Lecture 1:Introduction: Fuzzy Sets, Logic and Systems & Applications By Prof. Nishchal K. Verma

Summary

This lecture introduces fuzzy logic as a key component of artificial intelligence, highlighting its multi-valued logic system that deals with uncertainties and imprecision. It traces AI's history, from Turing's machine to modern deep learning, and positions fuzzy systems as essential for handling complex, real-world problems where traditional mathematical models fall short. The lecture also distinguishes between AI, machine learning, and deep learning, emphasizing fuzzy logic's role in natural language processing and its applicability in various disciplines.

Takeaways

• 🤖 Fuzzy logic is a multi-valued logic system and is closely linked to artificial intelligence.
• 🧠 Artificial intelligence (AI) involves algorithms that mimic human brain activities and includes fuzzy logic as a key component.
• 💡 The history of AI began with Alan Turing's Universal Turing Machine in the 1930s and includes milestones like neural networks, genetic algorithms, and fuzzy logic.
• 🕹️ John McCarthy coined the term 'artificial intelligence' in 1955, while Lotfi A. Zadeh introduced fuzzy logic in 1965.
• 📊 Fuzzy logic allows for handling partial truth values (degrees of truth), unlike traditional Boolean logic which is bivalent (true or false).
• 🌐 Fuzzy systems are vital in computational intelligence, which is used to solve complex, real-world problems where traditional models fail.
• 🔗 AI is a broad term that encompasses machine learning and deep learning, with fuzzy logic being an important aspect of AI's evolution.
• 🔍 Fuzzy logic excels in managing uncertainties due to vagueness, ambiguity, and imprecision, which are not easily addressed by probability theory.
• 🧩 Fuzzy systems are particularly useful in black-box or gray-box modeling, where not all system equations are known, enabling modeling of complex systems.
• ⚙️ Fuzzy logic is not necessary when exact mathematical models are known (white-box systems) or when dealing with simple, linear systems.

Q & A

What is the main focus of the lecture on Fuzzy Sets, Logic, and Systems?

The lecture primarily focuses on introducing Fuzzy Logic and its connection with Artificial Intelligence. It also aims to provide a brief history of Artificial Intelligence and how Fuzzy Systems play a key role in it.

How is Fuzzy Logic defined in the context of this lecture?

Fuzzy Logic is defined as a multi-valued logic that deals with approximate reasoning and is closely linked to Artificial Intelligence.

What is the historical starting point of Artificial Intelligence mentioned in the lecture?

The historical starting point of Artificial Intelligence is marked by Alan Turing's proposal of the Universal Turing Machine in 1936-37.

Who are considered the founding fathers of Artificial Intelligence and when was the term 'Artificial Intelligence' coined?

John McCarthy is considered one of the founding fathers of Artificial Intelligence, and he coined the term 'Artificial Intelligence' in 1955.

What is the significance of the year 1965 in the history of Artificial Intelligence and Fuzzy Logic?

The year 1965 is significant because it's when both Fuzzy Logic was proposed by Lotfi A. Zadeh and the term 'Deep Learning' was coined by Evancho and Lapa.

What is the role of Fuzzy Systems in the field of Artificial Intelligence according to the lecture?

Fuzzy Systems are considered one of the key agents of Artificial Intelligence, particularly useful for dealing with uncertainties due to ambiguity, imprecision, and vagueness.

What is the difference between bivalent logic and multivalent logic as explained in the lecture?

Bivalent logic, also known as Boolean logic, allows for truth values to be either true or false with no in-between. Multivalent logic, on the other hand, allows for truth values to be a matter of degree, existing anywhere between 0 and 1, which is the basis of Fuzzy Logic.

How does Fuzzy Logic handle uncertainties that cannot be addressed by probability theory?

Fuzzy Logic is particularly suited for handling uncertainties due to ambiguity, imprecision, and vagueness, which are different from the uncertainties due to randomness that probability theory addresses.

What is the relationship between Artificial Intelligence, Machine Learning, and Deep Learning as discussed in the lecture?

Artificial Intelligence is a broad term that encompasses Machine Learning, which in turn includes Deep Learning. Deep Learning is a subset of Machine Learning and involves hierarchical and intense learning processes.

Why is Fuzzy Logic considered a key component of Computational Intelligence?

Fuzzy Logic is considered a key component of Computational Intelligence because it provides nature-inspired methodologies to address complex real-world problems that conventional mathematical modeling may find intractable.

When should Fuzzy Logic not be used according to the lecture?

Fuzzy Logic should not be used when the physical laws governing a system are known (white box model), when dealing with linear systems, or when the system's complexity is moderate and can be managed with simple models.

Outlines

00:00

📚 Introduction to Fuzzy Sets, Logic, and Systems

The lecture begins with an introduction to Fuzzy Sets, Logic, and Systems, highlighting its connection with Artificial Intelligence (AI). Fuzzy logic is described as a multi-valued logic that plays a significant role in AI. The lecture aims to draw parallels between fuzzy logic and AI. A brief history of AI is provided, starting with Alan Turing's Universal Turing Machine in 1936-37, followed by the development of neural networks by Warren McCulloch and Walter Pitts in 1942-43. The lecture continues with the Turing Test in 1950, the formal naming of AI by John McCarthy in 1955, the introduction of the perceptron model in 1957, and the proposal of genetic algorithms in the 1960s. A pivotal moment is noted in 1965 with the proposal of fuzzy logic by Lotfi A. Zadeh and the coining of the term 'deep learning.'

05:01

🌐 Evolution of AI and Its Components

This paragraph discusses the evolution of AI and its components, including evolutionary computing in the 1970s, neural computing and swarm intelligence in the 1980s, and hybrid models like neuro-fuzzy systems in the 1990s. The paragraph emphasizes the synergy of fuzzy, neural, and genetic models in enhancing performance. It also outlines various research areas and systems that have emerged from these components, such as data mining, simulated annealing, and deep neural networks. The paragraph concludes by defining computational intelligence as a set of nature-inspired methodologies for solving complex real-world problems, positioning fuzzy systems as a key component of both computational and artificial intelligence.

10:03

🧠 AI, Machine Learning, and Deep Learning Interrelations

The lecture explores the relationship between AI, Machine Learning (ML), and Deep Learning (DL). AI is presented as an umbrella term that encompasses ML, which in turn includes DL. The paragraph explains that AI is an interdisciplinary field drawing from various areas like statistics, mathematics, and computer science. It also highlights the application of AI across different fields such as computer vision, natural language processing, and robotics. The paragraph introduces Lotfi A. Zadeh as the father of fuzzy systems theory, which was proposed in 1965, and differentiates fuzzy systems theory from conventional computing by emphasizing its multi-valued logic approach.

15:03

🔍 Fuzzy Systems Theory and Its Distinctions

This section delves into the differences between fuzzy systems theory and conventional computing. Fuzzy systems theory is based on multi-valued logic, allowing for degrees of truth and falsehood, as opposed to the binary true/false of conventional computing. The theory deals with uncertainties due to ambiguity, imprecision, and vagueness, which are not adequately addressed by probability theory. The lecture notes that fuzzy systems theory is multidisciplinary and can be applied across various fields. It also explains the concept of multivalent logic, where truth values can range between 0 and 1, in contrast to bivalent logic, which only allows for absolute truth or falsehood.

20:10

📈 Historical Context and Applications of Fuzzy Logic

The paragraph provides a historical context for fuzzy logic, starting with Aristotle's bivalent logic in 400 BC, Jan Lukasiewics's three-valued logic in 1900, and culminating in Lotfi A. Zadeh's fuzzy logic in 1965. It discusses the limitations of Boolean logic in handling partial truths and how fuzzy logic offers a more flexible framework for dealing with uncertainty and imprecision. The paragraph also touches on the reasons for using fuzzy logic, such as systems with uncertainties due to imprecision, vagueness, and ambiguity, and when it is not suitable, like when the physical laws of a system are well understood or when dealing with linear systems.

25:13

🛠️ Practical Considerations of Fuzzy Logic

The final paragraph addresses the practical applications of fuzzy logic, particularly in modeling systems that are not fully understood or accessible. It discusses the use of black box and gray box modeling approaches where fuzzy systems can be instrumental. The paragraph also outlines scenarios where fuzzy logic may not be necessary, such as when the mathematical model of a system is known (white box model), the system is linear, or the complexity is moderate. The lecture concludes with a预告 of the next session, which will focus on real-time applications of fuzzy systems.

Keywords

💡Fuzzy Logic

Fuzzy Logic is a form of multi-valued logic proposed by Lotfi A. Zadeh in 1965. It allows for degrees of truth rather than the conventional true/false (binary) distinctions of Boolean logic. In the video, fuzzy logic is introduced as an essential agent in artificial intelligence, capable of handling uncertainties, vagueness, and imprecision in systems.

💡Artificial Intelligence

Artificial Intelligence (AI) refers to the discipline that involves creating systems capable of mimicking human brain functions through algorithms and mechanisms. The video explains AI as a broad term encompassing fuzzy systems, neural networks, and evolutionary algorithms, making it an interdisciplinary field applied in areas such as computer vision and natural language processing.

💡Neural Networks

Neural Networks are computational models inspired by biological neurons. Introduced in the 1940s, they are a significant component of AI and machine learning. The video discusses how neural networks evolved, starting with the threshold logic and leading to modern artificial neural networks, which are integral to deep learning processes.

💡Deep Learning

Deep Learning is a subset of machine learning involving hierarchical, repetitive learning models to process complex data. The video highlights how deep learning, coined in 1965, is a more specialized form of machine learning that fits within AI's larger framework, helping systems recognize patterns and make decisions based on large datasets.

💡Evolutionary Algorithms

Evolutionary Algorithms are optimization algorithms based on the process of natural selection. These include genetic algorithms, which mimic biological evolution to solve optimization problems. The video traces their origin in the 1970s and explains their role as an AI agent for handling complex, evolving systems such as swarm intelligence and differential evolution.

💡Genetic Algorithms

Genetic Algorithms are a type of evolutionary algorithm used to find approximate solutions to optimization problems through mechanisms such as selection, crossover, and mutation. The video links genetic algorithms to artificial intelligence, showing how they work alongside fuzzy systems and neural networks to enhance AI’s problem-solving capabilities.

💡Computational Intelligence

Computational Intelligence refers to nature-inspired computational approaches for addressing complex real-world problems that conventional mathematical models cannot solve. The video equates computational intelligence with AI, emphasizing that fuzzy systems, neural networks, and evolutionary algorithms are key components in this field.

💡Bivalent Logic

Bivalent Logic, also known as Boolean logic, is the classical logic system where every proposition is either true or false. In the video, this logic is contrasted with fuzzy logic, which allows for intermediate values, demonstrating the limitations of bivalent logic in representing real-world complexities such as 'half-truths' or uncertainty.

💡Perceptron Model

The Perceptron Model is an early form of an artificial neural network developed in 1957. It is a single-layer neural network that uses a binary linear activation function. In the video, the perceptron model is presented as a critical development in the history of AI, marking a foundational step in the evolution of neural network-based learning systems.

💡Swarm Intelligence

Swarm Intelligence refers to collective behavior observed in decentralized, self-organized systems, such as ant colonies or bird flocking, applied to optimization problems. The video mentions swarm intelligence as one of the evolutionary computing methods in AI, used for solving complex, dynamic problems through algorithms like Particle Swarm Optimization and Ant Colony Optimization.

Highlights

Introduction to fuzzy logic, artificial intelligence, and their relationship.

Fuzzy logic is a multi-valued logic linked to artificial intelligence, serving as one of its key agents.

Artificial intelligence mimics brain activities using algorithms and mechanisms.

History of AI began with Alan Turing's Universal Turing Machine in 1936.

The perceptron model introduced in 1957 is an artificial neuron model with binary linear activation functions.

Fuzzy logic was proposed by Lotfi A. Zadeh in 1965, marking a key milestone in AI development.

Deep learning, also coined in 1965, correlates strongly with fuzzy logic.

AI has evolved through the 1970s and beyond, integrating neural networks, genetic algorithms, and hybrid models like neuro-fuzzy systems.

AI's interdisciplinary nature involves contributions from statistics, mathematics, engineering, and natural sciences.

Fuzzy systems theory handles uncertainties due to ambiguity, imprecision, and vagueness, unlike probability theory which deals with randomness.

Bivalent (Boolean) logic deals with absolute truth or falsehood, while fuzzy logic operates in a range between 0 and 1, handling partial truths.

Fuzzy logic allows for granular and perception-based information processing, making it useful for systems with complex uncertainties.

AI fields like computer vision, natural language processing, and robotics utilize fuzzy logic in their systems.

The introduction of multi-valued logic allows fuzzy logic to better describe real-world scenarios, such as a glass being half full.

Fuzzy logic is essential for modeling systems where physical laws are unknown or the system behaves non-linearly.

Transcripts

So, welcome to the first lecture of the course on Fuzzy Sets Logic and Systems and Applications.

This lecture is based on the Introduction of Fuzzy Logic and then the little bit of

introduction to artificial intelligence and I will try here to relate fuzzy logic with

Artificial Intelligence.

So, before I move to that part, I would like to tell you that fuzzy logic is a multi valued

logic and of course, as I have mentioned already that there is a linkage of fuzzy system with

artificial intelligence.

So, or in other words I would like to tell you that the fuzzy systems is one of the very

key agents of artificial intelligence.

So, when we talk of artificial intelligence, or machine intelligence in other words let

me briefly define what is artificial intelligence.

So, artificial intelligence is nothing but it is a discipline which involves all sort

of mechanisms, algorithms that deal with mimicking the activities of our brain.

I would like to go to brief history of artificial intelligence, since we are going finally,

to study fuzzy systems and as I mentioned that there is a linkage of fuzzy systems with

the artificial intelligence.

So, it is necessary to have our brief history of artificial intelligence.

So, artificial intelligence starts with the Allen’s Universal Turing Machine it is here

and it was the time in 1936 - 37.

So, around that it was proposed and with this the beginning of artificial intelligence is

seen here and then in 1942 - 43 Warren McCulloch and Walter Pitts created a computational model

for neural networks and that was also called threshold logic.

So, this was the time when artificial neural network started.

So, here it was basically a preposition of the ANN model and it was based on the biological

neuron and then in 1950 a Turing Test was proposed, in 1955 the formal name artificial

intelligence has come up and this name was given by John McCarthy.

As it’s written here that in 1955 the John McCarthy founding father of artificial intelligence

has coined the word artificial intelligence.

In 1957 a perceptron model was introduced.

So, a perceptron model is nothing, but it is again artificial neuron model, the difference

here is just the activation function.

So, perceptron model is ANN model with activation function as binary linear.

And then in 1960’s the genetic algorithm was proposed, in 1965 it is very important

to note here that in 1965 fuzzy logic was proposed by professor Lotfi A Zadeh.

And this is a time when the deep learning term which is very very relevant, very very

popular term being used nowadays, it was coined in 1965 by Evancho and Lapa.

So, I would say here that this year there were two main concepts were proposed, first

concept was fuzzy logic and then the deep learning.

And these two have a very high correlation.

In 1970’s evolutionary computing was proposed.

So, various algorithms of evolutionary computing were proposed and then 1980’s witnessed

neural computing swarm intelligence and then 1990’s hybrid models of these like neuro

fuzzy systems, neuro fuzzy genetic, fuzzy genetic like that the models were proposed.

So, in nutshell I would say the fuzzy neuro genetic all these were used together to give

a better model performance and these were proposed when studied.

Beyond 90’s the research areas based on all of these agents were helpful in giving

rise to various models, various systems.

For example, if systems, evolutionary computing, data mining, simulated annealing, particle

swarm algorithm, deep neural networks, deep fuzzy networks etcetera.

So, the artificial intelligence which started which was seen right from, I would say the

birth of artificial intelligence is seen around 1936 – 37, and it you know with the advent

of all these agents for example, fuzzy systems, neural network, genetic algorithm and many

more which I am I will be describing in due course of time.

So, we can call these are the agents of artificial intelligence, like fuzzy systems, artificial

neural systems, evolutionary systems.

And in evolutionary algorithms we mainly cover genetic algorithms differential evolution

and then in evolutionary systems we have meta heuristic and swarm intelligence.

Under these we have ant colony optimization, Bees Algorithm, Bat Algorithm, Cuckoo Algorithm,

Harmony search, Firefly Algorithm, Artificial Immune Systems, Particle Swarm Optimization.

And then as agents of artificial intelligence again we have probabilistic systems, for example,

Bayesian networks, Gaussian mixture models, hidden Marco models which is not mentioned

here and then we have as agent of AI, we have chaos theory simulated annealing, rough set

theory, support vector machines and there are many more agents which I have not been

mentioned here.

So, fuzzy system is also one of the key agents of computational intelligence.

So, computational intelligence is an equivalent name of artificial intelligence, these two

names go hand in hand and I would like to just briefly tell you the definition of a

computational intelligence.

So, Computational Intelligence basically a set of nature inspired computational methodologies

and approaches to address complex real world problems to which conventional mathematical

or traditional modelling can be useless.

For a few reasons, like the processes might be too complex, the processes for which we

are developing the model that could be too complex for mathematical reasoning.

It might contain some uncertainties during the process or the process might simply be

stochastic in nature.

So, the major constituents of computational intelligence are fuzzy systems, neural networks

evolutionary algorithms and other hybrid intelligent systems.

So, we can clearly see here fuzzy system which is also a key agents of computational intelligence.

So, what I mean here is that that artificial intelligence and computational intelligence

although these two go hand in hand are being interchangeably being used, the fuzzy system

is a key component of these two.

Let us now just look at the artificial intelligence, Machine Learning and Deep Learning.

So, at this stage let us now understand as to how the artificial intelligence which we

have just discussed and then machine learning and deep learning how are these three terms

related.

So, we see here that the artificial intelligence is a very broad term; what do I mean by broad

term here is that the artificial intelligence is a bigger set and machine learning is the

is actually part of artificial intelligence because the agents of artificial intelligence

like a fuzzy systems, neural network, artificial neural network, genetic algorithm and all

other which we have already mentioned.

So, they help us in managing the machine learning process or machine learning activities.

And then comes the deep learning which is again you see is a very smaller set than the

machine learning.

So, it means that machine learning is a bigger set and deep learning is smaller set and deep

learning is contained in the machine learning and artificial intelligence.

It means that the deep learning is part of artificial intelligence, deep learning is

part of machine learning and deep learning here would mean that it’s a part of machine

learning and in machine learning when there is an intense learning process or repetitive

learning hierarchically, so, this is termed as deep learning.

In nutshell I would say the deep learning is also part of artificial intelligence as

machine learning.

So, let me just briefly describe to how artificial intelligence the theory getting developed

through various the research experts of from various fields for example, the statistics,

mathematics, engineering, natural sciences, computer science.

So, the artificial intelligence is an interdisciplinary area and experts from these areas, but not

limited to these areas, they are contributing to the theory development of artificial intelligence.

And if we see here that the artificial intelligence is used by various fields for example, computer

vision and we see here the natural language processing, information, retrieval information

filtering, predictive analysis, decision analysis, robotics, but not limited to these, again

these are the few fields that are mentioned and there are many more where artificial intelligence

is contributing.

And then if we see they are separate applications again, I would say these applications are

the applications that are mentioned here are only a few applications, but there are so

many applications in respective fields which are being practiced which are being carried

out by the with the help of artificial intelligence.

So, now coming to the fuzzy systems theory which is based on fuzzy logic, professor Lotfi

A Zadeh which is who is also known as the father of fuzzy systems theory.

So, he proposed the idea of fuzzy logic in 1965.

Fuzzy systems theory differs from conventional computing because the conventional computing

is based on bivalent logic or the Boolean logic whereas, fuzzy logic is based on the

multi valued logic.

So, we can also say that the conventional computing is based on one of the cases of

or we can also say that the conventional computing that we have done.

So, far is one of the cases of fuzzy logic or the mathematics based on the fuzzy logic.

Fuzzy systems theory involves soft or partial truth or partial false; soft because the truth

if it is soft it means that it is true, but not 100 percent true or somewhere in between

0 to 100 percent or false in between 0 to 10 percent.

So, if it is 100 percent true the truth is hard or the false is 100 percent it means

the false is hard, but if there is a truth or the false which is not 100 percent or somewhere

in between 0 and 100 percent it is termed as soft.

Fuzzy systems theory also deals with the uncertainties due to ambiguity, imprecision and vagueness.

So, these are the uncertainties which are very special kinds of uncertainties because

these uncertainties cannot be dealt by any other artificial intelligent agents, so far

what we have done mainly about uncertainties due to randomness and which is which can be

dealt or which are dealt by probability theory because the uncertainty here is due to a randomness,

but this is different from the uncertainties due to randomness.

So, that is why fuzzy system theory is very well suited for tackling these uncertainties.

And let me make it very clear here that these uncertainties cannot be dealt by the probability

theory very well.

So, another thing is that fuzzy system theory is a multidisciplinary area, multidisciplinary

area here would mean that the concepts of fuzzy systems theory can be very well utilized

by many disciplines.

For example, the engineering science, humanities and so on and so forth.

As I already mentioned that fuzzy systems theory is based on fuzzy logic and fuzzy logic

is multivalent logic.

I already explained difference between bivalent logic which is nothing, but the Boolean logic

and the multivalent logic.

So, let us now understand in bivalent logic truth is bivalent means every proposition

is either true or false with no degree of truth allowed.

Means that truth is truth and the false is hard.

In multivalent logic as I already explained this also truth is a matter of degree or I

would say here as I mentioned just before the slide the truth or false is soft.

A Multivalent logic can take in multivalent logic the values of truth or false they can

take any value in between 0 and 1.

So, that is why if we talk of the degree, so degree can be can be infinite in number,

the number of values that can be assigned can be infinite.

So, fuzzy logic deals with partial which is a matter of degree.

So, partial information, imprecise information fuzzy logic deals with the granular information

granular here would mean that if we have linguistic information the fuzzy logic can deal with

this kind of information and manage to understand, manage to quantify from the linguistic information

and then fuzzy logic can also help in perception based information.

In other worse words perception based information can be quantified by fuzzy logic.

So, let me go through little historical background of fuzzy logic, classical logic of Aristotle

was proposed in 400 BC, 400 Before Christ.

So, it is now very clear here that the bivalent logic or the Boolean logic was proposed by

Aristotle, in 400 BC, the law of bivalence which is in use for more than 2000 years.

So, it means every proposition is either true or false, it means here true is hard and false

is also hard it means 100 percent true or a 100 percent false.

So, there is no intermediate value of true or false.

So, another logic here is was proposed by Jan Lukasiewics who proposed three valued

logic in 1900 AD, this logic is a three valued logic it means that we have true, false and

possible.

And then Lotfi A Zadeh proposed a fuzzy logic in 1965 which is bivalued logic and this is

again this is very popularly known as fuzzy logic.

So fuzzy logic is much more general as I already mentioned, than the traditional logic or conventional

logic these systems based on the traditional logic system.

So, I can say here the traditional logical systems.

So, this statement goes like this the fuzzy logic is much more general than traditional

logical system, fuzzy logic provides a foundation for the development of new tools for natural

language processing like computing with words.

So, this is a very important area where fuzzy logic is very very helpful.

In other words if fuzzy logic has the ability to deal with to understand the linguistic

information and to quantify it in such a way that linguistic information is properly understood

and processed and a suitable output is created.

The Aristotle came us with the binary logic which has been the principle foundation of

conventional mathematics.

Boolean logic states a glass can be full or not full.

So, if we have a case for example, that a glass is either half way filled.

So, by using the Boolean logic we cannot manage to define the half full glass of water or

anything.

So, this disapproves the Aristotle’s low of bivalent logic or in other words we can

say that the Boolean logic is not sufficient to manage to take up this kind of situation.

This concept of certain degree or multivalence is the fundamental concept is stated by Lotfi

A Zadeh this helps us in defining such situations very well.

So, basis on which the fuzzy logic was proposed is here as the complexity of a system increases

it becomes more difficult and eventually impossible to make a precise statement about its behavior,

eventually arriving at a point of complexity where the fuzzy logic method born humans is

the only way to get at the problems.

So, this statement was made by professor Lotfi A Zadeh.

A professor Lotfi A Zadeh claimed that many sets in the world surrounded by us are defined

by a non distinct boundary.

So, we will have few examples later and then we will see that the claim of professor Lotfi

A Zadeh is true.

Let us also understand and let us also know that why should we use fuzzy logic or fuzzy

systems theory.

So, we use fuzzy logic when we have systems with uncertainties due to imprecision.

I mean the systems which suffers from the uncertainty is due to imprecision, vagueness

ambiguity, randomness, partial truth and approximation.

Fuzzy logic can be very very helpful in managing with the black box model or gray box model

of a system, many times we do not have the idea of the exact physical laws of the system,

defining the defining the system and are many times the system which is which we are studying

are trying to model that is not accessible to us.

So, we do not have all the physical laws which are governing the system in order to model

the system mathematically.

So, we cannot get the exact mathematical equations.

So, when these situations occur we take the help of black box modeling where fuzzy system

is also one of the tools, one of the agents, one of the methods we can manage we can we

can model the system using black box modeling approach or the gray box modeling approach.

So, when we say gray box gray box means that a part of the system part of the system’s

mathematical equations are known or either known or can be known and that is how you

know the gray box kind of system can be can also use the fuzzy logic or fuzzy systems

theory in order to get the final model.

We should also know that when should we do not use the fuzzy logic like whenever we already

have the physics of the model known; obviously, we can have the mathematical equations known,

it means we have the model available mathematical model available.

And when we have mathematical model available then of course, this kind of model is also

termed as white box means the mathematical all the mathematical equations governing the

model is known.

So, we do not require any such agents like fuzzy systems theory or fuzzy based theory

to go for this black box modeling approach.

So, in this case when the model is completely known then fuzzy logic is not needed and then

here when we have a system which is a linear system, then also we do not need to use fuzzy

systems theory for understanding the behavior or the getting the model and then systems

with moderate nonlinearities we can use simple models and fuzzy logic is not needed.

Also the systems with moderate complexities, so unless we have a very high complexity we

should not use fuzzy systems theory for studying such models.

So, with this now I would like to stop here and in the next lecture I will discuss some

real time applications of fuzzy system.