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In the B.Tech AKTU Quantum Book, you will learn about the practical Application of Soft Computing. Discover crucial applications, frequently asked questions, and important tips for grasping this cutting-edge technology. **Unit-4 Fuzzy Logic-II (Fuzzy Membership, Rules)**

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**Q1. Define the membership function and state its importance in fuzzy logic. Also discuss the features of membership functions. **

**Ans. Membership function:**

- 1. A membership function for a fuzzy set A on the universe of discourse X is defined as μ
_{A}:X → [0,1], where each element of X is mapped to a value between 0 and 1. - 2. This number, known as membership value or degree of membership, quantifies the degree to which an element in X belongs to the fuzzy set A.
- 3. Whether the elements in fuzzy sets are discrete or continuous, membership functions characterise fuzziness (i.e., all the information in the fuzzy set).
- 4. Membership functions are a way for solving practical problems based on experience rather than knowledge.
- 5. Graphical forms are used to depict membership functions.

**Importance of membership function in fuzzy logic:**

- 1. It allows us to graphically represent a fuzzy set.
- 2. It helps in finding different fuzzy set operation.

**Features of membership function: **

**1. Core: **

- a. The core of a membership function for some fuzzy set Ā is defined as that region of the universe that is characterized by complete and full membership in the set.
- b. The core comprises those elements x of the universe such that μ
_{Ā}(x) = 1.

**2. Support:**

- a. The support of a membership function for some fuzzy set Ā is defined as that region of the universe that is characterized by nonzero membership in the set Ā,
- b. The support comprises those elements r of the universe such that μ
_{Ā}(x) > 0.

**3. Boundaries: **

- a. The boundaries of a membership function for some fuzzy set Ā are defined as that region of the universe containing elements that have a non-zero membership but not complete membership.
- b. The boundaries comprise those elements x of the universe such that 0< μ
_{Ā}(x) < 1.

**Q2. Define fuzziness of fuzzy set and what is a fuzzy function ?**

**Ans. **

- 1. Fuzziness of a fuzzy set directly comes from the membership function, i.e., height and width of a fuzzy set which correspond to (a) and (b) in Fig., respectively.

- 2. The fuzziness tends to be measured by the following two criteria:
- a. If the height of a fuzzy set is tall, the fuzziness is small.
- b. If the breadth of a fuzzy set is narrow, the fuzziness is small.

- 3. A fuzzy set should be judged to have small fuzziness even when the membership value becomes close to zero
- 4. Since the criterion (a) is not precise enough to represent this fuzziness, the criterion (a) is rewritten as the following criteria (i) and (ii), where (i) is equivalent to (a) and (ii) is newly added.
- i. If the membership value is close to 1, the fuzziness is small.
- ii. If the membership value is close to 0, the fuzziness is small.

- 5. The breadth that the criterion (b) is insufficient for measuring fuzziness. Although the fuzzy set is frequently used to represent utter ignorance, it is difficult to say that the fuzzy set is value. Therefore (b) should be removed from the criteria.
- 6. Finally, criteria (i) and (ii) help to measure the fuzziness of a fuzzy set.

**Fuzzy functions:**

- 1. Fuzzy functions are made up of two parts: a crisp function with a fuzzy constraint and a fuzzifying function.
- 2 Fuzzy function can be classified into following three groups:
- a. Crisp function with fuzzy constraint.
- b. Crisp function which propagates the fuzziness of independent variable to dependent variable.
- c. Function that is itself fuzzy.

**Q3. Given a conditional and qualified Fuzzy proposition ‘P’ of the form P: If x is A, then y is B is S where S is fuzzy truth qualifier and a fact is in the form “x is A” We want to make an inference in the form y is B”. Develop a method based on the truthvalue restrictions for getting the inference. **

**Ans. **1. A conditional and qualified fuzzy proposition is the from

where S is a fuzzy truth qualifier, and a fact is in the from “X is A”, we want to develop an inference in the form “Y is B”.

2. A method of truth-value constraints, created for this aim, is based on the manipulation of linguistic truth values.

3. The method involves the following four steps:

**Step 1:** Calculate the relative fuzzy truth value of A’ with respect to A, denoted by RT(A’ / A), which is a fuzzy set on the unit interval defined by

The relative fuzzy truth value RT(A’ / A) expresses the degree to which the fuzzy proposition (1) is true given the available fact “X is A”.

**Step 2: **Choose a suitable fuzzy implication J by which the fuzzy proposition “If X is A, then y is B is S” is interpreted. This is similar to the selection of fuzzy implication:

whose purpose is to express a conditional but unqualified fuzzy proposition as a fuzzy relation.

**Step 3: **Calculate the relative fuzzy truth value RT(B’ / B) by using the formula:

where S is the fuzzy qualifier as in (1). The role of the qualifier S is to modify the truth value of J(a, b), when S is true (i.e., S(a) = a) for all aє [0,1], then

The relative fuzzy truth value RT (B’/B) expresses the degree to which the conclusion of the fuzzy proposition (1) is true.

**Step 4:** Calculate the set B’ involved in the inference “y is B” by the equation

**Q4. What are the advantages and disadvantages of hybrid fuzzy controller in soft computing ?**

**Ans. Advantage of hybrid fuzzy controller:**

- 1. Similar to human reasoning.
- 2. Based on linguistic model.
- 3. High precision.
- 4. Rapid operation.
- 5. Use simple mathematics for non-linear, integrated and complex systems.

**Disadvantage of hybrid fuzzy controller:**

- 1. No real-time reaction.
- 2. The system’s slower pace and longer run duration.
- 3 The number of input variables that can be used is limited.
- 4. Inability to receive feedback on the application of a learning technique.
- 5. More fuzzy grades are required for greater precision, resulting in an exponential growth in the rule.

**Q5. For an air conditioner what will be the input and output in a fuzzy controller ?**

**Ans. **Various variables for the fuzzy controller are:

**1. Fuzzy input variables:**

**i. User temperature (Ut):**User temperature (Ut) is the temperature provided by the user through remote controller or thermostat. The range of this thermostat should vary between 18 °C and 30 °C. So; the user set the temperature accordingly.**ii. Temperature difference (Td):**Temperature difference (Td) is measure of the difference in the actual room temperature and the temperature which is provided by the user. The difference range is between -6 °C to + 6 °C.**iii. Dew point (TDew):**With constant air pressure, the dew point temperature is the temperature at which water vapour in the air condenses as dew, frost, or water droplets. It is defined as the temperature at which the saturation and real vapour pressures are equal.**iv. Occupancy (Occ):**The amount of persons exposed to the air conditioner is referred to as occupancy. The number of people will determine if the level of occupancy is low, medium, or high. In the absence of people, both the compressor and the fan are turned off. The ranges can be adjusted to suit various settings such as indoor stadiums, auditoriums, and so on.**v. Time of Day (TDay):**The time of day when the air conditioner will be turned on. According to IMD data, the temperature and dew point values vary dramatically between morning/night and afternoon. As a result, the range of requirements for optimal cooling and power consumption can be determined.

**2. Fuzzy output variables: **

**i. Compressor speed (Sc):**The compressor speed can be adjusted from 30% to 100%. As a result, it will modify the room temperature based on the input.**ii. Fan Speed (SD):**The fan speed indicates the speed of the fan inside the air conditioner. The fan speed is thus varied between 30 and 100%.**iii. Mode of Operation (Mo):**The air conditioning system can function as both a cooler and a dehumidifier. It will regulate the air to discharge cool air when in the cooling mode. But, as a dehumidifier, it can absorb the humidity in the air by blowing dry air into the area. This procedure has no effect on the temperature of the room. This setting preference is normally not specified by the user and is handled automatically by the AC. This parameter results in increased efficiency and comfort.**iv. Fin Direction (Fn):**The fins are a set of blades mounted to the air conditioner to provide a consistent flow of air in a specific direction. The direction of these fins determines whether air flows towards or away from the user. The propagation angle of blades is chosen accordingly, with 0° representing “towards” and 90° representing “away.”

**Q6. Explain the industrial applications of fuzzy logic. **

**Ans. Industrial application of fuzzy logic:**

**1. Aerospace:**In aerospace, fuzzy logic is used in the following areas:- i. Altitude control of spacecraft
- ii. Satellite altitude control
- iii. Flow and mixture regulation in aircraft deicing vehicles

**2. Automotive:**In automotive, fuzzy logic is used in the following areas:- i. Shift scheduling method for automatic transmission
- ii. Intelligent highway systems
- iii. Traffic control
- iv. Improving efficiency of automatic transmissions

**3. Business:**In business, fuzzy logic is used in the following areas:- i. Decision-making support systems
- ii. Personnel evaluation in a large company

**4. Defence:**In defence, fuzzy logic is used in the following area:- i. Underwater target recognition
- ii. Automatic target recognition of thermal infrared images
- iii. Control of a hypervelocity interceptor

**5. Electronics:**In electronics, fuzzy logic is used in the following areas:- i. Control of automatic exposure in video cameras
- ii. Air conditioning systems
- iii. Washing machine timing
- iv. Vacuum cleaners

**6. Finance:**In the finance field, fuzzy logic is used in the following areas:- i. Banknote transfer control
- ii. Fund management
- iii. Stock market predictions

**7. Manufacturing:**In the manufacturing industry, fuzzy logic is used in following areas:- i. Optimization of cheese production
- ii. Optimization of milk production

**8. Marine:**In the marine field, fuzzy logic is used in the following areas:- i. Autopilot for ships
- ii. Optimal route selection

**9. Medical:**In the medical field, fuzzy logic is used in the following areas:- i. Medical diagnostic support system
- ii. Control of arterial pressure during anesthesia
- iii. Radiology diagnoses

**10. Securities:**In securities, fuzzy logic is used in following areas:- i. Decision systems for securities trading
- ii. Various security appliances

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