Article

# Midpoints for fuzzy sets and their application in medicine

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain.
(Impact Factor: 2.02). 02/2003; 27(1):81-101. DOI: 10.1016/S0933-3657(02)00080-5
Source: PubMed

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.

2 Followers
·
• Source
• "FDEs models have a wide range of applications in many branches of engineering and in the field of medicine. These models are used in various applications including population models [1] [2] [3] [4], quantum optics gravity [5], control design [6] medicine [7] [8] [9] [10] and other applications [11]. In recent years semi analytical methods such as Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been used to solve "
##### Dataset: JAMEEL722015AJOMCOR1883

• Source
• "FDEs models have a wide range of applications in many branches of engineering and in the field of medicine. These models are used in various applications including population models [1] [2] [3] [4], quantum optics gravity [5], control design [6] medicine [7] [8] [9] [10] and other applications [11]. In recent years semi analytical methods such as Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been used to solve fuzzy problems involving ordinary differential equations. "
##### Article: SOLUTION OF FUZZY HEAT EQUATIONS BY HOMOTOPY PERTURBATION METHOD (HPM)
[Hide abstract]
ABSTRACT: n this paper, we develop and analyze the use of the Homotopy Perturbation Method (HPM) to find the approximate analytical solution for an initial value problem involving the fuzzy parabolic equation. HPM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The HPM will be studied for fuzzy initial value problems involving partial parabolic differential equations. Also HPM will be constructed and formulated to obtain an approximate analytical solution of fuzzy heat equation by using the properties of fuzzy set theory. The convergence theorem of this method in fuzzy case is presented and proved. Numerical examples involving fuzzy heat equation was solved to illustrate the capability of HPM in this regard. The numerical results that obtained by HPM were compared with the exact solution in the form of tables and figures.
• Source
• "FDEs models have a wide range of applications in many branches of engineering and in the field of medicine. These models are used in various applications including population models [1] [2] [3] [4], quantum optics gravity [5], control design [6] medicine [7] [8] [9] [10] and other applications [11]. In recent years semi analytical methods such as Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been used to solve "
##### Article: SOLUTION OF FUZZY HEAT EQUATIONS BY HOMOTOPY PERTURBATION METHOD (HPM)
[Hide abstract]
ABSTRACT: In this paper, we develop and analyze the use of the Homotopy Perturbation Method (HPM) to find the approximate analytical solution for an initial value problem involving the fuzzy parabolic equation. HPM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The HPM will be studied for fuzzy initial value problems involving partial parabolic differential equations. Also HPM will be constructed and formulated to obtain an approximate analytical solution of fuzzy heat equation by using the properties of fuzzy set theory. The convergence theorem of this method in fuzzy case is presented and proved. Numerical examples involving fuzzy heat equation was solved to illustrate the capability of HPM in this regard. The numerical results that obtained by HPM were compared with the exact solution in the form of tables and figures.