A new consistency definition of interval multiplicative preference relation

Abstract This paper presents a new consistency definition of interval multiplicative preference relation (IMPR). Several desirable properties of this new consistency are fully discussed, and the sufficient and necessary conditions of the new consistency definition are also provided. It is proven that this new consistency of IMPR has robustness and invariance with respect to permutation of the compared objects' labels. Moreover, comparative analyses are conducted to reveal the relationships among five existing consistency definitions and this new consistency definition of IMPR. Based on the new consistency definition of IMPR, a new consistency index is introduced to measure the consistency degree of IMPR. An iterative algorithm is proposed to improve the consistency level of an inconsistent IMPR. Subsequently, a goal programming model is built to derive an interval priority vector from an acceptably consistent IMPR. Eventually, a new individual decision making method with an IMPR is put forward. Numerical examples and simulation analyses are conducted to illustrate the superiority and validity of the proposed individual decision making method.

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