HOME

TheInfoList



Click Here for Items Related To - Fuzzy Differential Inclusion
OR:
Fuzzy Differential Inclusion on:   [Wikipedia]   [Google]   [Amazon]

Fuzzy differential inclusion is tha culmination of
Fuzzy concept A fuzzy concept is a kind of concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise mea ...
and
Differential inclusion In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form :\frac(t)\in F(t,x(t)), where ''F'' is a multivalued map, i.e. ''F''(''t'', ''x'') is a ''set'' rather than a single point ...
introduced by
Lotfi A. Zadeh Lotfi Aliasker Zadeh (; az, Lütfi Rəhim oğlu Ələsgərzadə; fa, لطفی علی‌عسکرزاده; 4 February 1921 – 6 September 2017) was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher, an ...
which became popular. x' (t) \epsilon f(t , x(t)\alpha , x(0) \epsilon _0\alpha f(t,x(t)] is a fuzzy valued continuous function on euclidian space which is collection of all normal, upper semi-continuous,
Convex set In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex r ...
,
Compact space In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i ...
, supported fuzzy subsets of R^n .


Second order differential

The second order differential is x''(t) \epsilon x \alpha where k \epsilon \alpha K is trapezoidal fuzzy number (-1,-1/2,0,1/2) x_0 is a trianglular fuzzy number (-1,0,1) .


Applications

Fuzzy differential inclusion (FDI) has applications in *
Cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson m ...
*
Artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
,
Neural network A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...
, *
Medical imaging Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to rev ...
*
Robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrat ...
*
Atmospheric dispersion modeling Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that include algorithms to solve the mathematical equations that govern the pollutant ...
*
Weather forecasting Weather forecasting is the application of science and technology forecasting, to predict the conditions of the Earth's atmosphere, atmosphere for a given location and time. People have attempted to predict the weather informally for millennia a ...
*
Cyclone In meteorology, a cyclone () is a large air mass that rotates around a strong center of low atmospheric pressure, counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere as viewed from above (opposite to an anti ...
*
Population biology The term population biology has been used with different meanings. In 1971 Edward O. Wilson ''et al''. used the term in the sense of applying mathematical models to population genetics, community ecology, and population dynamics. Alan Hastings us ...
*
Stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
,
Probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...


References

{{Reflist Dynamical systems Variational analysis Fuzzy logic