Fuzzy Sets Rough Sets Multisets & Clustering by Vicenç Torra, Anders Dahlbom, Yasuo Narukawa

By Vicenç Torra, Anders Dahlbom, Yasuo Narukawa

This booklet is devoted to Prof. Sadaaki Miyamoto and provides state-of-the-art papers in a few of the components during which he contributed. Bringing jointly contributions via best researchers within the box, it concretely addresses clustering, multisets, tough units and fuzzy units, in addition to their purposes in parts akin to decision-making.

The booklet is split in 4 elements, the 1st of which specializes in clustering and category. the second one half places the highlight on multisets, baggage, fuzzy luggage and different fuzzy extensions, whereas the 3rd bargains with tough units. Rounding out the insurance, the final half explores fuzzy units and decision-making.

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By Vicenç Torra, Anders Dahlbom, Yasuo Narukawa

This booklet is devoted to Prof. Sadaaki Miyamoto and provides state-of-the-art papers in a few of the components during which he contributed. Bringing jointly contributions via best researchers within the box, it concretely addresses clustering, multisets, tough units and fuzzy units, in addition to their purposes in parts akin to decision-making.

The booklet is split in 4 elements, the 1st of which specializes in clustering and category. the second one half places the highlight on multisets, baggage, fuzzy luggage and different fuzzy extensions, whereas the 3rd bargains with tough units. Rounding out the insurance, the final half explores fuzzy units and decision-making.

Show description

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Extra info for Fuzzy Sets Rough Sets Multisets & Clustering

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Otherwise, return to Step 2. Matrix R is called Euclidean if there exists a set of points {y1 , . . , y N } in R N −1 such that Rk,k˜ = yk − yk˜ 22 . The method of bRFCM may fail for non-Euclidean R caused by negative di,k in Step 3 of Algorithm 1. For example, in the case with 2 2 = {−1, 2}, we have {u i,1 }i=1 = {2, −1}, which violates C = 2, m = 2, and {di,1 }i=1 the condition given in Eq. (1). To overcome such the limitation, NEbRFCM is given by the following Algorithm [4]: Algorithm 2 (NEbRFCM [4]) Step 1.

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