Midpoints for fuzzy sets and their application in medicine.
ABSTRACT Using Kosko's hypercube, we identify a fuzzy set with a point in a unit hypercube. A non-fuzzy or crisp subset of a set is a vertex of the hypercube. We introduce some new ideas: the definition of the fuzzy segment joining two given fuzzy subsets of a set, the set of midpoints between those two fuzzy subsets, and the set of equidistant points from given points. We present some basic properties and relations between these concepts and provide a complete description of fuzzy segments and midpoints. In the majority of cases, there is no unique midpoint; one has an infinite set of possibilities to choose from. This situation is totally different from classical Euclidean geometry where, for two given points, there is a unique midpoint. We use the obtained results to study two sets of medical data and present two applications in medicine: the fuzzy degree of two concurrent food and drug addictions, and a fuzzy representation of concomitant causal mechanisms of stroke.
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ABSTRACT: In 2003, Nieto and Torres introduced the notions of segment and midpoint between fuzzy sets with the aim of giving applications to medicine [J.J. Nieto, A. Torres, Midpoints for fuzzy sets and their application in medicine, Artif. Intell. Med. 27 (2003) 81-101]. Since then the interest in the study of such concepts have grown significantly because of their applicability to model real problems where the solution can be associated with a range of “middle ways” between two given positions. Recently, J. Casasnovas and F. Roselló have generalized the previous work of Nieto and Torres, giving an explicit description of segments and midpoints between fuzzy sets for, among others, the well-known weighted maximum distance [J. Casasnovas, F. Roselló, Averaging fuzzy biopolymers, Fuzzy Sets Syst. 152 (2005) 139-158].Mathematical and Computer Modelling 05/2009; 49(9-10-49):1852-1868. DOI:10.1016/j.mcm.2008.08.003 · 2.02 Impact Factor
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ABSTRACT: In this paper we present a study of classification of the 20 amino acids via a fuzzy clustering technique. In order to calculate distances among the various elements we employ two different distance functions: the Minkowski distance function and the NTV metric. In the clustering procedure we take into account several physical properties of the amino acids. We examine the effect of the number and nature of properties taken into account to the clustering procedure as a function of the degree of similarity and the distance function used. It turns out that one should use the properties that determine in the more important way the behavior of the amino acids and that the use of the appropriate metric can help in defining the separation into groups.Journal of Theoretical Biology 12/2008; 257(1):17-26. DOI:10.1016/j.jtbi.2008.11.003 · 2.30 Impact Factor
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ABSTRACT: Following the mathematical formalism introduced by M. Schellekens [Elec-tronic Notes in Theoret. Comput. Sci. 1 (1995), 211-232] in order to give a common foundation for Denotational Semantics and Complexity Analysis, we obtain an application of the theory of midpoints for asymmetric distances defined between fuzzy sets to the complexity analysis of algorithms and pro-grams. In particular we show that the average running time for the algorithm known as Largetwo is exactly a midpoint between the best and the worst case running time of computing.01/2008; 15:251-261.