4.3. The fuzzy sets A, B, and C are all defined on the universe X = [0, 5] with the following membership functions: 2x and µc(x) = 1 HA(x) = HB(x) = 2-*, 1+5(x – 5)2' x +5 (a) Sketch the membership functions. (b) Define the intervals along the x axis corresponding to the à-cut sets for each of the fuzzy sets A, B, and C for the following values of À: (i) 2 = 0.2 (ii) A = 0.6 (iii) A = 0.9 (iv) A = 1.0.

4.3. The fuzzy sets A, B, and C are all defined on the universe X = [0, 5] with the following membership functions: 2x and µc(x) = 1 HA(x) = HB(x) = 2-*, 1+5(x – 5)2' x +5 (a) Sketch the membership functions. (b) Define the intervals along the x axis corresponding to the à-cut sets for each of the fuzzy sets A, B, and C for the following values of À: (i) 2 = 0.2 (ii) A = 0.6 (iii) A = 0.9 (iv) A = 1.0.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

For each pair of atomic sentences, give the most general unifier if it exists: 1. P(N, M, z), P(x, y, N). 2. Q(x, y, M), Q(N, M, x). 3. Knows(y, y), Knows(Father(x), x).
1. Here is a model M:Domain: {1, 2, 3, 4, 5}P : {1, 3, 5}, Q : {2, 4, 5}, R : ∅, S : {3, 4}a : 3, b : 4Is the proposition ∀x((P x ∧ Qx) → Sx) ∨ (Rb ↔ P a) true or false in M? Explain.
The room temperature x in Fahrenheit (F) is converted to y in Celsius (C) through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?
Suppose propositional sentences and knowledge-base here. We have a knowledge-base called KB. KBPrime is defined as an union of (1) KB and (2) the negation of a propositional predicate P. Answer true/false to the following questions. Note that "|=" is used to denote entailment, and "|-" is used to denote derivation through resolution. a) If KB |= P, then KB |- P. That is, if KB entails P, then KB derives (using resolution) P. b) If KB |- P, then KB |= P. c) If KBPrime |- [], then KBPrime is not satisfiable. d) If KBPrime is not satisfiable, then KBPrime |- [].
Consider the following NFA (M1) over the alphabet Σ = {0, 1}: * Attached Image * Two automata M1 and M2 are said to be equivalent if L(M1) = L(M2). In other words, two machines are equivalent if they accept the same string and reject the same strings. Create a new NFA M2 that is equivalent to M1 but does not use any empty (?) transitions. Hint: Define the transition function by δ: Q x Σ -> ?(Q)
This paper deals with Extended Huffman Codes. For instance, for a source emitting two symbols A and B, the second order extension involves coding messages AA, AB, BA and BB (2^2 in number). The third order extension involves messages such as AAA, AAB, etc. (2^3 in number). The probabilities of such strings are computed by multiplying the individual probabilities. Calculate third, fourth and fifth order extensions of a source message. 1. Choose an alphabet a set of at least six (6) symbols with assigned probabilities. It can be assigned as [ A=0.3; B= 0.7; C=0.1;D=0.2;E=0.5;F=0.15]. Compute the third, fourth and fifth order extension probabilities. Using the built-in algorithm, derive the Huffman Code for each extension. Compute the following quantities: (i) Average length of the codeword; (ii) The code efficiency; (iii) The Compression Ratio. Note: I am assuming but needs to be verified that if we need are using 6 symbols A to F. 6^3=216, the 6 to the third power comes…
Fuzzy databases make use of fuzzy set theory. In this theory, any subset ? of a universe ? is represented by a characteristic function ?? that maps ? to _________________. For every element ? ∈ ?, the value ??(?) is interpreted as the degree of confidence that ? ∈ ?. the set {0,1} the interval 0,1 the set ℜ of all real numbers the set ℤ of all integers
Think about the concept of extended transition functions δ* and ∆* of Deterministic Finite Automata and Nondeterministic Finite Automata respectively. Prove the following facts about those functions using mathematical induction. 1. Given a DFA M = (Q, Σ, δ, s0, F) and strings x, y ∈ Σ*, we have δ*(q, xy) = δ*(δ*(q, x), y). 2. Given a NFA N = (Q, Σ, ∆, S0, F), subsets A ⊆ Q, B ⊆ Q and a string x ∈ Σ∗, we have ∆* (A ∪ B, x) = ∆*(A, x) ∪ ∆*(B, x).
Let the Universal set be {a,b,c,d,e,f,g,h,i,j] Consider the subsets A = {a,d,h,i} B= {b,c,d.,f,i,j} C = {a,c,e,f,g,} What is (An B' )'?
1.suppose fuzzy set A is described by ua(x)=bell(x;a,b,c).show that the classical fuzzy component of A is described as ua(x)=bell(x;a,-b,c) 2. Find the level set A(alpha) and its width for a fuzzy set A defined by uA(x)= trapezoid(x;a,b,c,d).
1. If there is such a thing as an empty set, which contains nothing, can there be a “full set” that contains everything? (Y/N) 2. In a bivalent logical system, can a proposition have more than two truth values? (Y/N)
A 2-dimensional Turing machine has an infinite 2-dimensional grid asits storage device (one cell for every address (i, j) ∈Z×Z). Instead ofL and R, there are 5 options for the head to move from (i, j): Left (to(i −1, j), Right (to (i + 1, j)), Up (to (i, j + 1)), Down (to (i, j −1)),and Stay (remain at (i, j)) .Let us assume, that our 2-dimensional TM M has an additional 1-dimensional tape where the input is located as in a 1-tape TM. The2-dimensional storage device contains a blank symbol in every cell atthe start of the computation.Show that a 2-dimensional TM is not more powerful, i.e., every lan-guage accepted by a 2-dimensional TM M is accepted by one of ourstandard 1-dimensional TMs. You don’t have to simulate directly witha 1-tape TM, as you are allowed to use what we know about k-tape(1-dimensional) TMs without proof.Describe the moves of a simulating TM M ′ in plain English. For everypossible move of M , you have to design a sequence of moves of M ′that simulates that move of…