一维混合模糊软集及其决策应用
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摘要
大数据时代,现实决策面对的信息形态非常复杂,数据获取渠道多元,表达方式多样。文章针对以混合态进行模糊信息表达的软集决策问题,通过界定一维混合模糊软集将混合模糊信息融入统一的决策框架;提出基于距离定位的规格化策略以实现多型混合模糊数之间的相对融合;应用相似度量策略对水平软集决策方法进行强化,在保证决策过程均衡、柔性的同时,提升了对决策方案的分辨能力。最后通过相应实例对模型及决策方法进行了验证。
In the era of big data, the information form faced by realistic decision-making is very complex, with multiple data acquisition channels and diverse ways of expression. Aiming at the soft-set decision making based on fuzzy information representation in mixed state, this paper firstly blends fuzzy information into a unified decision framework by defining a one-dimension hybrid fuzzy soft set, and proposes the normalization strategy based on distance location to realize the relative fusion of polymorphic mixed fuzzy numbers. Then the paper uses the similarity measurement strategy to strengthen the level soft set decision making method, which not only ensures the balance and flexibility of the decision making process, but also improves the resolution ability of the decision making scheme. Finally, the model and decision method are verified by corresponding examples.
In the era of big data, the information form faced by realistic decision-making is very complex, with multiple data acquisition channels and diverse ways of expression. Aiming at the soft-set decision making based on fuzzy information representation in mixed state, this paper firstly blends fuzzy information into a unified decision framework by defining a one-dimension hybrid fuzzy soft set, and proposes the normalization strategy based on distance location to realize the relative fusion of polymorphic mixed fuzzy numbers. Then the paper uses the similarity measurement strategy to strengthen the level soft set decision making method, which not only ensures the balance and flexibility of the decision making process, but also improves the resolution ability of the decision making scheme. Finally, the model and decision method are verified by corresponding examples.
引文
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[4]Basu T M, Mahapatra N K, Mondal S K. A Balanced Solution of a Fuzzy Soft Set Based Decision Making Problem in Medical Science[J]. Applied Soft Computing, 2012, 12(10).
[5]Majumdar P, Samanta S K. Generalised Fuzzy Soft Sets[J]. Computers&Mathematics With Applications, 2010, 59(4).
[6]Peng X, Yang Y. Algorithms for Interval-valued Fuzzy Soft Sets in Stochastic Multi-criteria Decision Making Based on Regret Theory and Prospect Theory With Combined Weight[J]. Applied Soft Com?puting, 2017,(54).
[7]Xiao Z, Xia S, Gong K, et al. The Trapezoidal Fuzzy Soft Set and Its Application in MCDM[J]. Applied Mathematical Modelling, 2012,36(12).
[8]Muthukumar P, Krishnan G S S. A Similarity Measure of Intuitionistic Fuzzy Soft Sets and Its Application in Medical Diagnosis[J]. Applied Soft Computing, 2016,(41).
[9]Wang F, Li X, Chen X. Hesitant Fuzzy Soft Set and Its Applications in Multi criteria Decision Making[J]. Journal of Applied Mathematics,2014,(3).
[10]Zadeh L A. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning-II[J]. Information Sciences, 1975,8(3).
[11]Tran L, Duckstein L. Comparison of Fuzzy Numbers Using a Fuzzy Distance Measure[J]. Fuzzy Sets&Systems, 2002, 130(3).
[12]Kaufmann A, Gupta M M. Fuzzy Arithmetic:Theory and Applica?tions[M]. New York:Van Nostrand Reinhold, 1985.
[13]Atanassov K T. Intuitionistic Fuzzy Sets[J]. Fuzzy Sets&Systems,1986, 20(1).
[14]Wang W, Xin X. Distance Measure Between Intuitionistic Fuzzy Sets[J]. Mathematics in Practice&Theory, 2005, 26(13).
[15]Torra V. Hesitant Fuzzy Sets[J]. International Journal of Intelligent Systems, 2010, 25(6).
[16]Xia M, Xu Z. Hesitant Fuzzy Information Aggregation in Decision Making[J]. International Journal of Approximate Reasoning, 2011, 52(3).
[2]Kong Z, Gao L, Wang L. Comment on“A Fuzzy Soft Set Theoretic Ap?proach to Decision Making Problems”[J]. Journal of Computational&Applied Mathematics, 2009, 223(2).
[3]Feng F, Jun Y B, Liu X, et al. An Adjustable Approach to Fuzzy Soft Set Based Decision Making[J]. Journal of Computational&Applied Mathematics, 2010, 234(1).
[4]Basu T M, Mahapatra N K, Mondal S K. A Balanced Solution of a Fuzzy Soft Set Based Decision Making Problem in Medical Science[J]. Applied Soft Computing, 2012, 12(10).
[5]Majumdar P, Samanta S K. Generalised Fuzzy Soft Sets[J]. Computers&Mathematics With Applications, 2010, 59(4).
[6]Peng X, Yang Y. Algorithms for Interval-valued Fuzzy Soft Sets in Stochastic Multi-criteria Decision Making Based on Regret Theory and Prospect Theory With Combined Weight[J]. Applied Soft Com?puting, 2017,(54).
[7]Xiao Z, Xia S, Gong K, et al. The Trapezoidal Fuzzy Soft Set and Its Application in MCDM[J]. Applied Mathematical Modelling, 2012,36(12).
[8]Muthukumar P, Krishnan G S S. A Similarity Measure of Intuitionistic Fuzzy Soft Sets and Its Application in Medical Diagnosis[J]. Applied Soft Computing, 2016,(41).
[9]Wang F, Li X, Chen X. Hesitant Fuzzy Soft Set and Its Applications in Multi criteria Decision Making[J]. Journal of Applied Mathematics,2014,(3).
[10]Zadeh L A. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning-II[J]. Information Sciences, 1975,8(3).
[11]Tran L, Duckstein L. Comparison of Fuzzy Numbers Using a Fuzzy Distance Measure[J]. Fuzzy Sets&Systems, 2002, 130(3).
[12]Kaufmann A, Gupta M M. Fuzzy Arithmetic:Theory and Applica?tions[M]. New York:Van Nostrand Reinhold, 1985.
[13]Atanassov K T. Intuitionistic Fuzzy Sets[J]. Fuzzy Sets&Systems,1986, 20(1).
[14]Wang W, Xin X. Distance Measure Between Intuitionistic Fuzzy Sets[J]. Mathematics in Practice&Theory, 2005, 26(13).
[15]Torra V. Hesitant Fuzzy Sets[J]. International Journal of Intelligent Systems, 2010, 25(6).
[16]Xia M, Xu Z. Hesitant Fuzzy Information Aggregation in Decision Making[J]. International Journal of Approximate Reasoning, 2011, 52(3).