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.
Admissible orders on fuzzy numbers are total orders which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e. TFN's) and study some fundamental properties with its arithmetic and their relation with this admissible order. In addition, we also introduce the concepts of average function on TFN's and studies a generalized structure of the vector spaces. In particular we consider the case of TFN's.
The main goal in this work is to prove the exponential decay of the semigroup associated with a thermoelastic system composed of an Euler-Bernoulli type equation that models the transverse oscillation of a homogeneous microbeam with axial movement and in which a viscous damping is acting. In addition, to this microbeam has been endowed with a thermal effect given by the Coleman-Gurtin model which depends essentially on past history, representing an improvement of Fourier, Cattaneo and Green-Naghdi models. To achieve this goal, we will use mainly multiplicative techniques and standard tools of functional analysis.
This work deals with the study of a new total order Triangular Fuzzy Numbers and arithmetic properties that are maintained in relation to the operations of addition and subtraction. Additionally, we present as example of application the shortest path solution for the Travelling Salesman Problem with fuzzy distances.
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