B.TECH - Semester 7 fuzzy set theory and apllications Question Paper 2019 (jul)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- 706.1 : FUZZY SET THEORY AND APPLICATIONS (FR) (Elective II) Time : 3 Hours Max. Marks : 100 PART - A Answer all questions. Each question carries 4 marks. :
- (a) Considering the fuzzy sets $\underset{\sim}{A}, \underset{\sim}{B}$ and defined on the universe $X$, write the function theoretic form of the fuzzy set operation that can be defined for the fuzzy sets $A, B$ and $\underset{\sim}{C}$.
- (b) Draw the Venn-diagram for the fuzzy set operations.
- "The representation of imprecise data as fuzzy sets is a useful but not mandatory step when those data are used in fuzzy systems". Explain the meaning of this statement with the help of following diagram (a)
- "The representation of imprecise data as fuzzy sets is a useful but not mandatory step when those data are used in fuzzy systems". Explain the meaning of this statement with the help of following diagram (b) PART - B Answer any one full question fr...
- (a) Develop a reasonable membership function for the following fuzzy sets based on setting times, in minutes, of epoxies :
- (i) "extra fast", (ii) "fast", (iii) "slow."
- (b) How do you map classical sets to functions? Give Example.
- (c) Discuss the properties of fuzzy sets with the following example fuzzy sets. $$ \begin{aligned} & A=\left\{\frac{0.15}{1}+\frac{0.25}{2}+\frac{0.6}{3}+\frac{0.9}{4}\right\} \\ & \underset{\sim}{B}=\left\{\frac{0.2}{1}+\frac{0.3}{2}+\frac{0.5}{3}+...
- (d) Prove that following axioms of classical sets are not valid for fuzzy sets
- (i) Axiom of excluded middle (ii) Axiom of contradiction. OR
- (a) Compare and contrast classical sets and fuzzy sets.
- (b) Compare and contrast classical relations and fuzzy relations.
- (c) Discuss the operations and properties of crisp relations.
- (a) Discuss the different forms of membership functions.
- (b) Using your own intuition, develop fuzzy membership functions on the real line for the fuzzy number "approximately 2 or approximately 8 " using the . following function shapes:
- (i) symmetric triangles (ii) trapezoids (iii) Gaussian functions. (12)
- List the six straightforward methods in the literature to assign membership values or functions to fuzzy variables. Explain any four methods with simple illustrations. (20)
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Two fuzzy sets $A$ and $\underset{\sim}{B}$, both defined on $X$, are as follows : | $\mu\left(x_{i}\right)$ | $x_{1}$ | $x_{2}$ | $x_{3}$ | $x_{4}$ | $x_{5}$ | $x_{6}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | $\underset{\sim}{A}...
- Verify with an example the $\lambda$-cuts on fuzzy relations obey the following properties (a) $(\underset{\sim}{R} \cup \underset{\sim}{S})_{\lambda}=R_{\lambda} \cup S_{\lambda}$
- Verify with an example the $\lambda$-cuts on fuzzy relations obey the following properties (b) $(\underset{\sim}{R \cap S})_{\lambda}=R_{\lambda} \cap S_{\lambda}$
- Verify with an example the $\lambda$-cuts on fuzzy relations obey the following properties (c) $(\underset{\sim}{R}) \lambda \neq \bar{R}_{\sim}$
- Verify with an example the $\lambda$-cuts on fuzzy relations obey the following properties (d) For any $\lambda \leq \alpha, 0 \leq \alpha \leq 1$, then $R_{\alpha} \subseteq R_{\lambda}$.
- Explain how fuzzy logic can be used for clustering.
- (a) Considering the following similarity relation $$ \underset{\sim}{R}=\left[\begin{array}{ccccc} 1 & 0.8 & 0 & 0.1 & 0.2 \\
- 8 & 1 & 0.4 & 0 & 0.9 \\ 0 & 0.4 & 1 & 0 & 0 \\
- 1 & 0 & 0 & 1 & 0.5 \\
- 2 & 0.9 & 0 & 0.5 & 1 \end{array}\right] $$ Perform $\lambda$-cut operations for the values of $\lambda=0,0.9,1$. (b) Discuss the following methods for defuzzifying fuzzy output functions
- 2 & 0.9 & 0 & 0.5 & 1 \end{array}\right] $$ Perform $\lambda$-cut operations for the values of $\lambda=0,0.9,1$. (i) Mean max membership method (ii) Centre of largest area method.
- (a) Show that any $\lambda$-cut relation (for $\lambda>0$ ) of a fuzzy tolerance relation results in a crisp tolerance relation.
- (b) For the propositions P and Q , generate a truth table to show various logical connectives between them.
- (c) Write short notes on Tautologies.
- (a) List and discuss two real time applications where fuzzy logic is useful.
- (b) Discuss the overview of fuzzy controller.
- Discuss the following : (a) Fuzzy neural networks OR
- Discuss the following : (b) Fuzzy clustering. ( $\mathbf{4} \boldsymbol{\times} \mathbf{2 0} \boldsymbol{=} \mathbf{8 0}$ marks)