Essay: Using fuzzy logic to analyse blood pressure data

Admitting in expert system and fuzzy logic imprecision in truth. However, Aristotle’s said that is so significant today; the quote that follows uncertainty. It is an admonishment we should need that; we should make balance between with the certainty and uncertainty that exists. This thesis is mainly dedicated to the characterization and quantification of uncertainty within medical problems uncertainty and uncertainty can be expressed. When 1 ask myself why we should engage in this pursuit. Am I solving problems that require precision? The more complex system is, the more imprecise or inexact is the information that we have to characterize that system. It seems, then, that precision and information and complexity are inextricably related in the problems we pose for eventual solution. However, for most of the problems that we face, the quote above due to Professor Zadeh suggests that we can do a better job in accepting some level of imprecision. It seems intuitive that we should balance the degree of precision in a problem with the associated uncertainty in that problem. Hence, this book recognizes that uncertainty of various forms permeates all scientific endeavors and it exists as an integral feature of all abstractions, models, and solutions.
DEFINITION OF PROBLEM
Although measurement of Blood Pressure is easier, cheaper and available for people of any state or place.
In India people does not consider is seriously. By measuring Blood pressure only its occurrence can be checked but the probability of being high blood pressure cannot be checked.it is a real world problem. This proposed system is a Diagnosis system capable to give the possibility of being High blood pressure patient.SBP (Systolic bloodpressure), DBP (Diastolic blood pressure), Age and BMI (Body mass index) are major factors which affects the blood pressure.
After the brief study of fuzzy expert system and blood pressure rules are generated through which Risk of high blood pressure can be calculated.
THEORY
LOGIC
CRISP SET
FUZZY SET
FUZZY RELATION
APPLICATION
THEORY
LOGIC
Logic is but a small part of the human capacity to reason. Logic can be a means to compel us to infer correct answers, but it cannot by itself be responsible for our creativity or for our ability to remember. In other words, logic can assist us in organizing words to make clear sentences, but it cannot help us determine what sentences to use in various contexts. Consider the passage above from the nineteenth-century mathematician Lewis Carroll in his classic Through the Looking Glass. How many of us can see the logical context in the discourse of these fictional characters? Logic for humans is a way quantitatively to develop
a reasoning process that can be replicated and manipulated with mathematical precepts. The interest in logic is the study of truth in logical propositions; in classical logic this truth is binary ‘ a proposition is either true or false.
From this perspective, fuzzy logic is a method to formalize the human capacity of imprecise reasoning, or ‘ later in this chapter ‘ approximate reasoning. Such reasoning represents the human ability to reason approximately and judge under uncertainty. In fuzzy logic all truths are partial or approximate. In this sense this reasoning has also been termed interpolative reasoning, where the process of interpolating between the binary extremes of true and false is represented by the ability of fuzzy logic to encapsulate partial truths.
FUZZY LOGIC
The origin of fuzzy concept partly depends on the fact that the human brain does not operate like a computer which depends on bi-valued logic.
Fuzzy means vague, imprecise, and ambiguous.
It involves multi-valued logic.
it deals with flexible reasoning rather than fixed concepts.
It refers to logic of approximation.
Each member of the fuzzy set is identified by its membership function (degree of belonging) to the set.
FUZZY IS NOT PROBABILITY
Probability theory measures how likely the proposition is to be correct.
Fuzzy logic measures the degree of correctness to which the proposition is correct.
CRISP(CLASSICAL SET)
Definition of Crisp Set: The Non empty set of well-defined objects
Thus a crisp non-empty set is defined as the set is of ordered pairs, in which the first member is the element of the set and second member is the characteristics function whose value is either 1 or 0 which denotes the presence and absence of an elements in the set.
Example:- Let U={A1,A2,A3””Ar, Ar+1,} be the universe of discourse.
Consider the Set of Students ‘S’ present in the Seminar represented as
S=
CRISP OPERATION
CRISP UNION OF SETS
A= {1, 3, 5} AND
B= {1, 2, 3}
Is the set C= {1, 2, 3, 5}
that is A’B={1,3,5}'{1,2,3}={1,2,3,5}
CRISP INTERSECTION OF SETS
A= {1, 3, 5} AND
B= {1, 2, 3}
Is the set C= {1, 3}
that is A’B={1,3,5}'{1,2,3}={1,2,3,5}
CRISPCOMPLIMENT OF SET
Universal U= {1, 2, 3, 4, 5} AND
A= {1, 2, 3}
Is the set A`= {1, 2, 3, 5}
PROPERTIES OF CRISP SETS
Identity: A”=AA’U=A
Domination: A’U=U A”=’
Idempotent: A’A = A =A’A
Commutative: A’B=B’A A’B=B’A
Associative: A'(B’C)=(A’B)’C
A'(B’C)=(A’B)’C
Exactly analogous to (and derivable from) DE Morgan’s Law for propositions.
If A ‘ B ‘ C, then A ‘ C
FUZZY SETS
Definition: A fuzzy set is defined as the set of ordered pair given as
F=
Here Xi is the element of the fuzzy set and ??Xi is the membership function of Xi. Consider the set of intelligent Students in this Seminar. Here we can’t divide the students in to two separate groups of intelligent students and not intelligent students. There is lack of sharp boundary between an intelligent and not intelligent student.
OPERATION ON FUZZY SETS
Fuzzy union (‘): the union of two fuzzy sets is the maximum (MAX) of each element from two sets.
E.g.
A = {1.0, 0.20, 0.75}
B = {0.2, 0.45, 0.50}
A ‘ B = {MAX(1.0, 0.2), MAX(0.20, 0.45), MAX(0.75, 0.50)}
= {1.0, 0.45, and 0.75}
Fuzzy intersection (‘): the intersection of two fuzzy sets is just the MIN of each element from the two sets.
E.g.
A ‘ B = {MIN(1.0, 0.2), MIN(0.20, 0.45), MIN(0.75, 0.50)} = {0.2, 0.20, 0.50}
Complement (_c): The complement of a fuzzy set is composed of all elements’ complement.
Example:
Ac = {1 ‘ 1.0, 1 ‘ 0.2, 1 ‘ 0.75} = {0.0, 0.8, 0.25}
UNIION
‘A ‘ B(x) = ‘A(x) ”B(x)
= max (‘A(x), ‘B(x))
INTERSECTION
‘A ‘ B(x) = ‘A(x) ”B(x)
= min (‘A(x), ‘B(x))
COMPLIMENT
‘A'(x) = 1 – ‘A(x)
De Morgan’s Law also holds:
(A ‘ B)’ = A’ ‘ B’
(A ‘ B)’ = A’ ‘ B’
But, in general
A’A’
A’A’
COMMUTATIVITY
A ‘ B = B ‘ A
A ‘ B = B ‘ A
ASSOCIATIVITY
A ‘ (B ‘ C) = (A ‘ B) ‘ C
A ‘ (B ‘ C) = (A ‘ B) ‘ C
DISTRIBUTIVITY
A ‘ (B ‘ C) = (A ‘ B) ‘ (A ‘ C)
A ‘ (B ‘ C) = (A ‘ B) ‘ (A ‘ C)
IDEMPOTENCY
A ‘A = A A’A = A
IDENTITY
A ‘ X = X A ‘ X = A
A ” = A A” = ‘
TRANSITIVITY
If A ‘ B ‘ C, then A ‘ C
INVOLUTION
A” = A
DETERMINATION FOR MEMBERSHIP FUNCTION
Discrete set of alternatives
a. By intuitive judgment of a single decision maker (Judge). Who is expert and well experienced in making decisions concerning the associated problem? Such a judgment may be biased.
b. By intuitive judgment of a group of judges (Decision makers) and taking the suitable average or weighted average of their judgments given by the judges regarding the membership function. Such an articulation of the membership function is more rational and realistic.
Discrete Fuzzy Set
Discrete sets are defined as:
A = ??1 /x1+??2/x2+’..+??n/xn
or (in a more compact form)
x1,x2 , ‘.. xn: members of the set A
??1, ??2,’..??n: x1 , x2 ‘.. xn’s degree of membership.
Continuous set of alternatives
Continuous set gives a geometric curve which can be evaluated by the help of mathematical calculation.
It is more precise, since it does contain intuitive judgments.
It contains infinite number of elements.
A continuous fuzzy setA can be defined as:
Different Shapes of Membership Function (Continuous Sets)
Member function
Temp: {Freezing, Cool, Warm, Hot}
Degree of Truthfulness or “Membership’ .
How cool is 36 F’
It is 30% Cool and 70% freezing.
CRISP vs. FUZZY
CRISP FUZZY
APPLICATIONS OF FUZZY LOGIC
Business
Decision-making support systems, personnel Evaluation in a large company Data mining systems
Chemical Industry
Control of pH, drying, chemical distillation processes, polym??res extrusion production, a coke oven gas cooling plant..
Defence
Underwater target recognition, automatic target recognition of thermal infrared images, naval decision support aids, control of a hypervelocity interceptor, fuzzy set modelling of NATO decision making
Electronics
Control of automatic exposure in video cameras, humidity in a clean room, air conditioning systems, washing machine timing, microwave ovens, vacuum cleaners.
Financial
Banknote transfer control, fund management, stock market predictions.
Industrial
Cement kiln controls (dating back to 1982), heat exchanger control, activated sludge wastewater treatment process control, water purification plant control, quantitative patternanalysis for industrial quality assurance,control of constraint satisfaction problems instructural design, control of water purification plants.
Marine Autopilot for ships, optimal route selection, control of autonomous underwater vehicles,ship steering.