Approximation of fuzzy numbers by convolution method

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible non-differentiable points are the two endpoints of 1-cut. The constructing of smoothers is a key step in the construction process of approximations. It further points out that, if appropriately choose the smoothers, then one can use the convolution method to provide approximations which are differentiable, Lipschitz and preserve the core at the same time.Comment: Submitted to Fuzzy Sets and System at Sep 18 201

A fuzzy AHP multi-criteria decision-making approach applied to combined cooling, heating and power production systems

Most of the real-world multi-criteria decision-making (MCDM) problems contain a mixture of quantitative and qualitative criteria; therefore quantitative MCDM methods are inadequate for handling this type of decision problems. In this paper, a MCDM method based on the Fuzzy Sets Theory and on the Analytic Hierarchy Process (AHP) is proposed. This method incorporates a number of perspectives on how to approach the fuzzy MCDM problem, as follows: (1) combining quantitative and qualitative criteria (2) expressing criteria pair-wise comparison in linguistic terms and performance of the alternative on each criterion in linguistic terms or exact values when criterion is qualitative or quantitative, respectively, (3) converting all the assessments into trapezoidal fuzzy numbers, (4) using the difference minimization method to calculate the local weight of criteria, employing the algebraic operations of fuzzy numbers based on the concept of α-cuts, (4) calculating the global weight of criteria and the global performance of each alternative using geometric mean and the weighted sum, respectively, (5) using the centroid method to rank the alternatives. Finally, an illustrative example on evaluation of several combined cooling, heat and power production systems is used to demonstrate the effectiveness of the proposed methodology