| Summary: | 博士 === 大葉大學 === 電機工程學系 === 103 === In conventional fuzzy expert systems, the implication and composition steps require the excessive operations and spatial complexity using compositional rule based inference (CRI) and individual rule based inference (IRI). This thesis proposes three novel methods, sort compositional rule-based inference (SCRI), sort individual rule based inference 1 (SIRI1) and sort individual rule based inference 2 (SIRI2), aimed at reducing both temporal and spatial complexity by changing the implication and composition steps. The first method, SCRI, is an improvement of CRI in the implication step, which shows the time complexity in fuzzy expert systems as follows:
SISO r-rules: the CRI implication time complexity requires will be decreased to with n is the element of input, m is the element of output.
MISO single-rule-N-input: the CRI implication time complexity requires will be decreased to with nI is the element of the Ith input, m is the element of output.
MISO r-rule-N-input: the CRI implication time complexity requires will be decreased to with nI is the element of the Ith input, I=1,2,…,N, m is the element of output.
MIMO single-rule-N-input-M-output: the CRI implication time complexity requires will be decreased to with nI is the element of the Ith input, mJ is the element of the Jth output, J=1,2,…,M.
MIMO r-rules-N-input-M-output: the CRI implication time complexity requires will be decreased to
The second method, SIRI1, is an improvement of IRI in the implication step and it shows the time complexity in fuzzy expert systems as follows:
SISO r-rules: the IRI implication time complexity requires will be decreased to with n is the element of input, m is the element of output.
MISO single-rule-N-input: the IRI implication time complexity requires will be decreased to with nI is the element of the Ith input, m is the element of output.
MISO r-rule-N-input: the IRI implication time complexity requires will be decreased to with nI is the element of the Ith input, I=1,2,…,N, m is the element of output.
MIMO single-rule-N-input-M-output: the IRI implication time complexity requires will be decreased to with nI is the element of the Ith input, mJ is the element of the Jth output, J=1,2,…,M.
MIMO r-rules-N-input-M-output: the IRI implication time complexity requires will be decreased to
The third one, SIRI2, is an improvement of IRI in the implication and composition steps and it shows the time complexity in fuzzy expert systems as follows:
SISO r-rules: the IRI implication and composition time complexity require will be decreased to with n is the element of input, m is the element of output.
MISO single-rule-N-input: the IRI implication and composition time complexity require will be decreased to with nI is the element of the Ith input, m is the element of output.
MISO r-rule-N-input: the IRI implication and composition time complexity require will be decreased to with nI is the element of the Ith input, I=1,2,…,N, m is the element of output.
MIMO single-rule-N-input-M-output: the IRI implication and composition time complexity require will be decreased to with nI is the element of the Ith input, mJ is the element of the Jth output, J=1,2,…,M.
MIMO r-rules-N-input-M-output: the IRI implication and composition time complexity require will be decreased to
We compared 5 methods to one another in fuzzy expert systems and we showed that SIRI2 is the best of all in both time and space complexity. We also used a divide-and-conquer technique, called Quicksort, to verify the accuracy of SCRI, SIRI1 and SIRI2 algorithms deployment to easily outperform the CRI and IRI methods.
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