Fuzzy differential inclusion is the extension of

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 ...

fuzzy sets Fuzzy or Fuzzies may refer to: Music * Fuzzy (band), a 1990s Boston indie pop band * Fuzzy (composer), Danish composer Jens Vilhelm Pedersen (born 1939) * Fuzzy (album), ''Fuzzy'' (album), 1993 debut album of American rock band Grant Lee Buffalo ...

introduced by

Lotfi A. Zadeh Lotfi Aliasger Zadeh (; ; ; 4 February 1921 – 6 September 2017) was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher, and professor of computer science at the University of California, Berkeley. Zad ...

\alpha

with

\alpha

Suppose

f(t,x(t))

is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal,

upper semi-continuous In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (respectively, lower) semicontinuous at a point x_0 if, r ...

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

, compactly supported fuzzy subsets of

\mathbb^n

Second order differential

The second order differential is

\alpha

where

\alpha

K

is trapezoidal fuzzy number

(-1,-1/2,0,1/2)

, and

x_0

is a trianglular fuzzy number (-1,0,1).

Applications

Fuzzy differential inclusion (FDI) has applications in *

Cybernetics Cybernetics is the transdisciplinary study of circular causal processes such as feedback and recursion, where the effects of a system's actions (its outputs) return as inputs to that system, influencing subsequent action. It is concerned with ...

Artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

Neural network A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perfor ...

, *

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 revea ...

Robotics Robotics is the interdisciplinary study and practice of the design, construction, operation, and use of robots. Within mechanical engineering, robotics is the design and construction of the physical structures of robots, while in computer s ...

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 polluta ...

Weather forecasting Weather forecasting or weather prediction 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 info ...

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 ant ...

Pattern recognition Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their p ...

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 Hasting ...

References

{{Reflist Dynamical systems Variational analysis Fuzzy logic