A partiallyordered multiset or pomset is a generalizationof a string in which the total order has been relaxed to a partial order. Strings are often used as a model for sequential computation; pomsets are a natural model for parallel and distributed computation. By viewing pomsets as a generalization of strings, the question is raised whether concepts from language theory can be generalized to ...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

In this paper we begin with the basics of multisets and their operations introduced in [5, 22] and define a multiset relation, an equivalence multiset relation and explore some of their basic properties. We also define a partially ordered multiset as a multiset relation being reflexive, antisymmetric and transitive, chains and antichains of a partially ordered multiset, and extend Dilworth’s Th...

In this paper we propose the extension of some aggregation or arithmetic operations between discrete fuzzy numbers to discrete fuzzy number-valued multisets such as the addition, the union and the intersection and, even, the order. For this reason, we prove or recall some properties of discrete fuzzy numbers and we undertake their study on multisets.

This introduction to the R package sets is a (slightly) modified version of Meyer and Hornik (2009a), published in the Journal of Statistical Software. We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Fu...

Comparative evaluation operators for sets and multisets are proposed from a possibilistic point of view. In general, an evaluator estimates the possibility of (non) co-reference of two arbitrary (sub)-objects. Such operators can be used in a hierarchical possibilistic framework for finding co-referent objects with a complex structure. This paper first discusses properties of evaluators in gener...

The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...