|
|
|
| Linguistic Interval-Valued Intuitionistic Fuzzy Frank Operators |
| LIU Limei1, GONG Yinli1, YANG Yi1, WU Shaozhi2 |
1. Key Laboratory of Hunan Province for New Retail Virtual Reality Technology, Hunan University of Technology and Business, Changsha 410205;
2. School of Computer Science and Engineering, University of Elec-tronic Science and Technology of China, Chengdu 611731 |
|
|
|
|
Abstract Aiming at the aggregation problem of linguistic interval-valued intuitionistic fuzzy information, Frank aggregation operator is proposed. A group decision-making method is constructed to solve the problem of supplier selection. Firstly, linguistic interval-valued intuitionistic fuzzy Frank operational laws are defined by introducing the extended Frank t-norms and s-norms, and linguistic interval-valued intuitionistic fuzzy Frank weighted averaging (LIVIFFWA) operator and geometric (LIVIFFWG) operator are proposed. Secondly, some properties of these operators are proved, such as idempotency, closeness and monotonicity, and the degeneracy of these operators with respect to parameters is analyzed. Then, based on the proposed LIVIFFWA operators and LIVIFFWG operators, a linguistic interval-valued intuitionistic fuzzy multi-attribute group decision-making method is constructed to solve the supplier decision-making problem. Finally, the feasibility and flexibility of the decision-making method are demonstrated through the case analysis of the selection of suppliers with shared bicycle recycling. The influence of parameter variation on decision-making results is discussed, and the ability of parameters to represent and feed back the attitudes of decision makers is verified.
|
|
Received: 27 March 2020
|
|
|
| Fund:Supported by National Social Science Foundation of China(No.18BGL181) |
| About author:: (LIU Limei, Ph.D., professor. Her research interests include logistics management and artificial intelligence.);(GONG Yinli, master student. Her research interests include intelligent logistics and emergency decision-making.);(YANG Yi(Corresponding author), Ph.D., lecturer. His research interests include intelligent decision-making and computing with words.);(WU Shaozhi, Ph.D., associate professor. His research interests include data mining and its application.) |
|
|
|
[1] ZADEH L A. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning. Information Sciences, 1975, 8(3): 199-249.
[2] HERRERA F, MARTINEZ L. A 2-Tuple Fuzzy Linguistic Representation Model for Computing with Words. IEEE Transactions on Fuzzy Systems, 2000, 8(6): 746-752.
[3] XU Z S. Deviation Measures of Linguistic Preference Relations in Group Decision Making. Omega, 2005, 33(3): 249-254.
[4] WANG J H, HAO J Y. A New Version of 2-Tuple Fuzzy Linguistic Representation Model for Computing with Words. IEEE Transactions on Fuzzy Systems, 2006, 14(3): 435-445.
[5] RODRIGUEZ R M, MARTINEZ L, HERRERA F. Hesitant Fuzzy Linguistic Term Sets for Decision Making. IEEE Transactions on Fuzzy Systems, 2012, 20(1): 109-119.
[6] ZHANG G Q, DONG Y C, XU Y F. Consistency and Consensus Measures for Linguistic Preference Relations Based on Distribution Assessments. Information Fusion, 2014, 17: 46-55.
[7] WU Z B, XU J P. Possibility Distribution-Based Approach for MAGDM with Hesitant Fuzzy Linguistic Information. IEEE Transactions on Cybernetics, 2016, 46(3): 694-705.
[8] CHEN Z S, CHIN K S, LI Y L, et al. Proportional Hesitant Fuzzy Linguistic Term Set for Multiple Criteria Group Decision Making. Information Sciences, 2016, 357: 61-87.
[9] PANG Q, WANG H, XU Z S. Probabilistic Linguistic Term Sets in Multi-attribute Group Decision Making. Information Sciences, 2016, 369: 128-143.
[10] ZHANG Z, GUO C H, MARTÍNEZ L. Managing Multi-granular Linguistic Distribution Assessments in Large-Scale Multi-attribute Group Decision Making. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2017, 47(11): 3063-3076.
[11] 王洪东,侯雪辉,高蕴慧,等.基于语言值有序对三元组的多类型数据标准化方法.模式识别与人工智能, 2019, 32(3): 278-286.
(WANG H D, HOU X H, GAO Y H, et al. Unification of Multiple Class Data Based on Linguistic Ordered Pair 3-Tuple. Pattern Recognition and Artificial Intelligence, 2019, 32(3): 278-286.)
[12] 邹 丽,罗思元,史园园,等.基于语言值格蕴涵代数的偏好顺序结构评估决策方法.模式识别与人工智能, 2018, 31(4): 347-357.
(ZOU L, LUO S Y, SHI Y Y, et al. PROMETHEE Decision Method Based on Linguistic-Valued Lattice Implication Algebra. Pattern Recognition and Artificial Intelligence, 2018, 31(4): 347-357.)
[13] WANG J, WANG J Q, TIAN Z P, et al. A Multihesitant Fuzzy Linguistic Multicriteria Decision-Making Approach for Logistics Outsourcing with Incomplete Weight Information. International Transactions in Operational Research, 2018, 25(3): 831-856.
[14] AMORIM P, CURCIO E, ALMADA-LOBO B, et al. Supplier Selection in the Processed Food Industry under Uncertainty. Euro-pean Journal of Operational Research, 2016, 252(3): 801-814.
[15] 冯向前,刘 琦,魏翠萍.基于犹豫模糊二元语义的多属性决策方法.运筹与管理, 2018, 27(1): 17-22.
(FENG X Q, LIU Q, WEI C P. Hesitant Fuzzy 2-Tuple Linguistic Multiple Attribute Decision Making Method. Operations Research and Management Science, 2018, 27(1): 17-22.)
[16] 魏翠萍,马 京.犹豫模糊语言群决策的共识性模型.控制与决策, 2018, 33(2): 275-281.
(WEI C P, MA J. Consensus Model for Hesitant Fuzzy Linguistic Group Decision Making. Control and Decision, 2018, 33(2): 275-281.)
[17] 张 笛,孙 涛,高明美,等.多重偏好序下的复杂产品主制造商-供应商多阶段双边匹配方法.计算机集成制造系统, 2018, 24(3): 804-812.
(ZHANG D, SUN T, GAO M M, et al. Multi-stage Two-Sided Matching Method for Main Manufacturer and Suppliers of Complex Products with Multi-form Preference Ordinal. Computer Integrated Manufacturing Systems, 2018, 24(3): 804-812.)
[18] 牟能冶,常建鹏,陈振颂.基于PD-HFLTS与群决策理论的可持续供应商选择.计算机集成制造系统, 2018, 24(5): 1261-1278.
(MOU N Y, CHANG J P, CHEN Z S. Sustainable Supplier Selection Based on PD-HFLTS and Group Decision-Making Theory. Computer Integrated Manufacturing Systems, 2018, 24(5): 1261-1278.)
[19] 郭 钧,朱文豪,杜百岗,等.考虑协同效应的复杂产品系统绿色供应商多阶段选择方法[J/OL]. [2020-03-04]. http://kns.cnki.net/kcms/detail/11.5946.tp.20190301.1025.010.html.
(GUO J, ZHU W H, DU B G, et al. Multi-stage Green Supplier Selection for Complex Product System Considering Synergetic Effect. [J/OL].[2020-03-04]. http://kns.cnki.net/kcms/detail/11.5946.tp.20190301.1025.010.html.)
[20] TORRA V. Hesitant Fuzzy Sets. International Journal of Intelligent Systems, 2010, 25(6): 529-539.
[21] ZHANG H M. Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM[J/OL]. [2020-03-04]. http://downloads.hindawi.com/journals/jam/2014/432092.pdf.
[22] CHEN Z C, LIU P H, PEI Z. An Approach to Multiple Attribute Group Decision Making Based on Linguistic Intuitionistic Fuzzy Numbers. International Journal of Computational Intelligence Systems, 2015, 8(4): 747-760.
[23] ATANASSOV K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96.
[24] LIU P D, QIN X Y. Power Average Operators of Linguistic Intuitionistic Fuzzy Numbers and Their Application to Multiple-Attri-bute Decision Making. Journal of Intelligent and Fuzzy Systems, 2017, 32(1): 1029-1043.
[25] PENG H G, WANG J Q, CHENG P F. A Linguistic Intuitionistic Multi-criteria Decision-Making Method Based on the Frank Hero-nian Mean Operator and Its Application in Evaluating Coal Mine Safety. International Journal of Machine Learning and Cybernetics, 2018, 9(6): 1053-1068.
[26] LIU P D, LIU J L, MERIGO J M. Partitioned Heronian Means Based on Linguistic Intuitionistic Fuzzy Numbers for Dealing with Multi-attribute Group Decision Making. Applied Soft Computing, 2018, 62: 395-422.
[27] LIU P D, LIU J L. A Multiple Attribute Group Decision-Making Method Based on the Partitioned Bonferroni Mean of Linguistic Intuitionistic Fuzzy Numbers. Cognitive Computation, 2020, 12(1): 49-70.
[28] LIU P D, LIU X X. Linguistic Intuitionistic Fuzzy Hamy Mean Operators and Their Application to Multiple-Attribute Group Decision Making. IEEE Access, 2019, 7: 127728 -127744.
[29] YUAN R P, TANG J, MENG F Y. Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators. International Journal of Fuzzy Systems, 2019, 21(2): 407-420.
[30] XU Z S. Uncertain Linguistic Aggregation Operators Based Approach to Multiple Attribute Group Decision Making under Uncertain Linguistic Environment. Information Sciences, 2004, 168(1/2/3/4): 171-184.
[31] LIU P D, QIN X Y. A New Decision-Making Method Based on Interval-Valued Linguistic Intuitionistic Fuzzy Information. Cognitive Computation, 2019, 11(1): 125-144.
[32] GARG H, KUMAR K. Linguistic Interval-Valued Atanassov Intuitionistic Fuzzy Sets and Their Applications to Group Decision-Ma-king Problems. IEEE Transactions on Fuzzy Systems, 2019, 27(12): 2302-2311.
[33] XIA M M, XU Z S, ZHU B. Some Issues on Intuitionistic Fuzzy Aggregation Operators Based on Archimedean t-Conorm and t-Norm. Knowledge-Based Systems, 2012, 31: 78-88.
[34] QIN J D, LIU X W, PEDRYCZ W. Frank Aggregation Operators and Their Application to Hesitant Fuzzy Multiple Attribute Decision Making. Applied Soft Computing, 2016, 41: 428-452.
[35] 杨 艺,李延来,丁 恒,等.基于同构Frank t-模与s-模的勾股模糊Frank集结算子及其应用.控制与决策, 2018, 33(8): 1471-1480.
(YANG Y, LI Y L, DING H, et al. The Pythagorean Fuzzy Frank Aggregation Operators Based on Isomorphism Frank t-norm and s-norm and Their Application. Control and Decision, 2018, 33(8): 1471-1480.)
[36] TAO Z F, LIU X, CHEN H Y, et al. Using New Version of Extended t-Norms and s-Norms for Aggregating Interval Linguistic Labels. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2016, 47(12): 3284-3298.
[37] XU Z S. A Method Based on Linguistic Aggregation Operators for Group Decision Making with Linguistic Preference Relations. Information Sciences, 2004, 166(1/2/3/4): 19-30.
[38] KLIR G, YUAN B. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River, USA: Prentice Hall, 1995.
[39] GUNASEKARAN A, PATEL C, TIRTIROGLU E. Performance Mea-sures and Metrics in a Supply Chain Environment. International Journal of Operations and Production Management, 2001, 21(1/2): 71-87.
[40] KANNAN G, HAQ A N. Analysis of Interactions of Criteria and Sub-criteria for the Selection of Supplier in the Built-in-Order Su-pply Chain Environment. International Journal of Production Research, 2007, 45(17): 3831-3852.
[41] LA FORME F A G, GENOULAZ V B, CAMPAGNE J P. A Fra-mework to Analyse Collaborative Performance. Computers in Industry, 2007, 58(7): 687-697.
[42] RUSHTON A, CROUCHER P, DR BAKER P. The Handbook of Logistics and Distribution Management: Understanding the Supply Chain. London, UK: Kogan Page, 2014.
[43] CHRISTOPHER M. Logistics and Supply Chain Management: Stra-tegies for Reducing Costs and Improving Services. London, UK: Financial Time Pitman Publishing, 1992.
[44] MEADE L, SARKIS J. A Conceptual Model for Selecting and Evaluating Third-Party Reverse Logistics Providers. Supply Chain Management: An International Journal, 2002, 7(5): 283-295.
[45] RAVI V, SHANKAR R. Analysis of Interactions among the Barriers of Reverse Logistics. Technological Forecasting and Social Change, 2005, 72(8): 1011-1029. |
|
|
|
2020, Vol. 33 
