We present a method of fast factorization in formal concept analysis (FCA) of data with fuzzy attributes. The output of FCA consists of a partially ordered collection of clusters extracted from a data table describing objects and their attributes. The collection is called a concept lattice. Factorization by similarity enables us to obtain, instead of a possibly large concept lattice, its factor...

Based on the basic theory of fuzzy set, this paper suggests the notion of FCM fuzzy set, which is subject to the constraint condition of fuzzy c-means clustering algorithm. The cluster fuzzy degree and the lattice degree of approaching for the FCM fuzzy set are presented, and their functions in the validation process of fuzzy clustering are deeply analyzed. A new cluster validity index is propo...

Hesitant fuzzy linguistic term sets were introduced to grasp the uncertainty existing in human reasoning. In this paper, inspired by absolute order-of-magnitude qualitative reasoning techniques, an extension of the set of hesitant fuzzy linguistic term sets is presented to capture differences between non-compatible preferences. In addition, an order relation and two closed operations over this ...

Effect algebras [6] (or, equivalent in some sense, D-posets [13], [14]) were introduced as carriers of states or probability measures in the quantum (or fuzzy) probability theory (see [10], [11], [13]). Thus elements of these structures represent quantum effects or fuzzy events which have yes-no character that may be unsharp or imprecise. Unfortunately, there are even finite effect algebras adm...

It is a pivotal task how to organize and manage resources for Grid researchs and applications.This paper first proposes Grid resource management strategies by employing τ -parameter fuzzy concept lattice and fuzzy concept trie and combines FCA theory with Grid resource management technology.The formal concept definitions of Grid and resource are given and τ -parameter fuzzy concept lattice mode...

In this paper we introduce the notion of additive and multiplicative generators on the lattice L , which is the underlying lattice of interval-valued fuzzy set theory (which is equivalent to intuitionistic fuzzy set theory in the sense of Atanassov). We study the properties of these operators, some of which are similar to well-known results on ([0, 1],≤).