in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...

We show that a set of three axioms, together with modus ponens, suffices to build up a formal system for the class R of all quadruples (L,6,T,J), in which (L,6) is a partially ordered set with a top element, and T is a triangular norm on (L,6) that has a residuated implication J. We show that this R is not a variety. 2004 Elsevier Inc. All rights reserved.

Let (At | i e I) be an indexed family of nonempty intervals of a linearly ordered set {L, <). Let (/, E) be the intersection graph of (̂ 4, | I G / ) , that is {i,j}eE if and only if At n At J= 0 . In [6], R. Rado considered the following sentence R(K), where K is a cardinal number. If Chr(J, E n |V]) ^ K for all ; £ / , |J| ^ K + , then Chr(/ , E) < K. He proved (see [6, Theorem 2]) that R(K) h...

The COCOLOG system is a partially ordered family of rst order logical theories that describe the controlled evolution of the state of a given partially observered-nite machine M. Following the review of the general COCOLOG system and its Markovain fragment system , a mutil-complexity measurement called Joint is deened and further a partial order simplicity is introduced. Finally, some compariso...

In this paper, some fixed point theorems for nonexpansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support our results.

In this paper, at rst we describe a graph representing all the weak-order extensions of a partially ordered set and an algorithm generating them. Then we present a graph representing all of the minimal weak-order extensions of a partially ordered set, and implying a generation algorithm. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability inv...

Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space. Assuming the continuum hypothesis (CH), Oxtoby [9] constructed a Baire space whose square is not Baire. We will show in this paper that the assumption of CH is unnecessary. Such results are greatly enhanced by Krom [5], who showed that if there is such an example, then there...