This study uses three types of pairwise comparisons algorithm which are horizontal vertical and oblique to construct Multi-Criteria Decision Making with Incomplete Linguistic Preference Relations Model. The use of pairwise comparisons will not produce the problem of inconsistency, which even allows every decision expert to choose an explicit criterion or alternative for index unrestrictedly. Wh...

In this paper, we combine answer set programming with voting theory for the first time. For this, we use the voting procedures defined in [5], which allow winner determination under incomplete preference relations. We present the problem of scheduling a meeting for a research group as an application. In those scheduling problems, often no meetings are schedulable because of conflicting unavaila...

We consider the problem of representing a (possibly) incomplete preference relation by means of a vector-valued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice, and pa...

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...

In a very recent paper by Xu and Chen (Soft Comput 12:515–521, 2008), a novel procedure for group decision making with incomplete reciprocal relations was developed. In this note, we examine the function between the fuzzy preference relation and its corresponding priority vector developed by Xu and Chen with a numerical example and show that the function does not hold in general cases. Then, we...

This paper proposes a chi-square method (CSM) to obtain a priority vector for group 11 decision making (GDM) problems where decision-makers’(DMs’) assessment on alternative is 12 furnished as incomplete reciprocal preference relations with missing values. Relevant theorems 13 and iterative algorithm about CSM are proposed. Satty’s consistency ratio concept is adapted to 14 judge whether an inco...