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# Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value.

Computers & Mathematics with Applications (Impact Factor: 2.07). 01/2011; 61:1379-1401. DOI: 10.1016/j.camwa.2011.01.005

Source: DBLP

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**ABSTRACT:**The problem of the nearest approximation of fuzzy numbers by piecewise linear 1-knot fuzzy numbers is discussed. By using 1-knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study. They might be also perceived as a generalization of the trapezoidal approximations. Moreover, these approximations possess some desirable properties. Apart from theoretical considerations approximation algorithms that can be applied in practice are also given.Fuzzy Sets and Systems 02/2013; 233:26-51. · 1.75 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper firstly we extend to an arbitrary compact interval the definition of the nonlinear Bernstein operators of max-product kind, by proving that their order of uniform approximation is the same as in the particular case of the unit interval. Then, similarly to the particular case of the unit interval, we will prove that these operators preserve the quasi-concavity too. Since these properties will help us to generate in a simple way fuzzy numbers of the same support, it turns out that these results are very suitable in the approximation of fuzzy numbers. Moreover, these operators approximate the (non-degenerate) segment core with a good order of approximation. In addition, in the case when the fuzzy numbers are given in parametric form, the Bernstein max-product operator generates a sequence of fuzzy numbers whose widths, expected intervals, ambiguities and values, approximate with a convergent rate the width, the expected interval, the ambiguity and the value of the approximated fuzzy number. Finally, we obtain a quantitative approximation with respect to a well-known integral type metric for some subclasses of functions, leading to applications to the approximation of some subclasses of fuzzy numbers.Fuzzy Sets and Systems 01/2014; 257:41–66. · 1.75 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper presents a new possibilistic model for the portfolio selection problem. The uncertainty of future returns on a given portfolio is modeled using LR-fuzzy numbers. Some possibilistic moments are considered to measure the risk of and return on the investment. Since the joint possibility distribution of the returns on the assets is unknown, we consider the returns on a given portfolio as the historical dataset instead of considering the individual returns on the assets as the dataset. We introduce a coefficient of possibilistic skewness in order to incorporate a measurement of the asymmetry of the fuzzy return on a given portfolio. We solve the multi-objective optimization problems that are associated with the possibilistic mean-downside risk-skewness model by using an evolutionary procedure to generate efficient portfolios. The procedure provides different patterns of investment, whose portfolios meet the explicit restrictions imposed by the investor. Thus, from among the points in the efficient frontier, the investor may select a portfolio that optimizes an economically meaningful objective function. The performance of this approach is tested using a dataset of assets from the Spanish stock market.IEEE Transactions on Fuzzy Systems 06/2013; 21(3):585-595. · 5.48 Impact Factor

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