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Among these methods, the interval arithmetic approach and the standard approximation method are the most important and commonly used exact and approximate methods, respectively. In this paper, regarding the continuous and strictly monotone functions of triangular fuzzy numbers, we propose an inverse distribution approach to deriving the exact or well approximate membership functions for arithmetic results by embedding the credibility measure of fuzzy sets into fuzzy arithmetic. Besides, some non-complicated and complicated examples are given to illustrate the performance of the new approach, together with a detailed comparison with the interval arithmetic approach and the standard approximate method. Furthermore, the inverse distribution approach is also applied to the fuzzy system reliability calculation based on fault tree compared with several current related researches.<\/jats:p>","DOI":"10.3233\/jifs-172186","type":"journal-article","created":{"date-parts":[[2018,8,5]],"date-time":"2018-08-05T06:40:09Z","timestamp":1533451209000},"page":"3359-3374","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Arithmetic operations on triangular fuzzy numbers via credibility measures: An inverse distribution approach"],"prefix":"10.1177","volume":"35","author":[{"given":"Xuehui","family":"Xie","sequence":"first","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}]},{"given":"Yuanyuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China"}]},{"given":"Yujie","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}]},{"given":"Jian","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}]}],"member":"179","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151615"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.03.012"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2017.03.040"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90004-3"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2004.12.026"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(03)00139-1"},{"issue":"3","key":"e_1_3_2_8_2","first-page":"9","article-title":"Arithmetic of triangular fuzzy variable from credibility theory","volume":"2","author":"Chutia R.","year":"2011","unstructured":"ChutiaR., MahantaS. and DattaD., Arithmetic of triangular fuzzy variable from credibility theory, International Journal of Energy, Information and Communications 2(3) (2011), 9\u201320.","journal-title":"International Journal of Energy, Information and Communications"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.02.005"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207727808941724"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2012.10.003"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00140-1"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.06.007"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2010.05.010"},{"key":"e_1_3_2_15_2","volume-title":"Introduction to Fuzzy Arithmetic-theory and Applications","author":"Kaufmann A.","year":"1991","unstructured":"KaufmannA., GuptaM.M., Introduction to Fuzzy Arithmetic-theory and Applications, Van Nostrand Reinhold Company, New York, 1991."},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.06.036"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2010.520043"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1781-2"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-39987-2"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.800692"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2004.840098"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.06.009"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2014.04.013"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(90)90154-X"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2013.10.048"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0261-5177(01)00050-4"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-152173"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2012.01.007"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"e_1_3_2_31_2","unstructured":"ZadehL.A. 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