Some New Logarithmic Aggregation Operators and their Application to Group Decision Making Problem Based on t-Norm and t-Conorm

In this paper, a logarithmic operational law for intuitionistic fuzzy numbers is defined, in which the based1 is a real number such that1 ∈(0,1) with condition1 ≠ 1. Some properties of logarithmic operational laws have been studied and based on these, several Einstein averaging and Einstein geometric operators namely, logarithmic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted averaging (LIFEOWA) operator, logarithmic intuitionistic fuzzy Einstein hybrid averaging (LIFEHA) operator, logarithmic intuitionistic fuzzy Einstein weighted geometric (LIFEWG) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted geometric (LIFEOWG) operator, and logarithmic intuitionistic fuzzy Einstein hybrid geometric (LIFEHG) operator have been introduced, which can overcome the weaknesses of algebraic operators. Furthermore, based on the proposed operators a multi-attribute group decision-making problem is established under logarithmic operational laws. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.

Generalized derivation, SVEP, finite ascent, range closure

Let X be an infinite complex Banach space and consider two bounded linear operators A,B ? L(X). Let LA ? L(L(X)) and RB ? L(L(X)) be the left and the right multiplication operators, respectively. The generalized derivation ?A,B ? L(L(X)) is defined by ?A,B(X) = (LA-RB)(X) = AX-XB. In this paper we give some sufficient conditions for ?A,B to satisfy SVEP, and we prove that ?A,B-?I has finite ascent for all complex ?, for general choices of the operators A and B, without using the range kernel orthogonality. This information is applied to prove some necessary and sufficient conditions for the range of ?A,B-?I to be closed. In [18, Propostion 2.9] Duggal et al. proved that, if asc(?A,B-?)? 1, for all complex ?, and if either (i) A* and B have SVEP or (ii)?* A,B has SVEP, then ?A,B-? has closed range for all complex ? if and only if A and B are algebraic operators, we prove using the spectral theory that, if asc(?A,B-?) ? 1, for all complex ?, then ?A,B-? has closed range, for all complex ? if and only if A and B are algebraic operators, without the additional conditions (i) or (ii).

Some properties of (m,C)-isometric operators

In this paper, we study if T is an (m,C)-isometric operator and CT+C commutes with T, then T+ is an (m,C)-isometric operator. We also give local spectral properties and spectral relations of (m;C)-isometric operators, such as property (?), decomposability, the single-valued extension property and Dunford?s boundedness. We also investigate perturbation of (m,C)-isometric operators by nilpotent operators and by algebraic operators and give some properties.

Numerical modeling of a two-point correlator for the Lagrange solutions of some evolution equations

Статья посвящена двухточечным моментам решений, возникающих в простых лагранжевых моделях для уравнения индукции в случае конечного корреляционного времени случайной среды. Рассматривается вопрос о связи коммутационных свойств соответствующих алгебраических операторов с минимальным объемом выборки независимых случайных реализаций, который необходим в численном эксперименте для моделирования двуточечного коррелятора решения. Показано, что, как и для одноточечных моментов, численное исследование двуточечного коррелятора в случае коммутирующих операторов (случайные числа) требует существенно меньших объемов выборки, чем в случае, когда они не коммутируют (случайные матрицы). This paper is devoted to the two-point moments of the solutions arising in simple Lagrange models for the induction equations in the case of finite correlation time of a random medium. We consider the question on the connection between the commutative properties of the corresponding algebraic operators and the minimal sample size of independent random realizations necessary in numerical experiments for modeling the two-point correlator of the solution. It is shown that, as for the one-point moments, the numerical study of the two-point correlator in the case of commutating operators (random numbers) requires a much smaller sample size than in the case when they do not commute (random matrices).

Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.