Given a Brouwerian complete lattice (L,≤) and two referential sets K and E, and using a fuzzy relation R ∈ L which is reflexive and symmetric, certain fuzzy relations Ĥ ∈ L are characterized as solutions of X C R = X. These solutions Ĥ can be determinated by means of the L-fuzzy concepts associated with the K-labeled L-fuzzy context (L,K,E,E,R).

In this paper, we introduce a special algebra called EQ-algebra which has three binary operations (meet, product, fuzzy equality) and a top element. The fuzzy equality is reflexive, symmetric and transitive with respect to the product. EQ-algebra is a natural algebra proposed as an algebra of truth values on the basis of which the fuzzy type theory (a higher-order fuzzy logic) should be develop...

We study graded properties (α–properties) of fuzzy relations, which are parameterized versions of fuzzy relation properties defined by L.A. Zadeh. Namely, we take into account fuzzy relations which are: α–reflexive, α– irreflexive, α–symmetric, α–antisymmetric, α–asymmetric, α–connected, α–transitive, where α ∈ [0, 1]. We also pay our attention to the composed versions of these basic properties...

Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...

The representation theorem Cor F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F -transitive fuzzy relations on a set X, F being an Archimedean t-norm, is dense in the set of Ztransitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.

The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...

The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...