Fuzzy Linear Programming: Optimization of an Electric Circuit Model

• Autor(a) principal: BERTONE,A.M.A.
• Data de Publicação: 2017
• Outros Autores: JAFELICE,R.S.M., CÂMARA,M.A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300419
• topic: electrical circuit model; linear programming; fuzzy linear programming; fuzzy sets of type-1; fuzzy sets of type-2

ABSTRACT A problem of a voltage division circuit is modeled in order to determine the values of the resistors centered, in a way that the impedance of the resistance voltage divider is minimal. This problem is equivalent to maximizing the admittance, associated to the resistance, which is defined as the quotient of the electric current and its voltage, measured in Siemens. Three cases are analyzed for the components of the linear programming: real numbers, fuzzy numbers of type-1, and fuzzy sets of type-2. The first case is considered in order to validate the other two cases. The optimal solution in the fuzzy linear programming of type-1 is obtained through a linear defuzzification function, defined in the trapezoidal fuzzy numbers subspace of fuzzy numbers vector space, which allows to solve the corresponding linear programming problem with real components. A study upon the parameter for linear defuzzification is accomplished to determine the best representative of the family of parameters. The α−levels representation theorem is the method to obtain the optimal solution of type-2. For each α−level is solved a fuzzy linear programming problem of type-1, using the previous methodology. Numerical simulations illustrate the results in the three cases.