No abstract

From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this paper, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, it is given special attention to the partial order proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a strictly increasing upper dense sequence, proving that this order is admissible for a given partial order. Finally, we use admissible orders to ranking the path costs in fuzzy weighted graphs.

From the more than two hundred partial orders for fuzzy numbers proposes in the literature, only a few are totals. In this paper, we introduce the notion of admissible orders for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, is given special attention when thr partial order is the proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a strictly increasing upper dense sequence, proving that this order is admissible for a given partial order.

n-Dimensional fuzzy sets are a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0, 1] increasingly ordered, called n-dimensional intervals. The set of n-dimensional intervals is denoted by L n ([0, 1]). This paper aims to investigate semi-vector spaces over a weak semifield and aggregation functions concerning an admissible order on the set of n-dimensional intervals and the construction of aggregation functions on L n ([0, 1]) based on the operations of the semi-vector spaces. In particular, extensions of the family of OWA and weighted average aggregation functions are investigated. Finally, we develop a multi-criteria 1 group decision-making method based on n-dimensional aggregation functions with respect to an admissible order and give an illustrative example.

Moore and Yang defined an integral notion, based on an extension of Riemann sums, for inclusion monotonic continuous interval functions, where the integrations limits are real numbers. This integral notion extend the usual integration of real functions based on Riemann sums. In this paper, we extend this approach by considering intervals as integration limits instead of real numbers and we abolish the inclusion monotonicity restriction of the interval functions and this notion is used to determine interval probability density functions.