The induced 2-tuple linguistic generalized OWA operator and its application in linguistic decision making

[spa] Se presenta el operador de media ponderada ordenada generalizada lingüística de 2 tuplas inducida (2-TILGOWA). Es un nuevo operador de agregación que extiende los anteriores modelos a través de utilizar medias generalizadas, variables de ordenación inducidas e información lingüística representada mediante el modelo de las 2 tuplas lingüísticas. Su principal ventaja se encuentra en la posibilidad de incluir a un gran número de operadores de agregación lingüísticos como casos particulares. Por eso, el análisis puede ser visto desde diferentes perspectivas de forma que se obtiene una visión más completa del problema considerado y seleccionar la alternativa que parece estar en mayor concordancia con nuestros intereses o creencias. A continuación se desarrolla una generalización mayor a través de utilizar medias cuasi-aritméticas, obteniéndose el operador Quasi-2-TILOWA. El trabajo finaliza analizando la aplicabilidad del nuevo modelo en un problema de toma de decisiones sobre gestión de la producción.

The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.

The induced 2-tuple linguistic generalized OWA operator and its application in linguistic decision making

[spa] Se presenta el operador de media ponderada ordenada generalizada lingüística de 2 tuplas inducida (2-TILGOWA). Es un nuevo operador de agregación que extiende los anteriores modelos a través de utilizar medias generalizadas, variables de ordenación inducidas e información lingüística representada mediante el modelo de las 2 tuplas lingüísticas. Su principal ventaja se encuentra en la posibilidad de incluir a un gran número de operadores de agregación lingüísticos como casos particulares. Por eso, el análisis puede ser visto desde diferentes perspectivas de forma que se obtiene una visión más completa del problema considerado y seleccionar la alternativa que parece estar en mayor concordancia con nuestros intereses o creencias. A continuación se desarrolla una generalización mayor a través de utilizar medias cuasi-aritméticas, obteniéndose el operador Quasi-2-TILOWA. El trabajo finaliza analizando la aplicabilidad del nuevo modelo en un problema de toma de decisiones sobre gestión de la producción.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator by using the main characteristics of two well known aggregation operators: the generalized OWA and the induced OWA operator. Then, this operator uses generalized means and order inducing variables in the reordering process. With this formulation, we get a wide range of aggregation operators that include all the particular cases of the IOWA and the GOWA operator, and a lot of other cases such as the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator by using quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we also develop a numerical example of the new approach in a financial decision making problem.