An Attitudinal Nonlinear Integral and Applications in Decision Making

In the field of information fusion and decision making, integral is very common and important for aggregating a large variety of information. The integral to be used is usually nonlinear due to the nonadditive measure determined by the real world. In this study, we put forward a new nonlinear integral, which is first expressed as an interval, containing the infimum and supremum of the integrand on the nonadditive measure. Furthermore, an attitudinal nonlinear integral is defined by introducing the subjective attitude of the decision maker based on the integral interval obtained. A multi-criteria decision-making (MCDM) method considering the interaction between attribute features is developed based on the proposed attitudinal nonlinear integral and a case study is provided to demonstrate the usefulness of the decision-making method. Inspired by the golden rule representation, we define the generalized golden rule representative value of the interval integral and use it to solve the problem in the case study to illustrate its usefulness.

Automated summary

In this study, a new nonlinear integral method is proposed, considering the impact of nonadditive measures and introducing the subjective attitude of decision makers. A multi-criteria decision-making method is developed based on the proposed attitudinal nonlinear integral, and its usefulness is demonstrated through a case study.