Use of tranquility in determining the numerical compensation for a fuzzy multicriteria decision making problem

Several operators have been proposed for the aggregation of membership functions of the fuzzy sets reflecting the various objectives. However, they do not seem to be very suitable for modelling the real world problems. When the decision is modelled by minimum operator, no compensation is implied among the objectives combined. On the other hand the decision modelled with maximum operator is called fully compensatory in the sense that it achieves the full satisfaction of a single goal. These operators do not seem to be suitable for modelling the real world problems in many situations. To overcome this difficulty Zimmermann and Zysno have suggested a class of hybrid operators called compensatory operator with the help of a suitable parameter of compensation γ. They have, however, not given any method for determining the value of γ. The purpose of this paper is to provide a basis for giving an insight for determining the numerical value of γ taking into account the concept of tranquility. This method is an improvement over the procedure of Rao et al. for determining γ where the concept of personal utility function was used which is subjective to the extent that each decision maker articulates his/her preference in an individualistic manner. This paper provides a theoretical basis which is applicable to practical problems involving multiobjective decision making which are modelled mathematically as vectromaximum problems. A numerical example illustrating the procedure is presented.