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The final refracture design applies operational constraints to achieve optimal completion design with highest net present value.
Therefore, for incomplete data update, we prefer the nearest prototype strategy for hard clustering to the optimal completion strategy for fuzzy clustering.
OCSFCM OCSFCM is the algorithm proposed in [9] using the optimal completion strategy for incomplete data updates while clustering in the data space.
In our opinion, the incomplete data update approach in the nearest prototype strategy is a special case of that in the optimal completion strategy regardless of fuzziness for the membership of each vector.
As one of the first works, Hathaway and Bezdek [9] developed four different strategies handling incomplete data in fuzzy clustering: the whole data strategy (WDS), the partial distance strategy (PDS), the optimal completion strategy (OCS), the nearest prototype strategy (NPS) similar to OCS except for using the nearest prototypes.
As a kernel-based extension to OCSFCM, a kernel-based fuzzy c-means algorithm (KFCM) was proposed in [27] using a kernel-induced metric in the data space instead of the conventional Euclidean metric and the optimal completion strategy for incomplete data handling.
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Due to the ever-increasing necessity of producing oil reservoirs optimally by improving oil recovery, minimizing water production and better maintenance of reservoir pressure, engineers are plagued with challenges such as optimal completions zones for injectors and producers, optimal flood pattern to adopt and number/type of producers and injectors to use in oil field waterflood development.
Hence, engineers are regularly plagued with challenges such as optimal completions zones for injectors and producers, optimal flood pattern to adopt and number/type of producers and injectors to use in waterflood field development so as to improve oil recovery, but reduce water production.
Again, the two statistics can be carried out independently, yielding A2 · B2 total optimal completions.
□ We next establish two necessary conditions on optimal completions by culling the set of possible adjacencies of any such completion.
□ We are now ready to fully describe the collection of optimal completions when p Π, γ is even.
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