New Arithmetic Triangular Fuzzy Number for Solving Fully Fuzzy Linear System using Inverse Matrix

This paper present a new concept arithmetic of triangular fuzzy number, namely by using a board area concept of triangular fuzzy number, so that we will get a form multiplication of fuzzy numbers in some cases. This new arithmetic concept will be applied for solve the fully fuzzy linear system using inverse matrix. Furthermore, to illustration will given numerical examples of solving fully fuzzy linear system using inverse matrix with a case of multiplication positive fuzzy number and negative fuzzy number

Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems

Bipolar crisp numbers refer to two different functions and information in a given system, namely positive and negative components. Likelihood and unlikelihood information can be simultaneously represented by bipolar crisp numbers rather than classical crisp numbers. However, since bipolar crisp numbers are inadequate in dealing with uncertainty problem, bipolar fuzzy numbers (BFN) are used instead. BFN in Sylvester matrix equations (SME) plays an essential role in the control system such as in electrical controller. An electrical controller of RLC circuit consisting of resistor (R), inductor (L), and capacitor (C), is used to control the amount of electric currents flowing across the electric circuits. Besides, complex numbers which consist of real and imaginary parts are used in solving RLC circuit, where real numbers denote resistance, while imaginary numbers denote inductance or capacitance. To the best of our knowledge, the integration of SME with either BFN or complex BFN is not yet explored. Therefore, this study aims to construct analytical approaches in solving bipolar fuzzy Sylvester matrix equation (FSME), complex bipolar FSME, bipolar fully fuzzy Sylvester matrix equation (FFSME), and complex bipolar fully fuzzy linear system (FFLS) in left-right (LR) bipolar triangular fuzzy numbers. In order to obtain the solutions, bipolar FSME, complex bipolar FSME, and bipolar FFSME are converted into the bipolar linear system by utilizing Kronecker product and Vecoperator. Next, an equivalent bipolar linear system (EBLS), equivalent complex bipolar linear system (ECBLS), associated bipolar linear system (ABLS), and associated complex bipolar linear system (ACBLS) are established. Then, the final solutions of the constructed methods are obtained using inverse method. Therefore, four analytical approaches have been constructed in solving bipolar FSME, complex bipolar FSME, bipolar FFSME, and complex bipolar FFLS in LR forms. Several examples are presented to illustrate the constructed methods. Moreover, the application of RLC circuits with complex bipolar FSME and complex bipolar FFLS are also carried out. In conclusion, the new findings of analytical approaches add to the fuzzy equations body of knowledge with significant applications in bipolar electrical controllers

Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics, fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Comment: 10 pages, 17 reference

Lattice Calculation of Glueball Matrix Elements

Matrix elements of the form $$ are calculated using the lattice QCD Monte Carlo method. Here, $|G>$ is a glueball state with quantum numbers $0^{++}$, $2^{++}$, $0^{-+}$ and $G$ is the gluon field strength operator. The matrix elements are obtained from the hybrid correlation functions of the fuzzy and plaquette operators performed on the $12^{4}$ and $14^{4}$ lattices at $\beta = 5.9$ and $5.96$ respectively. These matrix elements are compared with those from the QCD sum rules and the tensor meson dominance model. They are the non-perturbative matrix elements needed in the calculation of the partial widths of $J/\Psi$ radiative decays into glueballs.Comment: 12 pages, UK/92-0

Monopoles and Solitons in Fuzzy Physics

Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining these features in a precise way. We study these problems of discrete physics and matrix models and discuss mathematically coherent discretizations of monopoles and solitons using fuzzy physics and noncommutative geometry. A fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one Author corrected. To appear in Commun.Math.Phy

Fractional quantum Hall effect on the two-sphere: a matrix model proposal

We present a Chern-Simons matrix model describing the fractional quantum Hall effect on the two-sphere. We demonstrate the equivalence of our proposal to particular restrictions of the Calogero-Sutherland model, reproduce the quantum states and filling fraction and show the compatibility of our result with the Haldane spherical wavefunctions.Comment: 26 pages, LaTeX, no figures, references adde