In metallurgy, materials are made with mixtures of various metals and other elements to achieve certain desirable properties. In a particular preparation of steel, three elements, namely, iron, manganese, and carbon, are mixed in two different proportions. The samples obtained from these two different proportions are placed on a normalized scale, as shown in Figure P4.9 and are represented as fuzzy sets Aj and A2. You are interested in finding some sort of "average" steel proportion. For the logical union of the membership functions shown, we want to find the defuzzified quantity. For each of the seven methods presented in this chapter, assess (a) whether each is applicable and, if so, (b) calculate the defuzzified value, z".

In metallurgy, materials are made with mixtures of various metals and other elements to achieve certain desirable properties. In a particular preparation of steel, three elements, namely, iron, manganese, and carbon, are mixed in two different proportions. The samples obtained from these two different proportions are placed on a normalized scale, as shown in Figure P4.9 and are represented as fuzzy sets Aj and A2. You are interested in finding some sort of "average" steel proportion. For the logical union of the membership functions shown, we want to find the defuzzified quantity. For each of the seven methods presented in this chapter, assess (a) whether each is applicable and, if so, (b) calculate the defuzzified value, z".

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

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Question

4.9. In metallurgy, materials are made with mixtures of various metals and other
elements to achieve certain desirable properties. In a particular preparation of steel,
three elements, namely, iron, manganese, and carbon, are mixed in two different
proportions. The samples obtained from these two different proportions are placed
on a normalized scale, as shown in Figure P4.9 and are represented as fuzzy sets
Aj and A2. You are interested in finding some sort of "average" steel proportion.
For the logical union of the membership functions shown, we want to find the
defuzzified quantity. For each of the seven methods presented in this chapter, assess
(a) whether each is applicable and, if so, (b) calculate the defuzzified value, z".
1
A1
0.5
0.5
A2
3
4
5
6.
3
4
5
(a)
(b)
FIGURE P4.9

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