Fuzzy Posets Research Articles

The Dedekind–MacNeille completions for fuzzy posets

In this paper, the Dedekind–MacNeille completion for an L-fuzzy poset, previously introduced by the authors, is built and characterized, which generalizes the Dedekind–MacNeille completion for an ordinary poset. The relationship between the L-fuzzy complete lattices defined by the authors and Bělohlávek's completely lattice L-ordered sets is discussed.

Fuzzy Galois connections on fuzzy posets

AbstractThe concept of fuzzy Galois connections is defined on fuzzy posets with Bělohlávek's fuzzy Galois connections as a special case. The properties of fuzzy Galois connections are investigated. Then the relations between fuzzy Galois connections and fuzzy closure operators, fuzzy interior operators are studied. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Representation functions and the Neggers–Stanley condition for weight-shaped-posets

We introduce the class of weight-shaped-posets and we define the representation functions of such w s -posets as generalizations of the representation polynomials of finite posets. We define the Brylawski decomposition of w s -posets and use it to construct the algorithm for the computation of the representation functions. The class of w s -posets contains a class of fuzzy posets for example. The Neggers–Stanley conjecture for w s -posets is also discussed.

Fuzzy posets on sets

In this paper we introduce the notion of a fuzzy poset defined on a set X via a triplet (L,G,P) of functions with domain X × X and range [0,1] satisfying a special condition L+G+P=1. Using this approach we are able to define special classes of fuzzy posets and to prove several standard theorems for posets in the setting of fuzzy posets. Furthermore, using a rounding-off procedure we are able to define the skeleton of a fuzzy poset and to obtain results on the behavior of deformations of skeleta of fuzzy posets as it relates to the structure of these fuzzy posets. If the fuzzy dimension is defined as the intersection of the least number of fuzzy chains which yield the fuzzy poset, then it is shown that the definition makes sense and in large classes equals the dimension of the skeleton. L is the “less than” function, G is the “greater than” function, and P is the “parallel” or “incomparability” function.

FUZZY QUANTUM POSETS

This paper discusses three types of fuzzy quantum posets, states and observables on these posets, representations of fuzzy quantum posets, representation of observables, and joint observables.

FUZZY QUANTUM MODELS

We present some models of quantum mechanics which use fuzzy set approaches: fuzzy measurable spaces and fuzzy quantum posets of two types. Also presented are compatibility problems, observables and their representations, functional calculus of observables, and states (= probability measures).