For the empirical and numerical relation system of Example 2.5, write a numerical assignment satisfy the representation conditionexample 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 if0.7M(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 thisparticular mapping M, the four numerical relations hold whenever the fourempirical 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 candefine the mapping as a measure for the attribute. Thus, if we think of theMFIGURE 2.5 A measurement mapping.=847242The Basics of Measurement ■ 37measure as a measure of height, we can say that Frankie's height is 84, Peter'sis 42, and Wonderman's is 72.M(Wonderman) = 72M(Frankie) = 84Not every assignment satisfies the representation condition. For instance,we could define the mapping in the following way:M(Peter) = 60 EXAMPLE 2.5In Section 2.1.1, we noted that there can be many relations on a givenset, and we mentioned several for the attribute height. The representa-tion condition has implications for each of these relations. Consider theseexamples:For the (binary) empirical relation taller than, we can have the numericalrelationx> yThen, 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 numericalrelation36 Software Metricsx > 70The representation condition requires that for any measure M,A is-tall if and only if M(A) > 70For the (binary) empirical relation much taller than, we might have thenumerical relationx>y+15The representation condition requires that for any measure M,A much taller than B if and only if M(A) > M(B) + 15For the (ternary) empirical relation x higher than y if sitting on z's shoulders,we could have the numerical relation0.7x + 0.8z>yThe representation condition requires that for any measure M,

Measurement in empirical and numerical relations is crucial for understanding attributes like…

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,

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Publisher:Wayne L. Winston

Chapter15: Deterministic Eoq Inventory Models

Section15.2: The Basic Economic Order Quantity Model

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