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The time complexity is determined by the number of multiplication, division, maximize and minimize operations required In the rst phase (ie, learning feature weights; Section 5411), the feature evaluation index function is differentiable (smooth) and the searching technique used is gradient descent; it can be guaranteed that the training algorithm is convergent if the learning rate is appropriately small The total time complexity of the training algorithm is O m2 , where m is the number of cases In the second phase (ie, partitioning cases into clusters; Section 5412), the clustering algorithm mainly involves multiplication of two similarity matrices Therefore, the time complexity is equal to O m2 The time complexity of the third phase (ie, the mining fuzzy rule using the rough-fuzzy method; Section 541.

This chapter explores four important ethical-legal concepts in the delivery of psychological services in the schools: privacy, informed consent, confidentiality, and privileged communication. School record keeping also is discussed. Privacy, informed consent, confidentiality, and record keeping are discussed together in this chapter because they are ethical-legal concerns that cut across all of the school psychologist s many roles. The chapter closes with a discussion of parent access to test protocols and the use of technology in communication and record keeping.

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Program planning then begins with the input data to be acquired Processing algorithms must be de ned Processing speed must be estimated to see if speed requirements can be met Finally, the way in which output data will be presented to the outside world must be decided Fuzzy control systems nearly always run on-line in real-time If they are relatively simple, compared to more general-purpose data-driven fuzzy reasoning systems, they may be able to do this with few dif culties Data-driven expert production systems are much more exible and powerful than fuzzy control systems, but tend to run more slowly Examples of noncontrol on-line real-time applications include alarm detection systems and fault detection and diagnosis programs But now that personal computers are very much faster than in the past, this speed disadvantage is of less importance.

3) is the sum of the steps performed by the three tasks In task 1, the time complexity for generating the reduct of the initial fuzzy rule is O nm , where n is the number of features In task 2, the time complexity is O m2 In task 3, the time complexity is O m Note that for the fourth phase (ie, predicting adjustment through reasoning and adaptation; Section 5414) the estimated solution for each case is calculated in the rst step of the case selection process of phase 5 (ie, step 1 of the case selection algorithm) This is shown below, where the computational effort is explained together with that required for the other steps in phase 5 In phase 5 (ie, selecting representative cases; Section 5415), the selection algorithm requires two major computations.

Another disadvantage of production systems for realtime on-line work has been that most non-fuzzy production systems run in serial mode, and keep all data in the computer s memory for backtracking and reference in debugging and explanation Most fuzzy expert systems run in parallel mode, much faster than sequential programs Since parallel programs do not backtrack, it is not necessary to keep all data in memory; this means that parallel systems can run inde nitely without over owing memory FLOPS furnishes an erase ON/OFF command; when erase is ON, data that a program no longer needs are removed from memory, and the space is returned to the operating system..

The rst step involves computing the case coverage in each cluster; on average this requires m=M m=M 1 m p operations, where m is the number of cases, M the number of clusters, m the average number of fuzzy adaptation rules for each case, and p the average number of antecedents in each rule Since m and p are very small compared with m, the complexity of step 1 in the selection algorithm is O m2 Steps 2 and 3 involve sorting the cases according to their coverage ability, and the computation complexity will not exceed O m2 Therefore, the overall computation complexity of the selection algorithm in this phase is also bounded by O m2 The space complexity is determined by the size of the case base and the temporary storage required in each phase described in Section 541.

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