基于决策过程中属性值信息的不确定性以及决策者对收益与损失风险态度的差异,提出了单值中智语言环境下的交互式多属性决策方法(TODIM).首先,利用单值中智语言集量化属性值信息中的不确定度并进一步地描述属性值信息;其次,基于改进后的语言标度函数定义了单值中智语言数的距离测度和集结算子;在此基础上,通过标准差计算属性权重,依据TODIM方法计算各方案的全局优势度并排序;最后,通过节能服务公司的选择案例验证了该方法的可行性与有效性.
Based on the uncertainty of attribute value information and the different risk attitudes of decision-makers towards gain and loss, an extended TODIM(an acronym in Portuguese of interactive and multi-criteria decision making)under single-valued neutrosophic linguistic environment is proposed. First, the uncertainty in attribute value information can be quantified directly by using single-valued neutrosophic language set. Second, based on the extended language scale function, the distance measure and aggregator of single-valued neutrosophic linguistic numbers are defined. Based on these, weights are calculated by standard deviation and ranks are obtained by the TODIM method. Finally, the practical application process of the proposed method is illustrated by the case of energy-saving service company selection, which verifies the feasibility and effectiveness of the method.
[1] SMARANDACHE F. A unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophy probability[M]. Rehoboth:American Research Press, 1999.
[2] ZADEH L A. Fuzzy sets[J]. Inform Control, 1965,8(3): 338-356. DOI: 10.1016/S0019-9958(65)90241-X.
[3] ATANASSOV K. Intuitionistic fuzzy sets[J]. Fuzzy Sets Systems, 1986,20(1): 87-96. DOI: 10.1016/S0165-0114(86)80034-3.
[4] YE J. A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets[J]. Journal of Intelligent & Fuzzy Systems, 2014, 26(5): 2459-2466. DOI: 10.3233/IFS-130916.
[5] WANG H, SMARANDACHE F, ZHANG Y Q, et al. Single valued neutrosophic sets[M]. Multispace Multistruct, 2010: 410-413.
[6] WANG H, SMARANDACHE F, ZHANG Y Q, et al. Interval neutrosophic sets and logic: theory and applications in computing[J].Computer Science, 2005,65(4):1-87.DOI:10.5281/zencdo.8818.
[7] WU X H, WANG J Q, PENG J J, et al. Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems[J]. International Journal of Fuzzy Systems, 2016, 18(6): 1104-1116. DOI:10.1007/s40815-016-0180-2.
[8] ��塁AHIN R. Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making[J]. Neural Computing and Applications, 2017,28(5): 1177-1187. DOI:10.1007/s00521-015-2131-5.
[9] PENG J J, WANG J Q, ZHANG H Y, et al. An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets[J]. Applied Soft Computing, 2014, 25: 336-346. DOI: 10.1016/j.asoc.2014.08.070.
[10] JI P, ZHANG H Y, WANG J Q. Selecting an outsourcing provider based on the combined MABAC-ELECTRE method using single-valued neutrosophic linguistic sets[J]. Computers & Industrial Engineering, 2018, 120: 429-441. DOI: 10.1016/j.cie.2018.05.012.
[11] XIAN S D, DONG Y F, LIU Y B, et al. A novel approach for linguistic group decision making based on generalized interval-valued intuitionistic fuzzy linguistic induced hybrid operator and TOPSIS[J]. International Journal of Intelligent Systems, 2018, 33(2): 288-314. DOI: 10.1016/j.cie.2018.05.012.
[12] 朱轮,杨波.单值中智信息熵及其多属性决策方法[J].计算机工程与应用,2018,54(15):107-111. DOI: 10.3778/j.issn.1002-8331.1712-0192.
[13] ZADEH L A. The concept of a linguistic variable and its application to approximate reasoning:I[J]. Information Sciences 1975, 8(3):199-249. DOI: 10.1016/0020-0255(75)90036-5.
[14] XIAN S D, DONG Y F, LIU Y B, et al. A novel approach for linguistic group decision making based on generalized interval-valued intuitionistic fuzzy linguistic induced hybrid operator and TOPSIS[J]. International Journal of Intelligent Systems, 2018, 33(2):288-314. DOI:10.1002/int.21931.
[15] ZHANG R C, LI Z M, LIAO H C. Multiple-attribute decision-making method based on the correlation coefficient between dual hesitant fuzzy linguistic term sets[J]. Knowledge-based Systems, 2018, 159: 186-192. DOI:10.1016/j.knosys.2018.07.014.
[16] 李海涛,罗党,王洁方.语言型群决策专家信息集结的随机EMD方法[J].统计与决策,2018,34(19):46-50. DOI:10.13546/j.cnki.tjyjc.2018.19.010.
[17] YE J. An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers[J]. Journal of Intelligent & Fuzzy Systems, 2015, 28(1): 247-255. DOI: 10.3233/IFS-141295.
[18] WANG J Q, YANG Y, LI L. Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators[J]. Neural Computing and Applications, 2018,30(5):1529-1547. DOI:10.1007/s00521-016-2747-0.
[19] GOMESL F A M. An application of the TODIM method to the multicriteria rental evaluation of residential properties[J]. European Journal of Operational Research, 2009, 193(1): 204-211. DOI:10.1016/j.ejor.2007.10.046.
[20] DELGADO M, VERDEGAY J L, VILA M A. Linguistic decision-making models[J]. International Journal of Intelligent Systems, 1992, 7(5): 479-492. DOI:10.1002/int.4550070507.
[21] XU Z S. A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision making with linguistic information[J]. Group Decision and Negotiation, 2006, 15(6):593-604. DOI:10.1007/s10726-005-9008-4.
[22] TIAN Z P, WANG J Q, WANG J, et al. Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development[J]. Group Decision and Negotiation, 2017, 26(3):597-627. DOI:10.1007/s10726-016-9479-5.
