Type-Reduction of General Type-2 Fuzzy Sets: The Type-1 OWA Approach

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Abstract
For general type-2 fuzzy sets, the defuzzification process is very complex and the exhaustive direct method of implementing type-reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type-2 fuzzy inferencing systems in real-world applications. The present situation will not be expected to change, unless an efficient and fast method of deffuzzifying general type-2 fuzzy sets emerges. Type-1 ordered weighted averaging (OWA) operators have been proposed to aggregate expert uncertain knowledge expressed by type-1 fuzzy sets in decision making. In particular, the recently developed alpha-level approach to type-1 OWA operations has proven to be an effective tool for aggregating uncertain information with uncertain weights in real-time applications because its complexity is of linear order. In this paper, we prove that the mathematical representation of the type-reduced set (TRS) of a general type-2 fuzzy set is equivalent to that of a special case of type-1 OWA operator. This relationship opens up a new way of performing type reduction of general type-2 fuzzy sets, allowing the use of the alpha-level approach to type-1 OWA operations to compute the TRS of a general type-2 fuzzy set. As a result, a fast and efficient method of computing the centroid of general type-2 fuzzy sets is realized. The experimental results presented here illustrate the effectiveness of this method in conducting type reduction of different general type-2 fuzzy sets.

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