In this paper, we introduce the concept and applications of gH-symmetrical derivative for interval-valued multi-objective functions, which is the generalization of generalized Hukuhara derivative (gH-derivative). By a suitable example it has been shown that gH-symmetrically derivative is an extension of gH-derivative. Furthermore, we apply this new derivative to investigate the Fritz John type optimality conditions for interval-valued multiobjective programming problems. We use LR type of order relation in this context.

In this paper we consider the design of FIR filters that satisfy magnitude specifications. We refer to such design problems as magnitude filter design problems. In this paper it is shown that by a change of variables, a wide variety of magnitude filter design problems can be posed as convex optimization problems, i.e., problems in which the objective and constraint functions are convex.

Taking into consideration gH-symmetrical derivative, we discuss Fritz John type optimality conditions for E-convex functions in interval-valued optimization problems. By a suitable example, we show that gH-symmetrical derivative is an extension of gH-derivative. We use LU type of order relation in this context.