##

**11 July 2017**

**08:00AM - 10:00AM**

##### Room: **Aragonese**

##### Chairs: **José Luis Verdegay and David Pelta**

## Engineering Applications of Fuzzy Sets-I

**Abstract - ** In this work we study optimization problems where both objective and constraints are given by fuzzy functions. In order to solve them, we first prove that such problems are equivalent to fuzzy optimization problems where the constraints are non-fuzzy (crisp) functions. Besides we prove a new and appropriate Karush-Kuhn-Tucker type necessary optimality condition based on the gH-differentiability and that has many computational advantages that we describe. The gH-derivative for fuzzy functions is a more general notion than Hukuhara and level-wise derivatives ones that are usually used in fuzzy optimization so far, in the sense that it can be applied to a wider number of fuzzy function classes than above concepts. With this new differentiability concept, we prove a KKT-type necessary optimality condition for fuzzy mathematical programming problems that is more operational and less restrictive that the few ones we can find in the literature so far.

**Abstract - ** This paper presents a general solution approach based on exploiting open georeferenced data by using a Geographic Information System. The suitability of this approach is assessed on a new practical multi-objective optimization problem arisen in the context of the location theory. It seeks to determine the locations of a known number of electric vehicle sharing stations in the city of San Francisco while considering fuzzy criteria. These new stations are the departure points of touristic routes aimed at visiting the most representative points of interest around the city. The computational experiments indicate that the solution approach can be easily used as an effective tool to support decision making processes in related problems.

**Abstract - ** The future of the smart society sets challenges for all types of existing telecommunication networks and links. For ensuring the optimal utilization of these networks precise performance predictions are necessary, especially in case of the symmetrical access networks with rather limited transmission capacity. It is also important to harness the already established infrastructure as long as it is technically possible, so that the use of the environmental resources would be minimal and the economical advantages would be maximal. In performance prediction of telecommunication links the high-dimensional input data, like the insertion loss spectrum, should be compessed. After reducing the dimension of the antecedent set, a fuzzy inference can be carried out for each of the lines. As the number of lines used for building the fuzzy sets is finite and the supports of the fuzzy set do not cover the whole space, a stabilized KH interpolation is used in the decision process. Wavelets constitute the basis of methods for compressing and analyzing data in many fields of science and technology. For the reduction of the input dimension, wavelets proved to be an effective tool. The applicability of various wavelet families with different sizes of filter coefficient sets are tested in the following considerations, with the result, that the wavelet type does not play an essential role as well as the length of the wavelets. Only the deepness of the wavelet transform influences essentially the goodness of the prediction: the remaining number of points should be 4 after the transformation.

**Abstract - ** This work considers a route-planning problem in the tourism sector, the Tourist Trip Design Problem which aims to design the routes that maximize the satisfaction of the visited points of interest. This paper proposes a model of a multi-day planning problem for sightseeing. In order to solve this optimization problem, a new Fuzzy Greedy Randomized Adaptive Search Procedure is developed to obtain high- quality solutions. Fuzzy approach is used to evaluate the point of interest to be included in the solution considering the ambiguity and imprecision of promising point of interest to visit and satisfactory solutions. The computational experiments indicate the fuzzy GRASP is able to report competitive solutions by using short computational times.

**Abstract - ** Quality control charts are one of the most important tools of statistical process control, used to analyze the behavior of different processes and to predict possible production failures. The use of a fuzzy approach in the design of control charts has allowed to improve the performance of traditional charts, as well as to be possible of a simple approach for the design of control charts for linguistic variables with multinomial distribution for both, the univariate case as for the multivariate case. In this paper we will show some of the main proposals of fuzzy control charts found in the literature.

**Abstract - ** Interference is usually viewed as an obstacle to communication in wireless networks. Therefore, we describe a way to find a doubly infinite nested lattice partition chain for the real dimension 2 in order to realize interference alignment onto these lattices and a procedure to find the minimum solution of the mean square error related to the corresponding channel quantization. Besides, we propose a new methodology based on the support function and Steiner points of fuzzy vectors to find the closest point of a coset in a lattice. Such a methodology is flexible enough to combine the fuzzy characterization with the geometric insights and it is able to maintain the inherent stochastic nature of the wireless communication networks.