We study the monoid generalizationMk,1 of the Thompson-Higman groups, and we characterize the Rand the L-preorder ofMk,1. Although Mk,1 has only one non-zero J -class and k−1 non-zero D-classes, the Rand the L-preorder are complicated; in particular, <R is dense (even within an L-class), and <L is dense (even within an R-class). We study the computational complexity of the Rand the L-preorder. ...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

based on a complete heyting algebra l, the relations between lfuzzifyingconvergence spaces and l-fuzzifying topological spaces are studied.it is shown that, as a reflective subcategory, the category of l-fuzzifying topologicalspaces could be embedded in the category of l-fuzzifying convergencespaces and the latter is cartesian closed. also the specialization l-preorderof l-fuzzifying convergenc...

Multi-context systems (MCS) presented by Brewka and Eiter can be considered as a promising way to interlink decentralized and heterogeneous knowledge contexts. In this paper, we propose preferential multicontext systems (PMCS), which provide a framework for incorporating a total preorder relation over contexts in a multi-context system. In a given PMCS, its contexts are divided into several par...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

Let L be a complete residuated lattice. Then we show that any L-preorder can be represented both by an implication-based graded inclusion as defined [1] and by a similarity-based graded inclusion as defined in [2]. Also, in accordance with a duality between [0,1]-orders and quasi-metrics, we obtain two corresponding representation theorems for quasi-metrics.

Abstract We obtain several characterizations of the existence greatest elements a total preorder. The pertain to unconstrained preorder and constrained on every nonempty compact subset its ground set. necessary sufficient conditions are purely topological and, in case elements, formulated by making use relation set all topologies that can be defined objective relation. Observing function into t...

The goal of this report is to prove correctness of a considerable subset of transformations w.r.t. contextual equivalence in an extended lambda-calculus LS with case, constructors, seq, let, and choice, with a simple set of reduction rules; and to argue that an approximation calculus LA is equivalent to LS w.r.t. the contextual preorder, which enables the proof tool of simulation. Unfortunately...