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With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and exactly calculating the inverse credibility distribution of some specific arithmetical operations based on the credibility measure. As an application of the operational law, an equivalent form of the expected value operator as well as a theorem for computing the expected value of strictly monotone functions is suggested. Finally, we utilize the operational law to construct a solution framework of fuzzy programming with parameters of regular LR fuzzy numbers, and such type of fuzzy programming problems can be handled by the operational law as the classic deterministic programming without any particular solving techniques.<\/jats:p>","DOI":"10.3233\/ifs-151712","type":"journal-article","created":{"date-parts":[[2016,1,15]],"date-time":"2016-01-15T12:21:08Z","timestamp":1452860468000},"page":"71-87","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":61,"title":["Fuzzy arithmetic on LR fuzzy numbers with applications to fuzzy programming"],"prefix":"10.1177","volume":"30","author":[{"given":"Jian","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,8,31]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"CharnesA. and CooperW.W. 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