Generalization of equitable efficiency in‎ ‎multiobjective optimization problems by the direct sum of matrices

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 اردیبهشت 1401  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.69731.1023

نویسندگان

Fatemeh Ahmadi؛ Ali Reza Salajegheh؛ Davoud Foroutannia

Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

چکیده

‎In this paper‎, ‎we suggest an a priori method by introducing the concept of $A_P$-equitable efficiency‎. ‎The preferences matrix $A_P$‎, ‎which is based on the partition $P$ of the index set of objective functions‎, ‎is given by the decision maker‎. ‎We state the certain conditions on the matrix $A_P$ that guarantee the preference relation $\preceq_{eA_P}$ satisfies the strict monotonicity and strict $P$-transfer principle axioms‎.
A problem most frequently encountered in multiobjective optimization‎ is that the set of Pareto optimal solutions provided by the optimization process is a large set‎. Hence‎, ‎the decision making based on selecting a unique preferred solution becomes difficult‎. Considering models with $A^r_P$-equitable efficiency and $A^{\infty}_P$-equitable efficiency relieve some of the burden from the decision maker by shrinking the solution set‎.

کلیدواژه‌ها

Nondominated؛ equitable efficiency؛ AP -equitable efficiency؛ Multiobjective programming