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3.1 Fuzzy Logic (FL)

Essentially, Fuzzy Logic (FL) is a multi-valued logic that allows middle values to be

defined between conventional evaluations like yes/no, true/false, black/white, etc.

Fuzzy Logic was introduced in 1965 by Prof. L. Zadeh at the University of California,

Berkeley [9]. The basic notion of fuzzy systems is a fuzzy set. for example, to classify

the fuzzy set of climate, which may be consisted of members like “Very cold”,

“Cold”, “Warm”, “Hot”, and “Very hot”. The theory of fuzzy sets enables us to struc-

ture and describe activities and observations, which differ from each other only

vaguely, to formulate them in models and to use these models for various purposes -

such as problem-solving and decision-making [9]. Suppose that µS(x) (or µ(S, x)) is

the degree of membership of x in set S that 0 ≤ µS(x) ≤1

µS(x) = 0 x is not at all in S,

µS(x) = 1 x is fully in S,

If µS(x) = 0 or 1, then the set S is crisp.

For example, pay attention to the diagram 1 (Fig. 1).

What is the meaning of 75 in diagram? We analyze this question as following:

A node that finished successfully 75% of its submitted jobs has simultaneously

Low, Medium, and High efficiency in various degrees. For example, it can be inter-

pret as 0.2 Low efficiency, 0.5 Medium efficiency and 0.3 High efficiency. In other

word, there is much status that needs to use of Fuzzy logic or fuzzy algorithm. For

instance, consider the following scenario:

Low

Medium

High

1.0

ȝ

60

75

90

Fig. 1.
This diagram shows the Node's efficiency

Let's assume that we have to select 3 computing nodes in between 20 existing

nodes. At the first time, efficiency and availability for all nodes is evaluated. Suppose

that 70% of nodes have efficiency in range 85 to 90, and 20% have near to 95 and

10% under 75. Therefore, in this case, the range (85-90) is considered as medium

efficiency and if there are nodes with high efficiency, it is not needed to use medium

efficiency nodes.

We will not discuss fuzzy set such natural extensions here and more about fuzzy

logic can be found in [13].

3.2 Fuzzy Decision Tree Algorithm

This algorithm is a developed version of ID3 that operate on fuzzy set and it will

produce a fuzzy decision tree (FDT). Before this, other researchers [3, 12] considered

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