{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T07:50:20Z","timestamp":1785916220450,"version":"3.56.0"},"reference-count":46,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,7]],"date-time":"2020-07-07T00:00:00Z","timestamp":1594080000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["NSERC IRCPJ 428226\u201315"],"award-info":[{"award-number":["NSERC IRCPJ 428226\u201315"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Determining contingency reserve is critical to project risk management. Classic methods of determining contingency reserve significantly rely on historical data and fail to effectively incorporate certain types of uncertainties such as vagueness, ambiguity, and subjectivity. In this paper, an interval type-2 fuzzy risk analysis model (IT2FRAM) is introduced in order to determine the contingency reserve. In IT2FRAM, the membership functions for the linguistic terms used to describe the probability, impact of risk and the opportunity events are developed, optimized, and aggregated using interval type-2 fuzzy sets and the principle of justifiable granularity. IT2FRAM is an extension of a fuzzy arithmetic-based risk analysis method which considers such uncertainties and addresses the limitations of probabilistic and deterministic techniques of contingency determination methods. The contribution of IT2FRAM is that it considers the opinions of several subject matter experts to develop the membership functions of linguistic terms. Moreover, the effect of outlier opinions in developing the membership functions of linguistic terms are reduced. IT2FRAM also enables the aggregation of non-linear membership functions into trapezoidal membership functions. A hypothetical case study is presented in order to illustrate the application of IT2FRAM in Fuzzy Risk Analyzer\u00a9 (FRA\u00a9), a risk analysis software.<\/jats:p>","DOI":"10.3390\/a13070163","type":"journal-article","created":{"date-parts":[[2020,7,7]],"date-time":"2020-07-07T10:41:09Z","timestamp":1594118469000},"page":"163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Interval Type-2 Fuzzy Risk Analysis Model (IT2FRAM) for Determining Construction Project Contingency Reserve"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9722-3440","authenticated-orcid":false,"given":"Seyed Hamed","family":"Fateminia","sequence":"first","affiliation":[{"name":"Hole School of Construction Engineering, Department of Civil and Environmental Engineering, University of Alberta, 9211 116 St NW, Edmonton, AB T6G 1H9, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vuppuluri","family":"Sumati","sequence":"additional","affiliation":[{"name":"Hole School of Construction Engineering, Department of Civil and Environmental Engineering, University of Alberta, 9211 116 St NW, Edmonton, AB T6G 1H9, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3744-273X","authenticated-orcid":false,"given":"Aminah Robinson","family":"Fayek","sequence":"additional","affiliation":[{"name":"Hole School of Construction Engineering, Department of Civil and Environmental Engineering, University of Alberta, 9211 116 St NW, Edmonton, AB T6G 1H9, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fateminia, S.H., Siraj, N.B., Fayek, A.R., and Johnston, A. 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