FUZZY LOGIC
In our day to day life, we’d face situations where we are unable to work out whether the state is true or false. Fuzzy refers to something which is unclear, uncertain or vague. Fuzzy logic in AI provides valuable flexibility for reasoning.
WHAT IS FUZZY LOGIC?
Fuzzy Logic (FL) may be a method of reasoning that resembles human reasoning. This approach is analogous to how humans perform deciding. And it involves all intermediate possibilities between 0 and 1 i.e. YES and NO. The fuzzy logic systems generate the logical output back to the uncertain, messy, deform, and incomplete fuzzy inputs.
The conventional logic block that a computer understands takes precise input and produces a particular output as TRUE or FALSE, which is like a person’s being’s YES or NO. The fuzzy logic was invented by Lotfi Zadeh who observed that unlike computers, humans have a special range of possibilities between YES and NO, such as:
IMPLEMENTATION
The fuzzy logic works on the amount of possibilities of input to attain a particular output. Now, talking about the implementation of this logic:
· It is often implemented in systems with different sizes and capabilities like micro-controllers, large networked or workstation-based systems.
· Also, it is often implemented in hardware, software or a mixture of both.
WHY FUZZY LOGIC?
Generally, we use fuzzy logic system for the practical also as commercial purposes.
· It can be used to control machines and consumer products.
· It gives acceptable reasoning rather than accurate reasoning.
· Also, this logic helps to deal with the uncertainty in engineering.
FUZZY LOGIC SYSTEMS ARCHITECTURE
Basically, four parts are shown within the architecture of fuzzy logic system-
a. Fuzzification Module
We use this module to remodel the system inputs. As tha is is crisp number. Also, helps in splitting the input into various five steps.
· LP — x is Large Positive.
· MP- x is Medium Positive.
· S — x is small.
· MN — x is Medium Negative.
· LN — x is Large Negative
b. knowledge base
In this, we’ve to store it in IF-THEN rules that were provided by experts.
c. Inference Engine
Generally, it helps in simulating the human reasoning process by making fuzzy inference on the IF-THEN rules and inputs.
d. Defuzzification Module
In this module, we’ve to rework fuzzy set into a crisp value. That set was obtained by an inference engine.
The membership functions always work on a same concept of fuzzy sets of variables.
Fuzzy set is characterized by membership function whose range is from 0 to 1.
MEMBERSHIP FUNCTION
Membership functions allow you to represent a fuzzy set graphically and quantify linguistic term. A membership function for a fuzzy set A on the universe of discourse X is defined as μA: X → [0, 1].
Here, each element of X is mapped to a worth between 0 and 1. it’s called membership value or degree of membership.
· x axis represents the universe of discourse.
· y axis represents the degrees of membership within the [0, 1] interval.
There are often multiple membership functions applicable to fuzzify a numerical value. Simple membership functions are used as use of complex functions doesn’t add more precision within the output.
Example of fuzzy set friendship F’= {01/1, 02/0.7, 03/0.4, 04/0}
Ø Person 01 has membership function of 1, i.e. best friend
Ø Person 01 has membership function of 0.7, i.e. good friend
Ø Person 01 has membership function of 0.4, i.e. friend
Ø Person 01 has membership function of 0, i.e. enemy.
EXAMPLE
Let us consider an air-con system with 5-level fuzzy logic system. This technique adjusts the temperature of air conditioning by comparing the room temperature and therefore the target temperature value.
Temp: {Freezing, Cool, Warm, Hot}
How cool is 36 F°? — It is 30% Cool and 70% freezing
METHODS OF DEFUZZIFICATION
Defuzzification is that the process of conversion of fuzzy quantity into a precise quantity.
[1] Max — membership principle:
M c (x∗) > M c (x) for all x ∈ X
[2] Centroid method: centre of mall, centre of gravity or area.
[3] Weighted average method: Valid for symmetrical output membership function.
Each membership function is weighted by its max membership value.
x∗=0.5a+0.8b/0.5+0.8
[4] Mean max membership method:
This is referred to as middle of the maxima.
[5] Centre of sums: Algebraic sum of individual fuzzy the union, here, interesting areas are value twice, the defuzzified value X+
[6] Centre of largest area: When output consists of at least two converse fuzzy subsets which aren’t overlapping. When o/p fuzzy set has at least two converse regions, then the centre of gravity of converse fuzzy sub region having the largest area is employed to get defuzzified value.
[7] First of maxima (last of maxima)
This method uses the overall output or union of all individual output fuzzy sets Ci for determining the littlest value of the domain maximized membership in Ci.
ALGORITHM
- Define linguistic Variables and terms (start)
- Construct membership functions for them. (start)
- Construct knowledge base of rules (start)
- Using membership functions, Convert crisp data into fuzzy data sets. (fuzzification)
- Evaluate rules in the rule base. (Inference Engine)
- Combine results from each rule. (Inference Engine)
- Convert output data into non-fuzzy values. (defuzzification)
APPLICATION
· It is employed within the aerospace field for altitude control of spacecraft and satellite.
· It has utilized in the automotive system for speed control, traffic control.
· It is employed for deciding support systems and private evaluation within the large company business.
· It has application in industry for controlling the pH, drying, chemical distillation process.
· Fuzzy logic is utilized in natural language processing and various intensive applications in AI.
ADVANTAGES OF FUZZY LOGIC SYSTEM
· FLSs are easy to construct and understand.
· You can modify a FLS by just adding or deleting rules thanks to flexibility of symbolic logic.
· Fuzzy reasoning containing mathematical concepts are very simple.
· Fuzzy logic Systems can take noisy, distorted, imprecise input information.
· Fuzzy logic may be a solution to complex problems altogether fields of life, including medicine, because it resembles human reasoning and deciding.
DISADVANTAGES OF FUZZY LOGIC SYSTEM
· They are understandable only if simple.
· There is not any systematic approach to fuzzy system designing.
· They are suitable for the issues which don’t need high accuracy.
