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EXAMPLE 2.5 In Section 2.1.1, we noted that there can be many relations on a given set, and we mentioned several for the attribute height. The representa- tion condition has implications for each of these relations. Consider these examples: For the (binary) empirical relation taller than, we can have the numerical relation x> y Then, the representation condition requires that for A taller than B if and only if M(A) > M(B) For the (unary) empirical relation is-tall, we might have the numerical relation 36 Software Metrics any measure M, X>70 The representation condition requires that for any measure M, A is-tall if and only if M(A) > 70 For the (binary) empirical relation much taller than, we might have the numerical relation x>y+15 The representation condition requires that for any measure M, A much taller than B if and only if M(A) > M(B) + 15 For the (ternary) empirical relation x higher than y if sitting on z's shoulders, we could have the numerical relation 0.7x + 0.8z>y The representation condition requires that for any measure M,

EXAMPLE 2.5 In Section 2.1.1, we noted that there can be many relations on a given set, and we mentioned several for the attribute height. The representa- tion condition has implications for each of these relations. Consider these examples: For the (binary) empirical relation taller than, we can have the numerical relation x> y Then, the representation condition requires that for A taller than B if and only if M(A) > M(B) For the (unary) empirical relation is-tall, we might have the numerical relation 36 Software Metrics any measure M, X>70 The representation condition requires that for any measure M, A is-tall if and only if M(A) > 70 For the (binary) empirical relation much taller than, we might have the numerical relation x>y+15 The representation condition requires that for any measure M, A much taller than B if and only if M(A) > M(B) + 15 For the (ternary) empirical relation x higher than y if sitting on z's shoulders, we could have the numerical relation 0.7x + 0.8z>y The representation condition requires that for any measure M,

Database System Concepts
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
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For the empirical and numerical relation system of Example 2.5, write a numerical assignment satisfy the representation condition

example 2.5 in text2_Fenton, Norman - Software Metrics_ A Rigorous and Practical Approach, Third Edition (2014, CRC Press).pdf 

The representation condition requires that for any measure M, A higher than B if sitting on C's shoulders if and only if 0.7M(A) +0.8M(C) > M(B) Consider the actual assignment of numbers M given in Figure 2.5. Wonderman is mapped to the real number 72 (i.e., M(Wonderman) = 72), Frankie to 84 (M(Frankie) = 84), and Peter to 42 (M(Peter) = 42). With this particular mapping M, the four numerical relations hold whenever the four empirical relations hold. For example, • Frankie is taller than Wonderman, and M(Frankie) > M(Wonderman). • Wonderman is tall, and M(Wonderman) = 72 > 70. ● Frankie is much taller than Peter, and M(Frankie) = 84 > 57 = M(Peter) + 15. Similarly Wonderman is much taller than Peter and M(Wonderman) 72 > 57 = M(Peter) + 15. Peter is higher than Frankie when sitting on Wonderman's shoulders, and 0.7M(Peter) + 0.8M(Wonderman) = 87 > 84 = M(Frankie) Since all the relations are preserved in this way by the mapping, we can define the mapping as a measure for the attribute. Thus, if we think of the M FIGURE 2.5 A measurement mapping. = 84 72 42 The Basics of Measurement ■ 37 measure as a measure of height, we can say that Frankie's height is 84, Peter's is 42, and Wonderman's is 72. M(Wonderman) = 72 M(Frankie) = 84 Not every assignment satisfies the representation condition. For instance, we could define the mapping in the following way: M(Peter) = 60
Transcribed Image Text:The representation condition requires that for any measure M, A higher than B if sitting on C's shoulders if and only if 0.7M(A) +0.8M(C) > M(B) Consider the actual assignment of numbers M given in Figure 2.5. Wonderman is mapped to the real number 72 (i.e., M(Wonderman) = 72), Frankie to 84 (M(Frankie) = 84), and Peter to 42 (M(Peter) = 42). With this particular mapping M, the four numerical relations hold whenever the four empirical relations hold. For example, • Frankie is taller than Wonderman, and M(Frankie) > M(Wonderman). • Wonderman is tall, and M(Wonderman) = 72 > 70. ● Frankie is much taller than Peter, and M(Frankie) = 84 > 57 = M(Peter) + 15. Similarly Wonderman is much taller than Peter and M(Wonderman) 72 > 57 = M(Peter) + 15. Peter is higher than Frankie when sitting on Wonderman's shoulders, and 0.7M(Peter) + 0.8M(Wonderman) = 87 > 84 = M(Frankie) Since all the relations are preserved in this way by the mapping, we can define the mapping as a measure for the attribute. Thus, if we think of the M FIGURE 2.5 A measurement mapping. = 84 72 42 The Basics of Measurement ■ 37 measure as a measure of height, we can say that Frankie's height is 84, Peter's is 42, and Wonderman's is 72. M(Wonderman) = 72 M(Frankie) = 84 Not every assignment satisfies the representation condition. For instance, we could define the mapping in the following way: M(Peter) = 60
EXAMPLE 2.5 In Section 2.1.1, we noted that there can be many relations on a given set, and we mentioned several for the attribute height. The representa- tion condition has implications for each of these relations. Consider these examples: For the (binary) empirical relation taller than, we can have the numerical relation x> y Then, the representation condition requires that for any measure M, A taller than B if and only if M(A) > M(B) For the (unary) empirical relation is-tall, we might have the numerical relation 36 Software Metrics x > 70 The representation condition requires that for any measure M, A is-tall if and only if M(A) > 70 For the (binary) empirical relation much taller than, we might have the numerical relation x>y+15 The representation condition requires that for any measure M, A much taller than B if and only if M(A) > M(B) + 15 For the (ternary) empirical relation x higher than y if sitting on z's shoulders, we could have the numerical relation 0.7x + 0.8z>y The representation condition requires that for any measure M,
Transcribed Image Text:EXAMPLE 2.5 In Section 2.1.1, we noted that there can be many relations on a given set, and we mentioned several for the attribute height. The representa- tion condition has implications for each of these relations. Consider these examples: For the (binary) empirical relation taller than, we can have the numerical relation x> y Then, the representation condition requires that for any measure M, A taller than B if and only if M(A) > M(B) For the (unary) empirical relation is-tall, we might have the numerical relation 36 Software Metrics x > 70 The representation condition requires that for any measure M, A is-tall if and only if M(A) > 70 For the (binary) empirical relation much taller than, we might have the numerical relation x>y+15 The representation condition requires that for any measure M, A much taller than B if and only if M(A) > M(B) + 15 For the (ternary) empirical relation x higher than y if sitting on z's shoulders, we could have the numerical relation 0.7x + 0.8z>y The representation condition requires that for any measure M,
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