalar 46021, Iraq.
a) pishtiwan.sabir@univsul.edu.iq
DOI: https://doi.org/10.31972/ticma22.16
Abstract
This paper investigates the study of -complex fuzzy sets. The -complex fuzzy set, where is a completely distributive lattice, is a generalization of the complex fuzzy set. The fundamental set theoretic operations on -complex fuzzy sets are discussed properly, including -complex fuzzy complement, union and intersection. New procedures are presented to combine the novel concepts of -complex fuzzy -norms and -conorms and look into the conditions that lead to a comparable representation theorem. We have used the axiomatic method, in the sense that our underlying assumptions, especially about, are abstract; it can thus be ascertained to what extent our results apply to some new problem. On the other hand, our method shows that if mathematics, as we use it, is consistent, so is fuzziness, as we formulate it.
Key Words: : Fuzzy set; Complex fuzzy set; -complex fuzzy set; Fuzzy -norm; Fuzzy -conorm.