Interval-valued intuitionistic multiplicative aggregation in group decision making

Interval-valued intuitionistic multiplicative information uses an unsymmetrical scale (Saaty's 1-9) instead of the ordinary symmetrical scale to reflect our intuition which is more objective in some special situations. Recently, studies on aggregation techniques with interval-valued intuitionistic multiplicative information for group decision making (GDM) have received increasing attention, and several techniques have been proposed. However, none of them have considered the use of pseudo-multiplication or Sugeno measure, and solved the GDM problems with interrelationships among input information. Since a pseudo-multiplication operator is given by weakening the axiomatic condition which is a key of fuzzy measure, and Sugeno measure is a representative non-additive measure, they are suitable for comprehensive evaluation problems which exist interactions. In this paper, we investigate interval-valued intuitionistic multiplicative aggregation operators and study the GDM problems where the preference information is given by the correlated decision makers. Based on the pseudo-multiplication, we first develop two aggregation operators (the interval-valued intuitionistic multiplicative weighted and ordered weighted averaging operators) and obtain several specific results when some specific forms are assigned. Then, for the situations where the input arguments have correlations or connections, we give the aggregation operator based on Choquet integral and Sugeno measure, and also study their properties. Based on the proposed aggregation operators, we present a method for GDM with interval-valued intuitionistic multiplicative preference relations, where some correlations or connections are reflected among the decision makers. Finally, we illustrate the given method with a practical example concerning the design of a satellite communication system.