(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 ?

Ans.

• 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

Where μ_A 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. 

Ans. 

Q4. Compare and contrast classical logic and fuzzy logic. 

Ans. 

Q5. Write short notes on fuzzy arithmetic.

Ans.

• 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 

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

Covering: 

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

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

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