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Order relation on the set of all interval\u2010valued numbers plays key role in the construction and resolution of the interval\u2010valued\u2010parameter fuzzy relation equation (IPFRE). The basic operations supremum (<jats:italic>a<\/jats:italic>\u2228<jats:italic>b<\/jats:italic>) and infimum (<jats:italic>a<\/jats:italic>\u2227<jats:italic>b<\/jats:italic>) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max\u2010<jats:italic>T<\/jats:italic> fuzzy relation equations system.<\/jats:p>","DOI":"10.1155\/2019\/8179763","type":"journal-article","created":{"date-parts":[[2019,2,17]],"date-time":"2019-02-17T23:31:16Z","timestamp":1550446276000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Resolution of Max\u2010Product Fuzzy Relation Equation with Interval\u2010Valued Parameter"],"prefix":"10.1155","volume":"2019","author":[{"given":"Xiaobin","family":"Yang","sequence":"first","affiliation":[]},{"given":"Haitao","family":"Lin","sequence":"additional","affiliation":[]},{"given":"Gang","family":"Xiao","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0228-4476","authenticated-orcid":false,"given":"Huanbin","family":"Xue","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7516-5323","authenticated-orcid":false,"given":"Xiaopeng","family":"Yang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,2,17]]},"reference":[{"volume-title":"Fuzzy Sets, Uncertainty, and Information","year":"1988","author":"Klir G. 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