Neural Networks, Fuzzy Models and Dynamic Logic

Perlovsky, Leonid

doi:10.1007/978-3-540-37522-7_17

Cited by 24 publications

(21 citation statements)

References 25 publications

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“…Thus, to get a more adequate description of the expert opinions and rules, it is necessary to take these changes into account, i.e., to take into account that the expert's degree of confidence in each statement A changes with time. In other words, to describe the expert's opinion about a state-ment A, instead of a single value a ∈ [0, 1], we need to use a function a(t) that describes how this degree changes with time t. Such dynamic fuzzy logic was proposed in [5,31,32,33].…”

Section: Fourth Promising Future Direction: Dynamic Fuzzy Setsmentioning

confidence: 99%

50 Years of fuzzy: from discrete to continuous to – Where?

Kreinovich

Nguyen

Kosheleva

et al. 2015

IFS

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Abstract. While many objects and processes in the real world are discrete, from the computational viewpoint, discrete objects and processes are much more difficult to handle than continuous ones. As a result, a continuous approximation is often a useful way to describe discrete objects and processes. We show that the need for such an approximation explains many features of fuzzy techniques, and we speculate on to which promising future directions of fuzzy research this need can lead us.Keywords: fuzzy techniques, discrete, continuous, interval-valued fuzzy, complex-valued fuzzy, computing with words, dynamical fuzzy logic, chemical kinetics, non-additive measures, symmetry Fuzzy Techniques as an Easier-to-Compute Continuous Approximation for Difficult-to-Compute Discrete Objects and ProcessesDiscrete objects and processes are ubiquitous. Many real-life objects are processes are discrete. On the macro level, there is an abrupt transition in space between physical bodies, there is an abrupt transition in time when, e.g., a glass breaks or a person changes his/her opinion. On the micro level, matter consists of discrete atoms and molecules, with abrupt transitions between different states of an atom.Continuous problems are easier to compute. While discrete objects and processes are ubiquitous in nature, from the computational viewpoint, it is often much easier to handle continuous problems. This may sound * Corresponding author. E-mail: vladik@utep.edu.counter-intuitive, since intuitively, if we restrict our search or optimization to only integer values, the problem would become easier -but it is not. For example, in the continuous case, it is relatively easy to find a solution x 1 , . . . , x n to a system of linearmany known feasible algorithms for that), the problem becomes NP-hard (computationally intractable) if we only allow discrete values of x i ; see, e.g., [9,28].Similarly, in the continuous case, it is relatively easy to find the values x 1 , . . . , x n that minimize a given quadratic function f (x 1 , . . . , x n ): it is sufficient to solve the corresponding system of linear equations ∂f ∂x i = 0. However, optimization of quadratic functions for discrete inputs, e.g., for x i ∈ {0, 1}, is NPhard [9,28]. Continuous approximations of discrete objects and processes are ubiquitous in physics. Because dealing with discrete objects and processes is often computationally complicated, physicists often approximate discrete objects with continuous ones. For example, it is not feasible to describe the changes in atmosphere by tracing all 10 23 molecules, but approximate equations that describe the atmosphere as a continuous field leads to many useful weather predictions. Similar, a solid body -in effect, a collection of atoms -is well described by a continuous density field, and an atomic nucleus -a collection of protons and neutrons -is well described by a continuous (liquid) model; see, e.g., [8].Such approximations are also useful in analyzing social phenomena. For example, in analyzing how epidemics spread, ...

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Section: Fourth Promising Future Direction: Dynamic Fuzzy Setsmentioning

confidence: 99%

50 Years of fuzzy: from discrete to continuous to – Where?

Kreinovich

Nguyen

Kosheleva

et al. 2015

IFS

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show abstract

“…Thus, to get a more adequate description of the expert opinions and rules, it is necessary to take these changes into account, i.e., to take into account that the expert's degree of confidence in each statement A changes with time. In other words, to describe the expert's opinion about a statement A, instead of a single value a ∈ [0, 1], we need to use a function a(t) that describes how this degree changes with time t. Such dynamic fuzzy logic was proposed in [2,6,7,8].…”

Section: Dynamic Fuzzy Logicmentioning

confidence: 99%

Dynamic fuzzy logic leads to more adequate 'and' and 'or' operations

Kreinovich

2014

IJKESDP

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In the traditional (static) fuzzy logic approach, we select an "and"-operation (tnorm) and an "or"-operation (t-conorm). The result of applying these selected operations may be somewhat different from the actual expert's degrees of belief in the corresponding logical combinations A & B and A ∨ B of the original statements -since these degrees depend not only on the expert's degrees of belief in statements A and B, but also in the extent to which the statements A and B are dependent. We show that dynamic fuzzy logic enables us to automatically take this dependence into accountand thus, leads to more adequate "and"-and "or"-operations.

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“…There are a few articles about dynamic fuzzy logic [2,3,4,5] but this direction is still not very well developed, and this is where a lot of progress still has to be made.…”

Section: Future Of Fuzzymentioning

confidence: 99%

In the Beginning Was the Word, and the Word Was Fuzzy

Kreinovich

2013

On Fuzziness

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Neural Networks, Fuzzy Models and Dynamic Logic

Cited by 24 publications

References 25 publications

50 Years of fuzzy: from discrete to continuous to – Where?

50 Years of fuzzy: from discrete to continuous to – Where?

Dynamic fuzzy logic leads to more adequate 'and' and 'or' operations

In the Beginning Was the Word, and the Word Was Fuzzy

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