in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

This paper considers fuzzy subbundles of a vector bundle. We define the operations sum, product, tensor product, Hom, and intersection of fuzzy subbundles and in each case, we characterize the corresponding flag of vector subbundles. We then propose two alternative definitions of integrability on fuzzy subbundles of a given type and discuss their naturality, merits, and shortcomings. We do thes...

The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This admits various modifications, which lead to 48 different rules, known the variations. They all result in that are measure-theoretically isomorphic by Halmos–von Neumann theorem. cut and project sets characteristic windows two-dimensional Euclidean internal space. Here, we an...

The purpose of this study is to construct the concept direct product bitonic algebras, and investigate some respective features. Also, commutative homomorphism are studied. Then notion algebras expanded finite family their qualifications practised.

We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: arity can differ from that constituents, and elements different multipliers be \textquotedblleft entangled\textquotedblright\ such is no longer componentwise. The main property we want preserve associativity, gained by using associativity quiver tech...

In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...