A valued Ferrers relation for interval comparison

Abstract

The paper deals with the valued comparison of intervals for decision making. Interval orders are classical preference structures where the comparison of intervals is done in an ordinal way. In this paper we focus on valued comparison where more information, especially the distance between end-points of intervals, is used in order to have more sophisticated preference structures. The generalization of an interval order as a valued structure requires the choice of de Morgan triplets. We propose a valued outranking relation for interval comparison and show that it satisfies different definitions of valued interval orders using different de Morgan triplet. The decomposition of our outranking relation into preference and indifference provides a valued preference structure where the preference is T -transitive and monotone.

Bi-oriented graphs and four valued logic for preference modelling

“…With respect to this framework, the reader will note that many of the representation theorems as well as many of the decision support procedures explicitly need to consider extended notions of transitivity, either well known ones such as "semi-transitivity" and "Ferrers" ( [21]), or new ones ( [23], [18], [20], [26]). Under such a perspective a problem still open in the relevant literature concerns the extension and/or generalisation of the concept of transitive closure, a key issue in many decision support procedures.…”

An interval‐valued exceedance method in MCDM with uncertain satisfactions

“…In anticipation of solving MCDM problems in situations in which the satisfaction of individual criteria by an alternative is provided in terms of an interval value from the unit interval rather than a precise value, the problem of ordering them must be considered . Many researchers have widely discussed the comparison methods around fuzzy intervals . Thus, to have the capability of obtaining the required ordering in the case of interval‐valued information, the Golden Rule representative value has been introduced by Yager to provide a scalar representative value for these intervals and has been applied to solve MCDM problems.…”

“…63 Many researchers have widely discussed the comparison methods around fuzzy intervals. [64][65][66] Thus, to have the capability of obtaining the required ordering in the case of interval-valued information, the Golden Rule representative value has been introduced by Yager 67 to provide a scalar representative value for these intervals and has been applied to solve MCDM problems.…”

A Generalized Golden Rule Representative Value for Multiple-Criteria Decision Analysis

“…Therefore, the midpoint method is not considered appropriately for the interval ranges. Many scholars have discussed this problem [32]- [35]. Compared with other methods, the intervals are generally converted into representative values and then ordered by comparing their scalar values.…”