This paper presents a comparative study of concept lattices of fuzzy contexts based on formal concept analysis and rough set theory. It is known that every complete fuzzy lattice can be represented as the concept lattice of a fuzzy context based on formal concept analysis [R. Bělohlávek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277–298]. This paper shows that ...

In this paper we use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that are nonlinear convolutions that can be expressed as supremum (resp. infimum) of fuzzy intersection (resp. union) norms. Our emphasis and differences with many previous works is the construction of pairs of fuzzy dilation (sup of fuzzy intersec...

We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

We define an 2-fuzzy congruence, which is a weakened fuzzy congruence, find the 2-fuzzy congruence generated by the union of two 2-fuzzy congruences on a semigroup, and characterize the 2-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all 2-fuzzy congruences on a semigroup is a complete lattice and that the collection of 2-fuzzy congruences und...

This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals) from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R) is isom...

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.

and Applied Analysis 3 3. Main Results Throughout this paper, we will consider lattices as complete lattices,X will denote space, and μ is a membership function of any fuzzy set X. Definition 3.1. If m : σ L → R ∪ {∞} satisfies the following properties, then m is called a lattice measure on the lattice σ-algebra σ L . i m ∅ L0. ii For all f, g ∈ σ L such that m f , m g ≥ L0 : f ≤ g ⇒ m f ≤ m g ...