It is natural to relate partially ordered sets (posets in short) and classes of equivalent words over partially commutative alphabets. Their common graphical representation are Hasse diagrams. We investigate this relation in detail and propose an efficient online algorithm that decompresses a concurrent word to its Hasse diagram. The lexicographically minimal representative of a trace (an equiv...

Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modif...

The last decades have seen a growing interest in theoretical and practical problems related to lexicographical user research. Starting with a discussion of the concept of lexicographically relevant user needs, this contribution analyses, utilising the lexicographical function theory, various types of needs to be taken into account when doing this kind of research. It then discusses the positive...

procedure ari thmetic (a, b, c, op); in t eger a, b, c, op; ¢ o n l m e n t This procedure will perform different order ar i thmetic operations with b and c, put t ing the result in a. The order of the operation is given by op. For op = 1 addit ion is performed. For op = 2 multiplicaLion, repeated addition, is done. Beyond these the operations are non-commutat ive. For op = 3 exponentiat ion, r...

The extension of mathematical morphology to colour, and more generally to multivariate image data, continues to be an open problem. As its underlying theory is defined in terms of complete lattices, the main challenge lies in introducing a complete lattice structure on the image intensity range, hence vectorial extrema computation methods are necessary. In this paper, we circumvent the need for...