Abstract: Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming (FNLP) problem with piecewise linear membership functions (PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.

Key words: fuzzy nonlinear programming, piecewise linear membership functions, modeling

摘要： Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming (FNLP) problem with piecewise linear membership functions (PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.

关键词: fuzzy nonlinear programming, piecewise linear membership functions, modeling