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(Aktu Btech) Application of Soft Computing Important Unit-3 Fuzzy Logic-I (Introduction)

B.Tech AKTU Quantum Book delves into the practical Application of Soft Computing. Learn about significant applications, frequently asked questions, and important takeaways for mastering this cutting-edge technology. Unit-3 Fuzzy Logic-I (Introduction)

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Q1. Define fuzzy logic and its importance in our daily life. What is role of crisp sets in fuzzy logic ?


  • 1. Fuzzy logic is a computing approach focused on “degrees of truth” rather than “true or false” (1 or 0).
  • 2. Fuzzy logic contains the extreme situations of truth, 0 and 1, as well as the different states of truth in between.
  • 3. Fuzzy logic enables the incorporation of human judgements into computing problems.
  • 4. It provides an effective method for resolving numerous criterion conflicts and better assessing options. 

Importance of fuzzy logic in daily life: 

  • 1. Fuzzy logic is required for Al to achieve human-like capabilities.
  • 2. It is used to create intelligent systems for decision making, identification, optimisation, and control.
  • 3. Many persons interested in research and development, such as engineers, mathematicians, computer software developers, and researchers, find fuzzy logic incredibly beneficial.
  • 4. Fuzzy logic has been employed in a wide range of applications, including facial recognition, air conditioners, hoover cleaners, weather forecasting systems, medical diagnostics, and stock trading.  

Role of crisp sets in fuzzy logic:

  • 1. It contains the precise location of the set boundaries. 
  • 2. It provides the membership value of the set.

Q2. Define classical set and fuzzy sets. State the importance of fuzzy sets.

Ans. Classical set:

  • 1. A classical set is a grouping of different things.
  • 2. In a set, each unique entity is referred to as a member or an element of the set.
  • 3. The classical set is defined in a way that divides the universe of discourse into two groups: members and non-members.

Fuzzy set: 

  • 1. Fuzzy set is a set having degree of membership between 1 and 0. 
  • 2. Fuzzy sets Ā in the universe of discourse U can be defined as set of ordered pair and it is given by
Define classical set and fuzzy sets. State the importance of fuzzy sets. Application of Soft Computing

Where μA is the degree of membership of x in Ā

Importance of fuzzy set: 

  • 1. It is used for the modeling and inclusion of contradiction in a knowledge base. 
  • 2. It also increases the system autonomy. 
  • 3. It act as an important part of microchip processor-based appliances. 

Q3. Consider three fuzzy sets given by: 

A = ((low, 1), (medium, 0.2), (high, 0.5) 

B = {(positive, 0.9), (zero, 0.4), (negative, 0.9)}

C = {(low, 0.1), (medium, 0.2), (high, 0.7)}  

i. Find the fuzzy relation for the Cartesian product of A and B. 

ii. Find CoR using max-min composition. 


Consider three fuzzy sets given by: Application of Soft Computing Aktu Btech
Consider three fuzzy sets given by: Application of Soft Computing

Q4. Compare and contrast classical logic and fuzzy logic. 


S. No.Crisp (classical) logicFuzzy logic
1.In classical logic an element either belongs to or does not belong to a set.  Fuzzy logic supports a flexible sense of membership of elements to a set.  
2.Crisp logic is built on a 2-state truth values (True/False).Fuzzy logic is built on a multistate truth values.
3.The statement which is either True’ or ‘False’ but not both is called a proposition in Crisp logic. A fuzzy proposition is a statement  which acquires a fuzzy truth value.
4.Law of excluded middle and law of non-contradiction holds good in crisp logic.Law of excluded middle and law of  contradiction is violated.  

Q5. Write short notes on fuzzy arithmetic.


  • 1. Fuzzy arithmetic is a generalisation of interval arithmetic in which, rather than evaluating intervals at a single fixed level, many levels in [0, 1] are examined.
  • 2. This is due to the fact that a fuzzy set allows for a degree of membership for a universal set element.
  • 3. It is useful in many applications, including fuzzy control, decision making, approximation reasoning, optimisation, and statistics with imprecise probabilities. 

Q6. Write note on partition and covering.

Ans. Partition: 

  • 1. A partition on set A is defined to be a set of non-empty subsets A, each of which is pair-wise disjoint and whose union yields the original set A. 
  • 2. Partition on set A is indicated as π (A), therefore 
Write note on partition and covering. Application of Soft Computing

3. The members Ai of the partition are known as blocks.

note on partition and covering.
Write note on partition and covering.


1. A covering on set A is defined to be a set of non-empty subsets Ai, whose union yields the original set A. 

2. The non-empty subsets need not to be disjoint.

Write note on partition covering.
Write note on partition and covering.
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