{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T12:28:48Z","timestamp":1777724928350,"version":"3.51.4"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T00:00:00Z","timestamp":1635379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study discusses how to fuzzify a feedforward neural network (FNN) to generate a fuzzy forecast that contains the actual value, while minimizing the average range of fuzzy forecasts. This topic has rarely been investigated in past studies, but is an essential step to constructing a precise fuzzy FNN (FFNN). Existing methods fuzzify all parameters at the same time, which re-sults in a nonlinear programming (NLP) problem that is not easy to solve. In contrast, in this study, the parameters of a FNN are fuzzified independently. In this way, the optimal values of fuzzy parameters can be derived theoretically. An illustrative example is used to illustrate the ap-plicability of the proposed methodology. According to the experimental results, fuzzifying the thresholds on hidden-layer nodes or the connection weights between input and hidden layers may not guarantee that all fuzzy forecasts contain the corresponding actual values. In contrast, fuzzi-fying the threshold on the output node and the connection weights between the hidden and out-put layers is more likely to achieve a 100% hit rate. The results lay a foundation for establishing a precise deep FFNN in the future.<\/jats:p>","DOI":"10.3390\/axioms10040282","type":"journal-article","created":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T23:50:28Z","timestamp":1635465028000},"page":"282","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Constructing a Precise Fuzzy Feedforward Neural Network Using an Independent Fuzzification Approach"],"prefix":"10.3390","volume":"10","author":[{"given":"Hsin-Chieh","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Management, Chaoyang University of Science and Technology, Taichung 413310, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tin-Chih Toly","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, National Yang Ming Chiao Tung University, 1001, University Road, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6938-2391","authenticated-orcid":false,"given":"Min-Chi","family":"Chiu","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411030, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,28]]},"reference":[{"key":"ref_1","unstructured":"Ishibuchi, H., Tanaka, H., and Okada, H. 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