非均衡语言信息的计算方法及其在TOPSIS法中的应用
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摘要
大多用语言描述偏好的决策问题假设语言是均匀、对称分布的,然而有些问题需要采用非均衡语言.针对这一问题,提出一种基于符号化方法的语言计算模型.首先,构造一种基于基础语言集合的加权图,用图形中的点描述非均衡语言;然后,定义图形中任意两点间的曼哈顿距离公式,用于计算非均衡语言的距离;最后,将其用于逼近于理想值的排序方法(TOPSIS),并给出算例.所提出的方法不仅图像化非均衡语言,而且在解决TOPSIS问题时比欧氏距离测度更具优越性.
Many decision problems using linguistic approaches to assess preferences are assumed that the linguistic term set is uniform and symmetrical distributed.However,there exist decision making problems whose assessments are unbalanced linguistic term sets.Theretore,a linguistic computational model based on symbolic models is proposed.Firstly,a weighted graph composed of basic labels is constructed.An unbalanced linguistic label is represented by some vertices in the graph.Then the Manhattan distance measure in the graph of any vertices is defined,with is applived to compute the distance between the two unbalanced linguistic terms.Finally,a decision model is designed to solve the TOPSIS problem.A numerical example is given to illustrate that the proposed method can visualise the unbalanced linguistic term set,and the Manhattan distance is better than the Euclidean distance when solving TOPSIS problems.
Many decision problems using linguistic approaches to assess preferences are assumed that the linguistic term set is uniform and symmetrical distributed.However,there exist decision making problems whose assessments are unbalanced linguistic term sets.Theretore,a linguistic computational model based on symbolic models is proposed.Firstly,a weighted graph composed of basic labels is constructed.An unbalanced linguistic label is represented by some vertices in the graph.Then the Manhattan distance measure in the graph of any vertices is defined,with is applived to compute the distance between the two unbalanced linguistic terms.Finally,a decision model is designed to solve the TOPSIS problem.A numerical example is given to illustrate that the proposed method can visualise the unbalanced linguistic term set,and the Manhattan distance is better than the Euclidean distance when solving TOPSIS problems.
引文
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[18]FalcóE,García-Lapresta J L,RosellóL.Allowing agents to be imprecise:A proposal using multiple linguistic terms[J].Information Sciences,2014,258(2):249-265.
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[20]廖貅武,李垣,董广茂.一种处理语言评价信息的多属性群决策方法[J].系统工程理论与实践,2006,26(9):90-98.(Liao X W,Li Y,Dong G M.A multi-attribute group decision-making approach dealing with linguistic assessment information[J].Systems Engineering—Theory&Practice,2006,26(9):90-98.)
[21]Herrera-Viedma E,Mata F,Martínez L,et al.Measurements of consensus in multi-granular linguistic group decision-making modeling decisions for artificial intelligence[M].Heidelberg:Springer Berlin,2004:194-204.
[2]Dong Y C,Li C C,Herrera F.An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level[J].Information Sciences,2015,292(1):27-38.
[3]Xu Y,Wang H.Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment[J].Applied Soft Computing,2011,11(5):3988-3997.
[4]Xu Z S.Induced uncertain linguistic OWA operators applied to group decision making[J].Information Fusion,2006,7(2):231-238.
[5]Herrera F,Herrera-Viedma E,Martinez L.A fuzzy linguistic methodology to deal with unbalanced linguistic term sets[J].IEEE Trans on Fuzzy Systems,2008,16(2):354-370.
[6]Herrera-Viedma E,López Herrera A G.A model of an information retrieval system with unbalanced fuzzy linguistic information[J].Int J of Intelligent Systems,2007,22(11):1197-1214.
[7]Meng D,Pei Z.On weighted unbalanced linguistic aggregation operators in group decision making[J].Information Sciences,2013,223(2):31-41.
[8]Herrera-Viedma E,Cabrerizo F J,Pérez I J,et al.Applying linguistic OWA operators in consensus models under unbalanced linguistic information[C].Studies in Fuzziness and Soft Computing.Heidelberg:Springer Berlin,2011:167-186.
[9]Cabrerizo F J,Pérez I J,Herrera-Viedma E.Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information[J].Knowledge-Based Systems,2010,23(2):169-181.
[10]Chen Z,Ben-Arieh D.On the fusion of multi-granularity linguistic label sets in group decision making[J].Computers and Industrial Engineering,2006,51(3):526-541.
[11]Herrera F,Herrera-Viedma E,Martinez L.A fusion approach for managing multi-granularity linguistic term sets in decision making[J].Fuzzy Sets and Systems,2000,114(1):43-58.
[12]Dong Y C,Wu Y Z,Zhang H J,et al.Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions[J].Knowledge-Based Systems,2015,82(7):139-151.
[13]Wang B L,Liang J Y,Qian Y H.A normalized numerical scaling method for the unbalanced multi-granular linguistic sets[J].Int J of Uncertainty Fuzziness and Knowledge-Based Systems,2015,23(2):221-243.
[14]Herrera F,Martinez L.A 2-tuple fuzzy linguistic representation model for computing with words[J].IEEE Trans on Fuzzy Systems,2000,8(6):746-752.
[15]姜艳萍,樊治平.基于不同粒度语言判断矩阵的群决策方法[J].系统工程学报,2006,21(3):249-253.(Jiang Y P,Fan Z P.Approach to group decision making with multi-granularity linguistic comparison matrices[J].J of Systems Engineering,2006,21(3):249-253.)
[16]RosellóL,Sánchez M,Agell N,et al.Using consensus and distances between generalized multi-attribute linguistic assessments for group decision-making[J].Information Fusion,2014,17(5):83-92.
[17]Pedrycz W,Song M.Granular fuzzy models:A study in knowledge management in fuzzy modeling[J].Int J of Approximate Reasoning,2012,53(7):1061-1079.
[18]FalcóE,García-Lapresta J L,RosellóL.Allowing agents to be imprecise:A proposal using multiple linguistic terms[J].Information Sciences,2014,258(2):249-265.
[19]Xu M H,Liu Y Q,Huang Q L,et al.An improved Dijkstra’s shortest path algorithm for sparse network[J].Applied Mathematics and Computation,2007,185(1):247-254.
[20]廖貅武,李垣,董广茂.一种处理语言评价信息的多属性群决策方法[J].系统工程理论与实践,2006,26(9):90-98.(Liao X W,Li Y,Dong G M.A multi-attribute group decision-making approach dealing with linguistic assessment information[J].Systems Engineering—Theory&Practice,2006,26(9):90-98.)
[21]Herrera-Viedma E,Mata F,Martínez L,et al.Measurements of consensus in multi-granular linguistic group decision-making modeling decisions for artificial intelligence[M].Heidelberg:Springer Berlin,2004:194-204.
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