Improving the consistency of incomplete hesitant multiplicative preference relation

Abstract

As it know, most decision processes are depends on preference relations as in the forms by comparing different alternatives over criteria. In the process of decision making, a decision maker may give his/her judgement by means of hesitant multiplicative preference relation (HMPR) using the scale of $$1/9-9$$ for hesitancy and uncertainty. Shortage of of time, experience and lack of the experts’ professional knowledge lead to form an incomplete hesitant multiplicative preference relation. In this paper we have defined a multiplicative transitive property of HMPR that preserves the hesitancy property. Another aim of this paper is to characterise two different approaches to calculate the missing element of incomplete HMPR from the incomplete one. The first approach involves two step, estimating step calculate the initial values of the missing element and the adjusting step minimizing the error. A linear programming model is developed in the second approach to calculate the missing values of incomplete hesitant multiplicative preference relation. The satisfaction degree and the acceptable consistency of complete HMPR is also checked. The whole procedure is explained with a suitable example.