Preference relations as information representation form are widely used to manage complexity and uncertainty in practical decision-making cases. Intuitionistic trapezoidal fuzzy numbers (ITrFNs) can convey more fuzzy messages than other fuzzy numbers. This paper defines intuitionistic trapezoidal fuzzy preference relations (ITrFPRs) to adequately describe the preferences of decision makers (DMs). To optimize the decision-making selection process, this paper constructs a three-cycle decision-making selection mechanism with ITrFPRs. To build this mechanism, firstly, a possibility degree formula is presented to rank ITrFNs. Secondly, ITrFPRs, consistent ITrFPRs, acceptable consistent ITrFPRs and a new consistency index are defined. Thirdly, a novel consistency transformation method is built to elevate the consistency of ITrFPRs. Fourthly, considering the relationship between consistency conditions and priority weight, a priority weight derivation method is exploited to derive intuitionistic trapezoidal fuzzy weights. Ultimately, a three cycle selection mechanism integrated with consistency checking, consistency improvement and priority weight derivation procedures is constructed and applied into the case of trip itinerary selection. Sensitive and comparative analyses are carried out to illustrate the effectiveness and applicability of the proposed mechanism.
R.X.Nie, J.Wang and L.Li, A shareholder voting method for proxy advisory firm selection based on 2-tuple linguistic picture preference relation, Applied Soft Computing60 (2017), 520–539.
2.
F.Meng, J.Lin, C.Tan and Q.Zhang, A new multiplicative consistency based method for decision making with triangular fuzzy reciprocal preference relations, Fuzzy Sets and Systems315 (2017), 1–25.
3.
J.Wu, F.Chiclana and H.Liao, Isomorphic multiplicative transitivity for intuitionistic and interval-valued fuzzy preference relations and its application in deriving their priority vectors, IEEE Transactions on Fuzzy Systems26(1) (2018), 193–202.
4.
F.Meng, J.Tang and H.Fujita, Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making, Information Fusion46 (2019), 77–90.
5.
F.Liu, Z.Liu and Y.Wu, A group decision making model based on triangular fuzzy additive reciprocal matrices with additive approximation-consistency, Applied Soft Computing65 (2018), 349–359.
6.
T.Y.Chen, Likelihoods of interval type-2 trapezoidal fuzzy preference relations and their application to multiple criteria decision analysis, Information Sciences295 (2015), 303–322.
7.
F.Meng and X.Chen, An approach to incomplete multiplicative preference relations and its application in group decision making, Information Sciences309 (2015), 119–137.
8.
F.Meng and C.Tan, A new consistency concept for interval multiplicative preference relations, Applied Soft Computing52 (2017), 262–276.
9.
H.Garg, Generalized interaction aggregation operators in intuitionistic fuzzy multiplicative preference environment and their application to multicriteria decision-making, Applied Intelligence48(8) (2018), 2120–2136.
10.
H.Garg, H.Garg and H.Garg, A robust ranking method for intuitionistic multiplicative sets under crisp, interval environments and its applications, IEEE Transactions on Emerging Topics in Computational Intelligence1(5) (2017), 366–374.
11.
H.Garg, Distance and similarity measures for intuitionistic multiplicative preference relation and its applications, International Journal for Uncertainty Quantification7(2) (2017), 117–133.
12.
F.Liu, W.G.Zhang and L.H.Zhang, Consistency analysis of triangular fuzzy reciprocal preference relations, European Journal of Operational Research235(3) (2014), 718–726.
13.
H.Garg and K.Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Computing (2018), 10–1007.
14.
G.Kaur and H.Garg, Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process, Arabian Journal for Science and Engineering44(3) (2019), 2775–2794.
15.
H.Garg and D.Rani, Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process, Arabian Journal for Science and Engineering44(3) (2019), 2679–2698.
16.
H.Garg and R.Arora, Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multicriteria decision-making, International Journal of Intelligent Systems34(2) (2019), 215–246.
17.
H.Garg and S.Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators, Iranian Journal of Fuzzy Systems15(5) (2018), 69–93.
18.
X.Zhang, H.Zhang and J.Wang, Discussing incomplete 2-tuple fuzzy linguistic preference relations in multi-granular linguistic MCGDM with unknown weight information, Soft Computing23(6) (2019), 2015–2032.
19.
J.Li and J.Wang, Multi-criteria decision-making with probabilistic hesitant fuzzy information based on expected multiplicative consistency, Neural Computing and Applications (2018). DOI: 10.1007/s00521-018-3753-1
20.
S.Luo, H.Zhang, J.Wang and L.Li, Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations, Journal of the Operational Research Society (2018). DOI: 10.1080/01605682.2018.1510806
21.
F.Jin, Z.Ni, H.Chen and Y.Li, Approaches to decision making with linguistic preference relations based on additive consistency, Applied Soft Computing49 (2016), 71–80.
22.
Z.Zhang and W.Pedrycz, Goal programming approaches to managing consistency and consensus for intuitionistic multiplicative preference relations in group decision-making, IEEE Transactions on Fuzzy Systems26(6) (2018), 3261–3275.
23.
Y.Xu, Q.Wang, F.J.Cabrerizo and E.Herrera-Viedma, Methods to improve the ordinal and multiplicative consistency for reciprocal preference relations, Applied Soft Computing67 (2018), 479–493.
24.
Z.J.Wang, A goal programming approach to deriving interval weights in analytic form from interval fuzzy preference relations based on multiplicative consistency, Information Sciences462 (2018), 160–181.
25.
F.Meng and X.Chen, A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations, Fuzzy Optimization & Decision Making17 (2018), 1–25.
26.
Z.Zhang and W.Pedrycz, Models of mathematical programming for intuitionistic multiplicative preference relations, IEEE Transactions on Fuzzy Systems25(4) (2016), 945–957.
27.
J.Wu, Isomorphic multiplicative transitivity for intuitionistic and interval-valued fuzzy preference relations and its application in deriving their priority vectors, IEEE Transactions on Fuzzy Systems26(1) (2018), 193–202.
28.
J.Li, J.Wang and J.Hu, Consensus building for hesitant fuzzy preference relations with multiplicative consistency, Computers & Industrial Engineering128 (2019), 387–400.
29.
R.Nie, Z.Tian, X.Wang, J.Wang and T.Wang, Risk evaluation by FMEA of supercritical water gasification system using multi-granular linguistic distribution assessment, Knowledge-Based Systems162 (2018), 185–201.
30.
H.Peng, X.Wang, T.Wang and J.Wang, Multi-criteria game model based on the pairwise comparisons of strategies with Z-numbers, Applied Soft Computing74 (2019), 451–465.
31.
Z.Tian, H.Zhang, J.Wang and T.Wang, Green supplier selection using improved TOPSIS and best-worst method under intuitionistic fuzzy environment, Informatica29(4) (2018), 773–800.
32.
Q.Qin, F.Liang, L.Li, Y.W.Chen and G.F.Yu, A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers, Applied Soft Computing55 (2017), 93–107.
33.
J.Yuan and C.Li, A new method for multi-attribute decision making with intuitionistic trapezoidal fuzzy random variable, International Journal of Fuzzy Systems19(1) (2017), 15–26.
34.
C.Liang, S.Zhao and J.Zhang, Multi-criteria group decision making method based on generalized intuitionistic trapezoidal fuzzy prioritized aggregation operators, International Journal of Machine Learning and Cybernetics8(2) (2017), 597–610.
35.
H.Garg and K.Kumar, Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making, Granular Computing4(2) (2019), 237–247.
36.
H.Garg and K.Kumar, Group decision making approach based on possibility degree measures and the linguistic intuitionistic fuzzy aggregation operators using Einstein norm operations, Journal of Multiple-Valued Logic and Soft Computing31(1-2) (2018), 175–209.
37.
H.Garg and K.Kumar, Group decision making approach based on possibility degree measure under linguistic interval-valued intuitionistic fuzzy set environment, Journal of Industrial and Management Optimization (2018). DOI: org/10.3934/jimo.2018162
38.
S.Chen and W.Han, An improved MADM method using interval-valued intuitionistic fuzzy values, Information Sciences467 (2018), 489–505.
39.
S.Wan and J.Dong, A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making, Journal of Computer and System Sciences80(1) (2014), 237–256.
40.
C.Wang and J.Wang, A multi-criteria decision-making method based on triangular intuitionistic fuzzy preference information, Intelligent Automation & Soft Computing22(3) (2015), 473–482.
41.
F.Liu, W.Pedrycz, Z.Wang and W.Zhang, An axiomatic approach to approximation-consistency of triangular fuzzy reciprocal preference relations, Fuzzy Sets and Systems322 (2017), 1–18.
42.
X.Liu, Y.Pan, Y.Xu and S.Yu, Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations, Fuzzy Sets & Systems198(198) (2012), 1–19.
43.
F.Meng and X.Chen, A new method for group decision making with incomplete fuzzy preference relations, Knowledge-Based Systems73 (2015), 111–123.
44.
H.Liao and Z.Xu, Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency, IEEE Transactions on Fuzzy Systems22(6) (2014), 1669–1681.
45.
Y.Xu, Q.Da and H.Wang, A note on group decision-making procedure based on incomplete reciprocal relations, Soft Computing15(7) (2011), 1289–1300.
46.
Z.J.Wang and K.W.Li, Goal programming approaches to deriving interval weights based on interval fuzzy preference relations, Information Sciences193(193) (2012), 180–198.
47.
M.Dong, S.Li and H.Zhang, Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP, Expert Systems with Applications42(21) (2015), 7846–7857.
48.
Z.Tian, R.Nie, J.Wang and H.Zhang, A two-fold feedback mechanism to support consensus-reaching in social network group decision-making, Knowledge-Based Systems162 (2018), 74–91.
49.
D.Rani and H.Garg, Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making, Expert Systems35(6) (2018), 10–1111.
50.
H.Garg and R.Arora, Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making, Engineering Applications of Artificial Intelligence71 (2018), 100–112.
51.
X.Peng and G.Selvachandran, Pythagorean fuzzy set: State of the art and future directions, Artificial Intelligence Review (1) (2017), 1–55.
52.
X.Peng and Y.Yang, Some results for Pythagorean fuzzy sets, International Journal of Intelligent Systems30(11) (2015), 1133–1160.
53.
H.Garg, New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications, International Journal of Intelligent Systems34(1) (2019), 82–106.
54.
H.Garg, New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making, International Journal of Intelligent Systems33(3) (2018), 653–683.
55.
X.Peng and Y.Yang, Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight, Applied Soft Computing54 (2016), 415–430.
56.
X.Peng and C.Liu, Algorithms for neutrosophic soft decision making based on EDAS and new similarity measure, Journal of Intelligent & Fuzzy Systems32(1) (2017), 955–968.
57.
H.Garg and R.Arora, Dual hesitant fuzzy soft aggregation operators and their application in decision-making, Cognitive Computation10(5) (2018), 769–789.
