{"title":"Adaptation of Iterative Methods to Solve Fuzzy Mathematical Programming Problems","authors":"Ricardo C. Silva, Luiza A. P. Cantao, Akebo Yamakami","volume":20,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":614,"pagesEnd":620,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6547","abstract":"Based on the fuzzy set theory this work develops two\r\nadaptations of iterative methods that solve mathematical programming\r\nproblems with uncertainties in the objective function and in\r\nthe set of constraints. The first one uses the approach proposed by\r\nZimmermann to fuzzy linear programming problems as a basis and\r\nthe second one obtains cut levels and later maximizes the membership\r\nfunction of fuzzy decision making using the bound search method.\r\nWe outline similarities between the two iterative methods studied.\r\nSelected examples from the literature are presented to validate the\r\nefficiency of the methods addressed.","references":"[1] L. A. ZADEH, \"Fuzzy sets,\" Information and Control, vol. 8, pp. 338-\r\n353, 1965.\r\n[2] R. C. SILVA, L. A. P. CANTA\u2566\u00a3 O, and A. YAMAKAMI, \"Meta-heuristic\r\nto mathematical programming problems with uncertainties,\" in II International\r\nConference on Machine Intelligence, 2005, pp. 306-311.\r\n[3] Y. H. LEE, B. H. YANG, and K. S. MOON, \"An economic machining\r\nprocess model using fuzzy non-linear programming and neural network,\"\r\nInternational Journal Production Research, vol. 37, no. 4, pp. 835-847,\r\n1999.\r\n[4] J.-F. C. TRAPPEY, C. R. LIU, and T.-C. CHANG, \"Fuzzy non-linear\r\nprogramming: Theory and application in manufaturing,\" International\r\nJournal Production Research, vol. 26, no. 5, pp. 975-985, 1988.\r\n[5] C. XU, \"Fuzzy optimization of structures by the two-phase method,\"\r\nComputers & Structures, vol. 31, no. 4, pp. 575-580, 1989.\r\n[6] H. J. ZIMMERMANN, \"Fuzzy mathematical programming,\" Computer\r\n& Operation Research, vol. 10, no. 4, pp. 291-298, 1983.\r\n[7] L. A. P. CANTA\u2566\u00a3 O, \"Programac\u252c\u00a9a\u2566\u00a3o na\u2566\u00a3o-linear com para\u2566\u00e5metros fuzzy,\"\r\nPh.D. dissertation, FEEC - UNICAMP, Campinas, Maro 2003.\r\n[8] G. J. KLIR and B. YUAN, Fuzzy Sets and Fuzzy Logic: Theory and\r\nApplications. New Jersey: Prentice Hall, 1995.\r\n[9] W. PEDRYCS and F. GOMIDE, An Introduction of Fuzzy Sets: Analisys\r\nand Design. A Bardford Book, 1998.\r\n[10] R. E. BELLMAN and L. A. ZADEH, \"Decision-marking in a fuzzy\r\nenvironment,\" Management Science, vol. 17, no. 4, pp. B141-B164, 1970.\r\n[11] R. C. SILVA, \"Contribuic\u252c\u00a9 \u2566\u00a3oes ao estudo de programac\u252c\u00a9 \u2566\u00a3ao n\u2566\u00a3ao-linear com\r\nincertezas,\" Master-s thesis, FEEC - UNICAMP, Campinas, Maio 2005.\r\n[12] K. SCHITTKOWSKI, More Test Examples for Nonlinear Programming\r\nCodes. Spring-Verlag, 1987.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 20, 2008"}