Restricted accessResearch articleFirst published online 2019-09-09
The consistency improvement of probabilistic linguistic hesitant fuzzy preference relations and their application in venture capital group decision making
Driven by the entrepreneurial trend of mass entrepreneurship and innovation, venture capital(VC) has been widely concerned and valued by investors. There is no doubt that investment decision plays a critical role in venture capital, however, due to the complexity of the investment environment, it is often difficult for investors to make a definite judgement on an innovative solution. Consequently, to express more accurately the hesitation and ambiguity of investors in the decision-making process, this paper proposes the probabilistic linguistic hesitant fuzzy preference relation(PLHFPR) based on the probabilistic linguistic hesitant fuzzy set(PLHFS). Unlike hesitant fuzzy preference relation (HFPR), PLHFPR not only provides flexible linguistic expression for decision makers, but also gives the occurrence probability of each element in the PLHFPR. Considering that it is difficult for investors to give the exact probability of each element in the PLHFPR, a new probability calculation method is proposed based on the consistency analysis. What’s more, the convex consistency index(CCI) is defined to measure the consistency level of the PLHFPR by considering decision maker’s risk attitude. For the inconsistent PLHFPR, a weighted nonlinear programming model(WNPM) is constructed to derive an acceptable convex consistent PLHFPR and obtain the PLHFPR priority weight vector. Finally, an example about the venture capital is offered to verify the effectiveness of the proposed method.
X.Cheng, J.Gu and Z.S.Xu, Venture capital group decision-making with interaction under probabilistic linguistic environment, Knowledge-Based Systems140 (2018), 82–91.
2.
B.Aouni, C.Colapinto and D.La Torre, A cardinality constrained stochastic goal programming model with satisfaction functions for venture capital investment decision making, Annals of Operations Research205 (2013), 77–88.
3.
T.L.Babcock-lumish, Venture capital decision-making and the cultures of risk: An application of Q methodology to US and UK innovation clusters, Competition and Change9 (2005), 329–356.
4.
M.Knockaert, B.Clarysse and M.Wright, The extent and nature of heterogeneity of venture capital selection behaviour in new technology-based firms, R and D Management40 (2010), 357–371.
5.
A.Lockett and M.Wright, The syndication of venture capital investments, Omega: The international journal of management science29 (2001), 375–390.
6.
F.F.Jinet al.,Approaches to group decision making with linguistic preference relations based on multiplicative consistency, Computers and Industrial Engineering114 (2017), 69–79.
7.
S.Massanet, J.Vicente Riera, J.Torrens and E.Herrera-Viedma, A model based on subjective linguistic preference relations for group decision making problems, Information Sciences355 (2016), 249–264.
8.
Y.J.Xu, H.Sun and H.M.Wang, Optimal consensus models for group decision making under linguistic preference relations, International Transactions In Operational Research23 (2016), 1201–1228.
9.
B.Z.Sun and W.M.Ma, An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application, Omega: The international journal of management science51 (2015), 83–92,
10.
C.Q.Tan, D.D.Wu and B.J.Ma, Group decision making with linguistic preference relations with application to supplier selection, Expert Systems with Applications38 (2011), 14382–14389.
11.
R.M.Rodrl'lguez, L.Martinez and F.Herrera, A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets, Information Sciences241 (2013), 28–42.
12.
F.Y.Meng, X.H.Chen and Q.Zhang, Multi-attribute decision analysis under a linguistic hesitant fuzzy environment. Information Sciences267 (2014), 287–305.
13.
W.Zhou and Z.S.Xu, Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency, IEEE Transactions on Fuzzy Systems26 (2018), 1367–1378.
14.
Y.X.Zhang, Z.S.Xu, H.Wang and H.C.Liao, Consistency-based risk assessment with probabilistic linguistic preference relation, Applied Soft Computing49 (2016), 817–833
15.
B.Zhu, Decision method for research and application based on preference relation[J]. Southeast University, Nanjing, 2014.
16.
B.Zhu and Z.S.Xu, Consistency measures for hesitant fuzzy linguistic preference relations, IEEE Transactions on Fuzzy Systems22 (2014), 35–45.
17.
T.Tanino, Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems12 (1984), 117–131.
18.
Y.J.Xu, X.Liu and H.M.Wang, The additive consistency measure of fuzzy reciprocal preference relations, International Journal of Machine Learning and Cybernetics9 (2018), 1141–1152.
19.
H.Wang and Z.S.Xu, Some consistency measures of extended hesitant fuzzy linguistic preference relations, Information Sciences297 (2015), 316–331.
20.
B.Zhu, Studies on consistency measure of hesitant fuzzy preference relations, Procedia Computer Science17 (2013), 457–464.
21.
C.C.Li, R.M.Rodriguez, L.Martinez, Y.Dong and F.Herrera, Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index, Information Sciences432 (2018), 347–361.
22.
Y.J.Xu and H.M.Wang, A group consensus decision support model for hesitant 2-tuple fuzzy linguistic preference relations with additive consistency, Journal of Intelligent and Fuzzy Systems33 (2017), 41–54.
23.
Z.B.Wu, B.M.Jin and J.P.Xu, Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations, Applied Soft Computing Journal67 (2018), 691–705.
24.
Z.Zhang, X.Y.Kou and Q.X.Dong, Additive consistency analysis and improvement for hesitant fuzzy preference relations, Expert Systems with Applications98 (2018), 118–128.
25.
H.Wang, Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making, International Journal of Computational Intelligence Systems8 (2015), 14–33.
26.
Z.S.Chen, K.S.Chin, Y.L.Li and Y.Yang, Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making, Information Sciences357 (2016), 61–87.
27.
H.J.Zhang, J.Xiao, I.Palomares, H.M.Liang and Y.C.Dong, Linguistic distribution-based optimization approach for large-scale GDM with comparative linguistic information. An application on the selection of wastewater disinfection technology, IEEE Transactions on Fuzzy Systems (2019), doi:10.1109/TFUZZ.2019.2906856.
28.
C.C.Li, Y.C.Dong, Y.J.Xu, F.Chiclana, E.Herrera-Viedma and F.Herrera, An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and fusion: Taxonomy and future directions, Information Fusion52 (2019), 143–156.
29.
Z.Zhang, X.Y.Kou, W.Y.Yu and C.H.Guo, On priority weights and consistency for incomplete hesitant fuzzy preference relations, Knowledge-Based Systems143 (2018), 115–126.
30.
Z.Zhang and C.H.Guo, Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations, International Journal of Systems Science47 (2016), 2572–2587.
31.
H.B.Liu, Y.Ma and L.Jiang, Managing incomplete preferences and consistency improvement in hesitant fuzzy linguistic preference relations with applications in group decision making, Information Fusion51 (2019), 19–29.
32.
C.C.Li, R.M.Rodriguez, L.Martinez, Y.C.Dong and F.Herrera, Consensus building with individual consistency control in group decision making, IEEE Transactions on Fuzzy Systems27 (2019), 319–332.
33.
B.W.Zhang, Y.C.Dong and E.Herrera-Viedma, Group decision making with heterogeneous preference structures: An automatic mechanism to support consensus reaching, Group Decision and Negotiation (2019), doi:10.1007/s10726-018-09609-y.
