In this paper,  we introduce  the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures.It is proved that  the category  {bf MYCSA2}  can be embedded in  the category  {bf  MYIS}  as a reflective subcategory, where  {bf MYCSA2} and   {bf  MYIS} denote  the category of $M$-fuzzifying convex structures of...

L. Lovász has shown in [9] that Sperner’s combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. We prove that Ky Fan’s theorem admits an oriented matroid generalization of similar nature (Theorem 3.1). Classical Ky Fan’s theorem is obtained as a corollary if the underlying oriented matroid is chosen to be the alternating ...

Let M to be a matroid defined on a finite set E and L ⊂ E. L is locked in M if M |L and M∗|(E\L) are 2-connected, and min{r(L), r∗(E\L)} ≥ 2. In this paper, we prove that the nontrivial facets of the bases polytope of M are described by the locked subsets. We deduce that finding the maximum–weight basis ofM is a polynomial time problem for matroids with a polynomial number of locked subsets. Th...

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

By fuzzifying the number of occurrences of an element of a multiset, we obtain a new fuzzy structure; similarly, by fuzzifying the number of occurrences of an element of a hybrid set, we obtain another new fuzzy structure. The aim of the present work is twofold: to provide a concise definition of these new fuzzy structures and their properties and to apply them in natural computing. More specif...

in this paper,  we introduce  the notion of $m$-fuzzifying interval spaces, and discuss the relationship between $m$-fuzzifying interval spaces and $m$-fuzzifying convex structures.it is proved that  the category  {bf mycsa2}  can be embedded in  the category  {bf  myis}  as a reflective subcategory, where  {bf mycsa2} and   {bf  myis} denote  the category of $m$-fuzzifying convex structures of...

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...