{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T17:56:32Z","timestamp":1777571792949,"version":"3.51.4"},"reference-count":33,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T00:00:00Z","timestamp":1592179200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In real-world approximation problems, precise input data are economically expensive. Therefore, fuzzy methods devoted to uncertain data are in the focus of current research. Consequently, a method based on fuzzy-rough sets for fuzzification of inputs in a rule-based fuzzy system is discussed in this paper. A triangular membership function is applied to describe the nature of imprecision in data. Firstly, triangular fuzzy partitions are introduced to approximate common antecedent fuzzy rule sets. As a consequence of the proposed method, we obtain a structure of a general (non-interval) type-2 fuzzy logic system in which secondary membership functions are cropped triangular. Then, the possibility of applying so-called regular triangular norms is discussed. Finally, an experimental system constructed on precise data, which is then transformed and verified for uncertain data, is provided to demonstrate its basic properties.<\/jats:p>","DOI":"10.2478\/jaiscr-2020-0018","type":"journal-article","created":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T10:56:44Z","timestamp":1598612204000},"page":"271-285","source":"Crossref","is-referenced-by-count":26,"title":["Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems"],"prefix":"10.2478","volume":"10","author":[{"given":"Janusz T.","family":"Starczewski","sequence":"first","affiliation":[{"name":"Department of Computational Intelligence , Czestochowa University of Technology , al. Armii Krajowej 36, 42-200 Cz\u0119stochowa , Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Goetzen","sequence":"additional","affiliation":[{"name":"Information Technology Institute , University of Social Sciences , 90-113 \u0141\u00f3dz , and Clark University Worcester, MA 01610, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Napoli","sequence":"additional","affiliation":[{"name":"Department of Computer, Control and Management Engineering , Sapienza University of Rome , Via Ariosto 25 Roma 00185, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"2026042812101515815_j_jaiscr-2020-0018_ref_001_w2aab3b7b6b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] Almohammadi, K., Hagras, H., Alghazzawi, D., and Aldabbagh, G. 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