<p>Fractional programming provides a robust and efficient mathematical framework for dealing with real-world optimization problems where objectives are expressed as ratio form. When such systems are affected by uncertainty and imprecision, intuitionistic fuzzy fractional programming becomes an effective tool for capturing both membership and non-membership uncertainties in decision variables and parameters. This study introduces a novel algorithm to address fuzzy multi-objective linear fractional programming problems in which the uncertainty present in the objective functions and constraint parameters is handled by the triangular intuitionistic fuzzy numbers. The primary aim is to develop a simple yet efficient solution methodology for multi-objective linear fractional programming problems under intuitionistic fuzzy environments. The proposed algorithm starts by using a component-wise method to transform fuzzy objective functions into equivalent crisp forms. To handle the fuzzy constraints, an appropriate ranking function is utilized, converting them into deterministic form. The fractional components are then linearized using a suitable variable transformation, yielding a crisp multi-objective linear programming problem. This multi-objective linear programming problem is further transformed into a single-objective linear programming problem using the fuzzy harmonic mean approach, and then a fuzzy goal programming technique is subsequently applied to obtain the optimal solution. Finally, a ranking formula is used to defuzzify the fuzzy results into crisp outputs. The effectiveness and practicality of the proposed method are illustrated through the solution of one existing numerical example and one real-world case, with comparisons highlighting the superiority of the proposed approach over existing techniques.</p>

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Fuzzy harmonic mean-based method for solving intuitionistic fuzzy multi-objective linear fractional optimization problems and its application in organizational planning

  • Vaishaly Verma,
  • Pitam Singh

摘要

Fractional programming provides a robust and efficient mathematical framework for dealing with real-world optimization problems where objectives are expressed as ratio form. When such systems are affected by uncertainty and imprecision, intuitionistic fuzzy fractional programming becomes an effective tool for capturing both membership and non-membership uncertainties in decision variables and parameters. This study introduces a novel algorithm to address fuzzy multi-objective linear fractional programming problems in which the uncertainty present in the objective functions and constraint parameters is handled by the triangular intuitionistic fuzzy numbers. The primary aim is to develop a simple yet efficient solution methodology for multi-objective linear fractional programming problems under intuitionistic fuzzy environments. The proposed algorithm starts by using a component-wise method to transform fuzzy objective functions into equivalent crisp forms. To handle the fuzzy constraints, an appropriate ranking function is utilized, converting them into deterministic form. The fractional components are then linearized using a suitable variable transformation, yielding a crisp multi-objective linear programming problem. This multi-objective linear programming problem is further transformed into a single-objective linear programming problem using the fuzzy harmonic mean approach, and then a fuzzy goal programming technique is subsequently applied to obtain the optimal solution. Finally, a ranking formula is used to defuzzify the fuzzy results into crisp outputs. The effectiveness and practicality of the proposed method are illustrated through the solution of one existing numerical example and one real-world case, with comparisons highlighting the superiority of the proposed approach over existing techniques.