In this research article, a new connection between serial fuzzy relations and an extended version of rough sets in algebraic structure quantale is established. The notion consists successor class overlap the element quantale. Thus approximation space based on via overlaps quantales, are introduced. main purpose study to provide basic structures fuzzy-relations. way, acquires certain appealing p...

Any totally positive $(k+m)\times n$ matrix induces a map $\pi_+$ from the Grassmannian ${\rm Gr}_+(k,n)$ to Gr}(k,k+m)$, whose image is amplituhedron $\mathcal{A}_{n,k,m}$ and endowed with top-degree form called canonical ${\bf\Omega}(\mathcal{A}_{n,k,m})$. This construction was introduced by Arkani-Hamed Trnka, where they showed that ${\bf\Omega}(\mathcal{A}_{n,k,4})$ encodes scattering ampli...

Let k be a field of characteristic not equal to two, B a smooth projective curve of genus g(B) over k, and F its function field. A quadric hypersurface fibration is a flat projective morphism π : X → B such that each geometric fiber is a quadric hypersurface with at worst an isolated singularity and the generic fiber is smooth. Sections σ : B → X of π are in bijection with rational points X(F )...

One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${bf Z}/n {bf Z},$ calculating their fuzzy grades.

It is observed that the axioms for partial metrics with values in quantales coincide with the axioms for Q-sets (M -valued sets, sets with fuzzy equality, quantale-valued sets) for commutative quantales. Ω-sets correspond to the case of partial ultrametrics.

If the standard concepts of partial-order relation and subset are fuzzified, taking valuation in a unital commutative quantale Q, corresponding concepts of joins and join-preserving mappings can be introduced. We present constructions of limits, colimits and Hom-objects in categories Q-Sup of Q-valued fuzzy joinsemilattices, showing the analogy to the ordinary category Sup of join-semilattices.

Let K be a function field over a field k of characteristic 0, and let j : U ⊂ PK be a Zariski open set of the projective line. We consider a flat connection (E,∇) on U . The de Rham cohomology groups H i DR(U/K,∇/K) carry a K/k connection, the Gauß-Manin connection, and taking the alternate tensor of the determinant connections ⊗(detH i DR(U/K,∇/K),Gauß−Manin) (−1)i , one defines the Gauß-Manin...

With the unit interval [0,1] as the truth value table, Chen and Wupresented the concept of  possibility computation over dcpos.Indeed, every possibility computation can be considered as a[0,1]-valued Scott open set on a dcpo. The aim of this paper is tostudy Chen-Wu's duality on quantale-valued setting. For clarity,with a commutative unital quantale $L$ as the truth value table, weintroduce a c...

Let P be a set of n points in R. In the projective clustering problem, given k, q and norm ρ ∈ [1,∞], we have to compute a set F of k q-dimensional flats such that ( ∑ p∈P d(p,F)) is minimized; here d(p,F) represents the (Euclidean) distance of p to the closest flat in F . We let f k (P, ρ) denote the minimal value and interpret f k (P,∞) to be maxr∈P d(r,F). When ρ = 1, 2 and ∞ and q = 0, the ...