Solving Fractional Geometric Programming Problems via Relaxation approach

In the optimization literature , Geometric Programming problems play a very important role rather than primary in engineering designs. The geometric programming problem is a nonconvex optimization problem that has received the attention of many researchers in the recent decades. Our main focus in this issue is to solve a Fractional Geometric Programming(FGP) problem via linearization technique[1]. Linearizing separately both the numerator and denominator of the fractional geometric programming problem in the objective function, causes the problem to be reduced to a Fractional Linear Programming problem (FLPP) and then the transformed linearized FGP is solved by Charnes and Cooper method which in fact gives a lower bound solution to the problem. To illustrate the accuracy of the final solution in this approach, we will compar our result with the LINGO software solution of the initial FGP problem and we shall see a close solution to the globally optimum. A numerical example is given in the end to illustrate the methodology and efficiency of the proposed approach

Inference for the Rayleigh Distribution Based on Progressive Type-II Fuzzy Censored Data

Classical statistical analysis of the Rayleigh distribution deals with precise information. However, in real world situations, experimental performance results cannot always be recorded or measured precisely, but each observable event may only be identified with a fuzzy subset of the sample space. Therefore, the conventional procedures used for estimating the Rayleigh distribution parameter will need to be adapted to the new situation. This article discusses different estimation methods for the parameters of the Rayleigh distribution on the basis of a progressively type-II censoring scheme when the available observations are described by means of fuzzy information. They include the maximum likelihood estimation, highest posterior density estimation and method of moments. The estimation procedures are discussed in detail and compared via Monte Carlo simulations in terms of their average biases and mean squared errors. Finally, one real data set is analyzed for illustrative purposes

Inference for the weibull distribution based on fuzzy data

Los procedimientos clásicos de estimación para los parámetros de la distribuciónWeibull se encuentran basados en datos precisos. Se asume usualmenteque los datos observados son números reales precisos. Sin embargo,algunos datos recolectados podrían ser imprecisos y ser representados en laforma de números difusos. Por lo tanto, es necesario generalizar los métodosde estimación estadísticos clásicos de números reales a números difusos.En este artículo, diferentes métodos de estimación son discutidos para los parámetros de la distribución Weibull cuando los datos disponibles estánen la forma de números difusos. Estos incluyen la estimación por máximaverosimilitud, la estimación Bayesiana y el método de momentos. Los procedimientosde estimación se discuten en detalle y se comparan vía simulacionesde Monte Carlo en términos de sesgos promedios y errores cuadráticosmedios

PORTFOLIO OF MUTUAL FUNDS USING STOCHASTIC MODELS BASED ON CREDIBILITY THEORY AND THEIR’S PERFORMANCE EVALUATING

Credibility measure theory was introduced by Liu and Liu [1]; Then X. Li, Z. Qin and D. Ralescu [2]. On using this theory are converted mean-variance model to credibility mean-variance. Mutual funds are the most important investment mechanism in financial market. In this paper, we use rate of return of 46 mutual funds of TSE. At first, we analyze data and then implement credibility mean-variance in MATLAB. We also survey Performance of case study sample with market Performance

A Full-Newton Step Interior Point Method for Fractional Programming Problem Involving Second Order Cone Constraint

Some efficient interior-point methods (IPMs) are based on using a self-concordant barrier function related to the feasibility set of the underlying problem.Here, we use IPMs for solving fractional programming problems involving second order cone constraints. We propose a logarithmic barrier function to show the self concordant property and present an algorithm to compute $\varepsilon-$solution of a fractional programming problem. Finally, we provide a numerical example to illustrate the approach

Inferencia para la distribución Weibull basada en datos difusos

Classical estimation procedures for the parameters of Weibull distribution are based on precise data. It is usually assumed that observed data are precise real numbers. However, some collected data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. In this paper, different methods of estimation are discussed for the parameters of Weibull distribution when the available data are in the form of fuzzy numbers. They include the maximum likelihood  estimation, Bayesian estimation and method of moments. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their average biases and mean squared errors. Finally, a real data set taken from a light emitting diodes manufacturing process is investigated to illustrate the applicability of the proposed methods.Los procedimientos clásicos de estimación para los parámetros de la distribución Weibull se encuentran basados en datos precisos. Se asume usualmente que los datos observados son números reales precisos. Sin embargo, algunos datos recolectados podrían ser imprecisos y ser representados en la forma de números difusos. Por lo tanto, es necesario generalizar los métodos de estimación estadísticos clásicos de números reales a números difusos. En este artículo, diferentes métodos de estimación son discutidos para los parámetros de la distribución Weibull cuando los datos disponibles están en la forma de números difusos. Estos incluyen la estimación por máxima verosimilitud, la estimación Bayesiana y el método de momentos. Los procedimientos de estimación se discuten en detalle y se comparan vía simulaciones de Monte Carlo en términos de sesgos promedios y errores cuadráticos medios

Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints

In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and non-parametric forms of the interval valued functions along with their convexity properties. Two approaches are developed to obtain efficient and properly efficient solutions. Furthermore, the efficient solutions or Pareto optimal solutions of fractional and non-fractional programming problems over R + n ⋃ { 0 } are also discussed. The main idea of the present article is to introduce a new concept for efficiency, called efficient space, caused by the lower and upper bounds of the respective intervals of the objective function which are shown in different figures. Finally, some numerical examples are worked through to illustrate the methodology and affirm the validity of the obtained results