In this paper it is presented the use of preference degrees to solve decision-making problems where linguistic preference relations are used to represent decision-makers' opinions. From a linguistic preference relation are deened a linguistic non-dominance degree, a linguistic dominance degree, and a stric domoninance degree, using linguistic quantiiers and the ordered weight linguistic aggrega...

In multiperson decision making situations, it is quite natural that different decision makers who may have different background and knowledge will provide their preferences by different kinds of preference relations. This paper proposes a linguistic multiperson decision making model (LMDMM) based on linguistic preference relations, integrating fuzzy preference relations, different types of mult...

Let U be a set with three or more elements, let W be the set of weak orderings of U, let T be the set of total orderings of U, and let f be an n-ary function mapping Wn to W. Arrow’s Impossibility Theorem asserts that if f satisfies Arrow’s Condition P (“Pareto”) and Condition 3 (“independence of irrelevant alternatives”) then f is a projection function on total orderings, i. e., there is some ...

8 This article investigates the consistency of interval fuzzy preference relations based on interval 9 arithmetic, and new definitions are introduced for additive consistent, multiplicative consistent 10 and weakly transitive interval fuzzy preference relations. Transformation functions are put 11 forward to convert normalized interval weights into consistent interval fuzzy preference relations...

We introduce two criteria for judging “goodness” of the result when combining preference relations in information systems: completeness and consistency. Completeness requires that the result must be the union of all preference relations, while consistency requires that the result must be an acyclic relation. In other words, completeness requires that the result contain all pairs appearing in th...

We define preference in terms of a constraint sequence, a concept from optimality theory. In case agents only have incomplete information, beliefs are introduced. We propose three definitions to describe different procedures agents may follow to get a preference relation using the incomplete information. Changes of preference are explored w.r.t their sources: changes of the constraint sequence,...

In this paper, we investigate group decision making problems with multiple types of linguistic preference relations. The paper has two parts with similar structures. In the first part, we transform the uncertain additive linguistic preference relations into the expected additive linguistic preference relations, and present a procedure for group decision making based on multiple types of additiv...

In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve intuitionistic fuzzy preference relations. We describe the operations which preserve intuitionist...

We introduce two criteria for judging “goodness” of the result when combining preference relations in information systems: completeness and consistency. Completeness requires that the result must be the union of all preference relations, while consistency requires that the result must be an acyclic relation. In other words, completeness requires that the result contain all pairs appearing in th...

Pairwise comparison matrix as a crucial component of AHP, presents the preference relations among alternatives. However, in many cases, the pairwise comparison matrix is difficult to complete, which obstructs the subsequent operations of the classical AHP. In this paper, based on DEMATEL which has ability to derive the total relation matrix from direct relation matrix, a new completion method f...