Assignment of items to multiple categories requires suitable statistical methods. The present paper provides a new approach to solve this task. The concept of fuzzy sets is extended to cover sets (sets of overlapping clusters) in a simple manner introducing a vector of item membership sums. The application of the new concept is exemplified by modifying the fuzzy cluster analysis algorithm of Kaufman and Rousseeuw (Finding groups in data: an introduction to cluster analysis, 1990) to cover set cluster analysis appropriately. Wide equivalence of the numerical problems is demonstrated from Lagrange multipliers and Karush-Kuhn-Tucker conditions. Additionally, some extensions are introduced to the algorithm to improve its behavior for suboptimal large or small numbers of clusters. The adapted algorithm in most cases reproduces single sortings for correct numbers of clusters. Two applications to empirical free fuzzy sorting data sets are provided. Limitations of the algorithm are discussed.
Quality & Quantity – Springer Journals
Published: Apr 23, 2011
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera