# American Institute of Mathematical Sciences

## Analytic expression of optimal solution of M & A matching based on fuzzy number method

 1 College of Accounting and Finance, Jiangxi University of Engineering, Xinyu 338000, China 2 School of Marxism, Hainan University, Haikou 570228, China

*Corresponding author: Hongping Yan

Received  May 2019 Revised  May 2019 Published  February 2020

Research on the merger and acquisition matching focuses on strategic matching, organizational matching and resource matching in academic circles, but merger and acquisition matching is more in line with the rational decision from the efficiency and scale, and the existing DEA research has not paid sufficient attention to this topic. In order to increase the flexibility of M & A matching, this paper studies the M & A matching problem from efficiency and scale using DEA model and fuzzy number method, and gives Analytic Expression of Optimal Solution of M & A Matching of two methods. The example shows that the method is feasible and effective and has important practical significance for strategic M & A.

Citation: Manwen Tian, Shurong Yan, Lina Wang, Weihong Li, Hongping Yan. Analytic expression of optimal solution of M & A matching based on fuzzy number method. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020271
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CCR Efficiency of 20 Listed Chinese New Energy Companies
 DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 0.9986 1 0.8967 1 1 1 0.9873 1 0.9978 0.9986 DMU11 DMU12 DMU13 DMU14 DMU15 DMU16 DMU17 DMU18 DMU19 DMU20 0.9968 1 0.9885 1 1 0.8637 0.9786 0.6543 1 0.9769
 DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 0.9986 1 0.8967 1 1 1 0.9873 1 0.9978 0.9986 DMU11 DMU12 DMU13 DMU14 DMU15 DMU16 DMU17 DMU18 DMU19 DMU20 0.9968 1 0.9885 1 1 0.8637 0.9786 0.6543 1 0.9769
Relative Efficiency Matrix ($\theta )$ of M & A Match
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 0.7896 1 0.8795 0.8897 0.8973 0.8794 0.7968 0.7947 1 0.8969 DMU7 0.9876 0.9974 0.8975 0.9828 1 0.9756 0.9984 0.8756 1 1 DMU9 0.9683 1 0.9567 0.9357 1 0.9875 0.9684 0.8896 1 1 DMU11 0.9354 1 0.9785 0.9657 1 0.9165 0.9145 0.9831 1 1 DMU12 0.8796 1 0.9867 0.9375 1 0.8673 0.8891 0.9456 1 1 DMU13 0.9843 1 0.9781 0.9680 1 0.9147 0.9602 0.9063 1 1 DMU16 0.8731 1 0.8834 0.9601 1 0.9364 0.8798 0.8634 1 0.9934 DMU17 0.8897 1 0.8986 0.9976 0.9912 0.9671 0.9561 0.8697 1 1 DMU18 0.8354 0.9934 0.8613 0.9182 1 0.8794 0.8672 0.8437 1 0.9634 DMU20 0.8679 0.9987 0.8891 0.9683 1 0.9861 1 0.8793 1 1
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 0.7896 1 0.8795 0.8897 0.8973 0.8794 0.7968 0.7947 1 0.8969 DMU7 0.9876 0.9974 0.8975 0.9828 1 0.9756 0.9984 0.8756 1 1 DMU9 0.9683 1 0.9567 0.9357 1 0.9875 0.9684 0.8896 1 1 DMU11 0.9354 1 0.9785 0.9657 1 0.9165 0.9145 0.9831 1 1 DMU12 0.8796 1 0.9867 0.9375 1 0.8673 0.8891 0.9456 1 1 DMU13 0.9843 1 0.9781 0.9680 1 0.9147 0.9602 0.9063 1 1 DMU16 0.8731 1 0.8834 0.9601 1 0.9364 0.8798 0.8634 1 0.9934 DMU17 0.8897 1 0.8986 0.9976 0.9912 0.9671 0.9561 0.8697 1 1 DMU18 0.8354 0.9934 0.8613 0.9182 1 0.8794 0.8672 0.8437 1 0.9634 DMU20 0.8679 0.9987 0.8891 0.9683 1 0.9861 1 0.8793 1 1
Return-to-Scale Matrix (T) of M & A Match
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 Decreasing Decreasing Unchanged Unchanged Unchanged Increasing Decreasing Increasing Decreasing Decreasing DMU7 Decreasing Unchanged Unchanged Unchanged Unchanged Decreasing Decreasing Increasing Unchanged Unchanged DMU9 Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Increasing Unchanged Increasing DMU11 Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Increasing Unchanged Unchanged DMU12 Increasing Unchanged Decreasing Increasing Decreasing Decreasing Decreasing Unchanged Increasing Decreasing DMU13 Decreasing Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Increasing Decreasing Increasing DMU16 Decreasing Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Decreasing Increasing Unchanged DMU17 Decreasing Decreasing Unchanged Decreasing Increasing Decreasing Decreasing Increasing Decreasing Unchanged DMU18 Decreasing Unchanged Decreasing Decreasing Decreasing Decreasing Decreasing Unchanged Unchanged Decreasing DMU20 Decreasing Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Increasing Unchanged Unchanged
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 Decreasing Decreasing Unchanged Unchanged Unchanged Increasing Decreasing Increasing Decreasing Decreasing DMU7 Decreasing Unchanged Unchanged Unchanged Unchanged Decreasing Decreasing Increasing Unchanged Unchanged DMU9 Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Increasing Unchanged Increasing DMU11 Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Decreasing Increasing Unchanged Unchanged DMU12 Increasing Unchanged Decreasing Increasing Decreasing Decreasing Decreasing Unchanged Increasing Decreasing DMU13 Decreasing Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Increasing Decreasing Increasing DMU16 Decreasing Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Decreasing Increasing Unchanged DMU17 Decreasing Decreasing Unchanged Decreasing Increasing Decreasing Decreasing Increasing Decreasing Unchanged DMU18 Decreasing Unchanged Decreasing Decreasing Decreasing Decreasing Decreasing Unchanged Unchanged Decreasing DMU20 Decreasing Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Increasing Unchanged Unchanged
Goodness or Badness of M & A Match When $\theta _{dk}^L = 0.6$
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 Inferior Inferior Neutral Neutral Neutral Superior Inferior Superior Inferior Inferior DMU7 Inferior Neutral Neutral Neutral Neutral Inferior Inferior Superior Neutral Neutral DMU9 Inferior Inferior Inferior Inferior Inferior Inferior Inferior Superior Neutral Superior DMU11 Inferior Inferior Inferior Inferior Inferior Inferior Inferior Superior Neutral Neutral DMU12 Superior Neutral Inferior Superior Inferior Inferior Inferior Neutral Superior Inferior DMU13 Inferior Neutral Neutral Neutral Neutral Neutral Neutral Superior Inferior Superior DMU16 Inferior Neutral Neutral Neutral Neutral Neutral Neutral Inferior Superior Neutral DMU17 Inferior Inferior Neutral Inferior Superior Inferior Inferior Superior Inferior Neutral DMU18 Inferior Neutral Inferior Inferior Inferior Inferior Inferior Neutral Neutral Inferior DMU20 Inferior Neutral Neutral Neutral Neutral Neutral Neutral Superior Neutral Neutral
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 Inferior Inferior Neutral Neutral Neutral Superior Inferior Superior Inferior Inferior DMU7 Inferior Neutral Neutral Neutral Neutral Inferior Inferior Superior Neutral Neutral DMU9 Inferior Inferior Inferior Inferior Inferior Inferior Inferior Superior Neutral Superior DMU11 Inferior Inferior Inferior Inferior Inferior Inferior Inferior Superior Neutral Neutral DMU12 Superior Neutral Inferior Superior Inferior Inferior Inferior Neutral Superior Inferior DMU13 Inferior Neutral Neutral Neutral Neutral Neutral Neutral Superior Inferior Superior DMU16 Inferior Neutral Neutral Neutral Neutral Neutral Neutral Inferior Superior Neutral DMU17 Inferior Inferior Neutral Inferior Superior Inferior Inferior Superior Inferior Neutral DMU18 Inferior Neutral Inferior Inferior Inferior Inferior Inferior Neutral Neutral Inferior DMU20 Inferior Neutral Neutral Neutral Neutral Neutral Neutral Superior Neutral Neutral
Cross Efficiency Matrix of M & A Match when $\theta _{dk}^L = 0.6$
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 0.6985 0.6491 0.7819 0.8943 DMU7 DMU9 0.9051 DMU11 0.5163 0.6897 0.6015 0.8652 DMU12 0.9325 0.6135 0.8465 0.8956 DMU13 0.7614 0.8616 0.9824 0.7635 0.8165 0.8357 DMU16 0.8156 0.8952 0.9102 0.7024 0.8167 DMU17 0.8014 DMU18 0.6354 0.9164 DMU20 0.9861 0.8816 0.8165
 DMU1 DMU3 DMU4 DMU5 DMU6 DMU8 DMU10 DMU14 DMU15 DMU19 DMU2 0.6985 0.6491 0.7819 0.8943 DMU7 DMU9 0.9051 DMU11 0.5163 0.6897 0.6015 0.8652 DMU12 0.9325 0.6135 0.8465 0.8956 DMU13 0.7614 0.8616 0.9824 0.7635 0.8165 0.8357 DMU16 0.8156 0.8952 0.9102 0.7024 0.8167 DMU17 0.8014 DMU18 0.6354 0.9164 DMU20 0.9861 0.8816 0.8165
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