{"title":"New Fuzzy Preference Relations and its Application in Group Decision Making","authors":"Nur Syibrah Muhamad Naim, Mohd Lazim Abdullah, Che Mohd Imran Che Taib, Abu OsmanMd. Tap","volume":30,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":418,"pagesEnd":424,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2189","abstract":"Decision making preferences to certain criteria\r\nusually focus on positive degrees without considering the negative\r\ndegrees. However, in real life situation, evaluation becomes more\r\ncomprehensive if negative degrees are considered concurrently.\r\nPreference is expected to be more effective when considering both\r\npositive and negative degrees of preference to evaluate the best\r\nselection. Therefore, the aim of this paper is to propose the\r\nconflicting bifuzzy preference relations in group decision making by\r\nutilization of a novel score function. The conflicting bifuzzy\r\npreference relation is obtained by introducing some modifications on\r\nintuitionistic fuzzy preference relations. Releasing the intuitionistic\r\ncondition by taking into account positive and negative degrees\r\nsimultaneously and utilizing the novel score function are the main\r\nmodifications to establish the proposed preference model. The\r\nproposed model is tested with a numerical example and proved to be\r\nsimple and practical. The four-step decision model shows the\r\nefficiency of obtaining preference in group decision making.","references":"[1] Atanassov K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems,\r\n110(1986) 87 - 96.\r\n[2] Abu Osman M.T., Conflicting bifuzzy evaluation, Proceeding and\r\nMathematics Symposium (CSMS06). Kolej Universiti Sains dan\r\nTeknologi Malaysia, Kuala Terengganu, Malaysia (8 - 9 Nov 2006) In\r\nMalay.\r\n[3] Deschrijver, G. and Kerre, E. E., 2007, On the position of intuitionistic\r\nfuzzy set theory in the framework of theories modeling imprecision,\r\nInformation Sciences, Accepted Manuscript, doi:\r\n10.1016\/j.ins.2007.03.019 (Printed on May 21, 2007)\r\n[4] Gianpiero C. and David C., Basic intuitionistic principle in fuzzy set\r\ntheories and its extension (A terminological debate on Atanassov IFS),\r\nFuzzy Sets and System, 157(2006) 3198 - 3219.\r\n[5] Herrera, E. Chicl by applying on ana, F., Herrera, F. , Alonso, S. (in\r\npress) . A Group decision making model with incomplete fuzzy\r\npreference relations based on additive consistency, IEEE Transactions\r\non System, Man and Cybernetics-Part B.\r\n[6] Hong D. J. and Choi C. H., Multiciretia fuzzy decisioan - making\r\nproblems based on vague set theory, Fuzzy Sets and Systems, 114(2000)\r\n103 - 113.\r\n[7] Imran, et.al. (2008). A new condition for conflicting bifuzzy sets based\r\non intuitionistic evaluation, International Journal of Computational and\r\nMathematical Sciences, 2(4), 161-165.\r\n[8] Przemyslaw G. and Edyta M., Some notes on (Atanassov-s)\r\nintuitionistic fuzzy sets, Fuzzy Sets and System, 156(2005) 492 - 495.\r\n[9] Saaty TH. L., The Analytic Hierarchy Process (McGraw - Hill, New\r\nYork, 1980)\r\n[10] Szmidt E., Kacprzyk J., Group Decision Making under intuitionistic\r\nfuzzy preference relations, in: Proceeding of 7th IPMU Conference, Paris\r\n(1998), pp. 172 - 178.\r\n[11] Scmidt, E. Kacprzyk. J, (2002). Using intuitionistic fuzzy sets in group\r\ndecision making, Control and Cybernetics 31, 1037-1053.\r\n[12] Tadeusz G. and Jacek M., Bifuzzy probabilistic sets, Fuzzy Sets and\r\nSystems, 71(1995) 207 - 214.\r\n[13] Tamalika C. and Raya A.K., A new measure using intuitionistic fuzzy\r\nset theory and its application to edge detection, Applied Soft Computing,\r\nxxx(2007) xxx-xxx.\r\n[14] Wang J., Zhang J, and Liu S.Y., A new score function for fuzzy MCDM\r\nbased on vague set theory, International Journal of Computational\r\nCognition, Vol. 4, No. 1, (2006)\r\n[15] Xu Z.S., Intuitionistic preference relations and their application in group\r\ndecision making, Information Sciences, 177 (2007) 2363 - 2379.\r\n[16] Zadeh L. A., Fuzzy Sets, Information and Control, 8(1965) 338 - 353.\r\n[17] Zamali T., Lazim Abdullah M., Abu Osman, M.T. (2008). An\r\nintroduction to conflicting bifuzzy set theory, International Journal of\r\nMathematics and Statistics, 3(8), 86 - 95, (ISSN 0973 - 8347).\r\n[18] Zamali T., A novel linguistic aggregation method for group decision\r\nmaking, The 3rd International Conference on Mathematics and Statistics\r\n(ICoMS-3) Institut Pertanian Bogor, Indonesia, 5-6 August (2008).\r\n[19] Zhang, W. R. and Zhang, L., 2004, Yin Yang bipolar logic and bipolar\r\nfuzzy logic, Information Sciences, 165, 265 - 287.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 30, 2009"}