The priority problem of incomplete preference relations is investigated. Using the transformation relation between multiplicative preference relation and fuzzy preference relation, we develop a least-square model to obtain the collective priority vector of the incomplete preference relations presented by multiple decision makers, with the existence condition of the solution being developed. Mea...

The priority method of interval fuzzy preference relation is studied. A linear programming(LP) model based on multiplicative transitivity is constructed to derive interval weights from consistent or inconsistent interval fuzzy preference relation. By solving only one LP model, the proposed method can get the interval weights from an interval fuzzy preference relation, which can reduce the amoun...

In this paper, we define the concept of uncertain multiplicative linguistic preference relation, and introduce some operational laws of uncertain multiplicative linguistic variables. We propose some new aggregation operators including the uncertain linguistic geometric mean (ULGM) operator, uncertain linguistic weighted geometric mean (ULWGM) operator, uncertain linguistic ordered weighted geom...

Consistency of preference relations is associated with the study of the transitivity property. This is clearly related to the scales used for associating preferences values to judgements, and the conditions used to represent transitivity. Both issues, the scale to use and the consistency property, have been studied in the multiplicative model as well as in the fuzzy one. However, we make note t...

Intuitionistic fuzzy preference relation has turned out to be a powerful structure in representing the decision makers’ preference information especially when the decision makers are not able to express their preferences accurately due to the unquantifiable information, incomplete information, unobtainable information, partial ignorance, and so forth. The aim of this paper is to develop some te...

In this paper, the linear quadratic regulation problem for discrete-time systems with state delays and multiplicative noise is considered. The necessary and sufficient condition for the problem admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference equations. Our approach is based on the maximum...

The priority method on the intuitionistic fuzzy preference relation (IFPR) is proposed. In order to avoid the operational difficulty in dealing with the intuitionistic sets, the equivalent interval matrices of the IFPR are introduced. Based on the multiplicative consistent definition of the fuzzy interval preference relation (FIPR), the goal programming models for deriving the priority vector o...

This paper proposes a novel approach to cope with the multi-criteria group decision-making problems. We give the pairwise comparisons based on the best-worst-method (BWM), which can decrease comparison times. Additionally, our comparison results are determined with the positive and negative aspects. In order to deal with the decision matrices effectively, we consider the elimination and choice ...

The aim of this paper is to show that the normalizing rank aggregation method can not only be used to derive the priority vector for a multiplicative preference relation, but also for the additive transitive fuzzy preference relation. To do so, a simple functional equation between fuzzy preference’s element and priority weight is derived firstly, then, based on the equation, three methods are p...

In this paper, we present a procedure to estimate missing preference values when dealing with pairwise comparison and heterogeneous information. The procedure attempts to estimate the missing information in an expert's incomplete fuzzy preference relation using only the preference values provided by that particular expert. Our procedure to estimate missing values can be applied to incomplete fu...