Interferon-beta is one of the most widely prescribed disease-modifying therapies for multiple sclerosis patients. However, this treatment only partially effective, and a significant proportion patients do not respond to drug. This paper proposes an alternative fuzzy logic system, based on opinion neurology expert, classify relapsing–remitting as high, medium, or low responders interferon-beta. ...

This paper is a first approach to the study of beta coefficients using fuzzy regression. We intend to improve the calculation of the sector and subsector betas of the Spanish Stock Market using fuzzy regression in an attempt to incorporate all future inaccuracies and the subjectivity associated with decision making. Our objective is to use all the information provided by the market to determine...

In this paper, we defined the interval form of \(\alpha, \beta\) level set for triangular q-rung orthopair fuzzy (qROPF) number. To obtain a differentiability notion qROPF valued functions, Hukuhara (H-differentiability) and level-wise H-differentiability is defined. Using KKT optimality condition optimization problem with objective function are formulated.

Amalgamated free products of von Neumann algebras were first used by S. Popa ([26]) to construct an irreducible inclusion of (non-AFD) type II1 factors with an arbitrary (admissible) Jones index. Further investigation in this direction was made by K. Dykema ([10]) and F. Rădulescu ([27, 29]) based on Voiculescu’s powerful machine ([40, 41, 44]), and F. Boca ([4]) discussed the Haagerup approxim...

We define a notion of depth for an inclusion of multimatrix algebras B ⊆ A based on a comparison of powers of the inductionrestriction table M (and its transpose matrix). The depth of the semisimple subalgebra B in the semisimple algebra A is the least positive integer n ≥ 2 for which M ≤ qM for some q ∈ Z+. We prove that a depth two subalgebra is a normal subalgebra, and conversely. As a corol...

‎Let $mathcal{A}_p$ be the mod $p$ Steenrod algebra‎, ‎where $p$ is an odd prime‎, ‎and let $mathcal{A}$ be the‎ subalgebra $mathcal{A}$ of $mathcal{A}_p$ generated by the Steenrod $p$th powers‎. ‎We generalize the $X$-basis in $mathcal{A}$ to $mathcal{A}_p$‎.

We study the subalgebra of the lattice vertex operator algebra V√ 2A2 consisting of the fixed points of an automorphism which is induced from an order 3 isometry of the root lattice A2. We classify the simple modules for the subalgebra. The rationality and the C2-cofiniteness are also established.