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Electrical Engineering Dictionary - part 75

fusible element(s) are designed to melt and
interrupt the circuit when current above a
threshold value flows in the circuit.

fuse coordination

the process of match-

ing the fuse or circuit breaker interruption ca-
pability to overload current and short-circuit
current and insuring that the protective device
closest to a fault opens first so as to minimize
the service interruption.

fuse cutout

a primary distribution voltage

level fuse that employs a replaceable fusible
link and provides a means of disconnect. The
interrupting rating of a fuse cutout can be
somewhat lower than that of a power fuse,
however.

fuse link

used in nonerasable programma-

ble memory devices. Each bit in the mem-
ory device is represented by a separate fuse
link. During programming, the link is either
“blown” or left intact to reflect the value of
the bit. See also

fusible link ROM

fuse reducer

an adapter that allows fuses

to be installed in fuseclips designed for larger
fuses.

fuse saving

the practice of tripping distri-

bution line reclosers or circuit breakers on
a fast trip to beat sectionalizing fuses that
are protecting laterals.

The following re-

close will restore all load. If the fault re-
mains following the fast trip(s), subsequent
slow trip(s) will allow the fuse to operate on
a permanent fault on the lateral. Fuse saving
decreases the customer outage rate but causes
more sags to customers in a fault situation.

fused disconnect

a disconnect switch that

also employs fuse(s) for the purpose of over-
current protection.

fusible link ROM

read-only memory us-

ing fuse links to represent binary data. See
also

fuse link

fusion

a nuclear reaction in which two

light nuclei are combined into a heavier nu-
cleus with a release of energy. Fusion power
reactors have been proposed but as yet never
successfully constructed.

Futurebus

a bus specification standard-

ized by the IEEE, originally defined for CPU-
memory data transfers.

fuzz stick

a short hot-stick.

fuzzification

a procedure of transform-

ing a crisp set or a real-valued number into a
fuzzy set.

fuzzifier

a fuzzy system that transforms

a crisp (nonfuzzy) input value in a fuzzy set.
The most used fuzzifier is the singleton fuzzi-
fier, which interprets a crisp point as a fuzzy
singleton. It is normally used in fuzzy control
systems. See also

fuzzy inference system

fuzzy singleton

fuzziness

the degree or extent of impreci-

sion that is naturally associated with a prop-
erty, process or concept.

fuzzy adaptive control

adaptive con-

trol involving fuzzy logic concepts or fuzzy
control involving adaptation. Examples of
such control are self-organizing fuzzy con-
trol, model reference fuzzy adaptive control,
and fuzzy self-tuning control.

fuzzy aggregation network

artificial neu-

ral network that can be trained to produce a
compact set of fuzzy rules with conjunctive
and disjunctive antecedents. An aggregation
operator is used in each node.

fuzzy algorithm

an ordered set of fuzzy

instructions which upon execution yield an
approximate solution to a specified problem.
Examples of fuzzy algorithms include fuzzy
c-mean clustering, fuzzy-rule-based classifi-
cation, etc.

fuzzy AND

See

triangular norm

2000 by CRC Press LLC

fuzzy approximation

an action or pro-

cess of using a fuzzy system to approximate
a nonlinear function or mapping.

fuzzy associative memory

a look-up ta-

ble constructed from a fuzzy IF-THEN rule
base and inference mechanism to define a re-
lationship between the input and output of a
fuzzy controller, or a fuzzy system. See also

fuzzy inference system

fuzzy automata

based on the concept of

fuzzy sets, a class of fuzzy automata is formu-
lated similar to Mealy’s formulation of finite
automata.

fuzzy basis functions

a set of fuzzy mem-

bership functions or their combinations in a
fuzzy system that form a basis of a function
space, normally for function approximation.

fuzzy behavioral algorithm

a relational

algorithm that is used for the specific purpose
of approximate description of the behavior of
a system.

fuzzy C

the C programming language in-

corporating fuzzy quantities and fuzzy logic
operations.

fuzzy c-means (FCM)

a fuzzy version

of the commonly used K-means clustering
algorithm. The main feature of FCM is that
a type of membership function is utilized in
computing a distance measure. Also called
fuzzy ISODATA.

fuzzy clustering

a method used to cluster

data into subsets based on a distance or simi-
larity measure that incorporates fuzzy mem-
bership functions.

fuzzy cognitive map (FCM)

nonlinear

dynamical systems whose state trajectories
are constrained to reside in the unit hypercube
[0, 1]

. The components of the state vector

of an FCM stand for fuzzy sets or events that
occur to some degree and may model events,
actions, goals, etc. The trajectory of an FCM

can be viewed as an inference process. For
example, if an FCM’s trajectory starting from
an initial condition x

(0) converges to an equi-

librium state A, then this can be interpreted
as the FCM providing an answer to a question
“What if x

(0) happens?” In this sense it can

be interpreted that the FCM stores the rule
“IF x

(0) THEN the equilibrium A.” FCMs

were introduced by B. Kosko.

fuzzy complement

the complement of a

fuzzy set

A is understood as NOT (A).

fuzzy concentration

the concentration of

a fuzzy set produces a reduction by squaring
the membership function of that fuzzy set.

fuzzy conditional statement

an IF-

THEN statement of which either the an-
tecedents or consequent(s) or both may be
labels of fuzzy sets. Also know as fuzzy rule,
linguistic fuzzy model, linguistic rules. See

fuzzy IF-THEN rule

fuzzy control

the application of fuzzy

logic and fuzzy inference rules utilizing
knowledge elicited from human experts in
generating control decisions for the control of
processes. More specifically, a means of ex-
pressing an operator’s knowledge of control-
ling a process with a set of fuzzy IF-THEN
rules and linguistic variables.

fuzzy control system stability

stability of

a fuzzy control system that normally includes
a plant to be controlled and a fuzzy controller.

fuzzy controller

devices for implement-

ing fuzzy control, normally including the fol-
lowing components: a fuzzifier to transform
a crisp real-valued number to a fuzzy set; a
fuzzy rule base to define IF-THEN control
rules; a fuzzy inference engine to combine
the IF-THEN rules; and a defuzzifier to trans-
form a fuzzy set to a crisp real-valued num-
ber.

fuzzy controller design

a process of

determining a fuzzy controller including a

2000 by CRC Press LLC

fuzzifier, a fuzzy rule base, a fuzzy inference
engine, and a defuzzifier.

fuzzy decision rule

a decision rule with

fuzzified antecedents.

fuzzy decision tree

a decision tree with

fuzzy decision functions.

fuzzy decision tree algorithm

an algo-

rithm to generate a fuzzy decision tree, such
as the branch-bound-backtrack algorithm.

fuzzy decisional algorithm

a fuzzy algo-

rithm that serves to provide an approximate
description of a strategy or decision rule.

fuzzy definitional algorithm

a finite set

of possible fuzzy instructions that define a
fuzzy set in terms of other fuzzy sets (and
possibly itself, i.e., recursively).

fuzzy digital topology

an extension of the

topological concepts of connectedness and
surroundness in a digital picture using fuzzy
subsets.

fuzzy dilation

an operator that increases

the degree of belief in each object of a fuzzy
set by taking the square root of the member-
ship function.

fuzzy dynamic model

model involving

fuzzy logic concepts and system dynamics.
A typical example is a hierarchical model
with a higher level of fuzzy inference rules
and a lower level of analytical linear dynamic
equations.

fuzzy dynamic system

system involving

fuzzy logic concepts and system dynamics.
A typical example is a fuzzy control system
with a dynamic plant and a fuzzy controller.

fuzzy entropy

the entropy of a fuzzy set

is a functional to measure the degree of fuzzi-
ness of a fuzzy set based on Shannon’s func-
tion. It has been applied to provide a quanti-

tative measure of ambiguity to the problems
of gray-tone image enhancement.

fuzzy estimation

an action or process

of deducing state variables from given input
and output measurements in a fuzzy dynamic
state space model.

fuzzy expert system

a rule-based sys-

tem for approximate reasoning in which rules
have fuzzy conditions and their triggering are
driven by fuzzy matching with fuzzy facts.
See also

fuzzy inference system

fuzzy filter

a filter involving fuzzy logic

concepts.

A typical example is a filter

constructed from a number of local filters
through fuzzy membership functions.

fuzzy gain scheduling

gain scheduling

involving fuzzy logic concepts. A typical
example is the use of a number of fuzzy IF-
THEN rules to adjust a controller gain.

fuzzy generational algorithm

a fuzzy al-

gorithm serves to generate rather than define
a fuzzy set. Possible applications of genera-
tional algorithms include generation of hand-
written characters and generation of speech.

fuzzy geometry

a way to describe an im-

age by fuzzy subsets.

fuzzy global control

a fuzzy control for

an overall plant or a control based on a fuzzy
global model that consists of a number of
local models smoothly connected through a
set of membership functions.

fuzzy global model

a fuzzy dynamic

model consisting of a number of local linear
models or simple nonlinear models smoothly
connected through a set of nonlinear mem-
bership functions.

fuzzy grammar

an attributed grammar

that uses fuzzy primitives as the syntactic
units of a language.

2000 by CRC Press LLC

fuzzy H-infinity control

H-infinity con-

trol involving fuzzy logic concepts or fuzzy
control to achieve an H-infinity controller
performance index.

fuzzy H-infinity filter

an H-infinity filter

involving fuzzy logic concepts or a fuzzy fil-
ter to achieve an H-infinity filter performance
index.

fuzzy hierarchical systems

fuzzy sys-

tems of hierarchical structures.

A typical

example is a two-level fuzzy system with
a higher level of fuzzy inference rules and
lower level of analytical linear models.

fuzzy identification

a process of deter-

mining a fuzzy system or a fuzzy model. A
typical example is identification of fuzzy dy-
namic models consisting of determination of
the number of fuzzy space partitions, deter-
mination of membership functions, and de-
termination of parameters of local dynamic
models.

fuzzy IF-THEN rule

rule of the form

x is A THEN y is B

where

A and B are linguistic values defined

by fuzzy sets on universe of discourse

X and

Y respectively (abbreviated as A −→ B).
The statement “

x is A” is called the an-

tecedent or premise, while “

y is B” is called

the consequence or conclusion. A fuzzy IF-
THEN rule can be defined as a binary fuzzy
relation. The most common definition of a
fuzzy rule

A −→ B is as A coupled with B,

i.e.,

R = A −→ B = A × B ,

A×B

(x, y) = µ

(x) ? µ

(y) ,

where

? is a triangular norm.

See also

fuzzy implication

See

fuzzy IF-THEN

rule

fuzzy inference

a fuzzy logic principle of

combining fuzzy IF-THEN rules in a fuzzy
rule base into a mapping from a fuzzy set in
the input universe of discourse to a fuzzy set
in the output universe of discourse. A typical
example is a composition inference.

fuzzy inference engine

a device or com-

ponent carrying out the operation of fuzzy in-
ference, that is, combining fuzzy IF-THEN
rules in a fuzzy rule base into a mapping
from a fuzzy set in the input universe of dis-
course to a fuzzy set in the output universe of
discourse. See also

approximate reasoning

fuzzy inference system

fuzzy rule

fuzzy inference system

a computing

framework based on fuzzy set theory, fuzzy
IF-THEN rules, and approximate reasoning.
There are two principal types of fuzzy infer-
ence systems:

1. Fuzzy inference systems mapping

fuzzy sets into fuzzy sets (pure fuzzy infer-
ence systems) that are composed of a knowl-
edge base containing the definitions of the
fuzzy sets and the database of fuzzy rules
provided by experts; and a fuzzy inference
engine that performs the fuzzy inferences.

2. Fuzzy inference systems performing

non-linear mapping from crisp (nonfuzzy) in-
put data to crisp (nonfuzzy) output data. In
the case of a Mamdani fuzzy system, in ad-
dition to a knowledge base and a fuzzy in-
ference engine, there is a fuzzifier that rep-
resents real-valued inputs as fuzzy sets, and
a defuzzifier that transforms the output set to
a real value. In the case of a Sugeno fuzzy
system, special fuzzy rules are used, giving a
crisp (nonfuzzy) conclusion, and the output
of the system is given by the sum of those
crisp conclusions, weighted on the activation
of the premises of rules. Some fuzzy sys-
tems of this type hold the universal function
approximation property.

See also

universal function appro-

ximation property

2000 by CRC Press LLC

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