Les relations entre les équations pré-Schröder I
Les relations entre les équations pré-Schröder II
Structure of partially ordered cyclic semigroups
This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.
Properties of fuzzy relations powers
Properties of - compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider - powers of fuzzy relations under diverse assumptions about operation. At first, we remind fundamental properties of - composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....
Aggregations preserving classes of fuzzy relations
We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special...
Preservation of properties of fuzzy relations during aggregation processes
Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by -ary operations is considered. Namely, with the use of fuzzy relations and -argument operation on the interval , a new fuzzy relation is created. Characterization...
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