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 me ...
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.
,
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 ...
,
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
.
Second order differential
The second order differential is
where
K is trapezoidal fuzzy number (-1,-1/2,0,1/2)
is a trianglular fuzzy number (-1,0,1) .
Applications
Fuzzy differential inclusion (FDI) has applications in
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Cybernetics
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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 r ...
,
Neural network
A neural network is a network or neural circuit, 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 ...
,
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Medical imaging
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Robotics
Robotics is an interdisciplinarity, 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 human ...
*
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 to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th centu ...
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Cyclone
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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 ...
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Stochastic process ,
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