Abstract
The notion of Yager’s q-rung orthopair fuzzy set (QROFS) have gained considerable and continuously increasing attention as a useful tool for imprecision and uncertainty representation due to its capability to discard the constraints on the membership and nonmembership functions as generally required by its intuitionistic fuzzy counterpart. Among the generalizations and variants established in the past few years, the interval-valued QROFSs (IVQROFSs) have been diffusely considered to be a powerful generalization of the interval-valued fuzzy sets. The continuous ordered weighted averaging (COWA) operator has been extended successfully to some special cases of IVQROFSs, including interval-valued intuitionistic and Pythagorean fuzzy sets. Thus, to expand on previous studies, several continuous IVQROF (C-IVQROF) aggregation operators are proposed in this study. First, the dual C-GOWA operator is defined on the basis of the continuous generalized ordered weighted averaging (C-GOWA) operator and Yager class of fuzzy negation. Subsequently, the C-IVQROFOWA operator with two independent parameters is constructed, and the weighted C-IVQROFOWA operator is then proposed for aggregating a collection of IVQROFSs. The C-IVQROFOWA operator and its weighted version can model commendably the attitudinal characteristics of the decision-maker. Second, a parameter optimization model and its algorithm-solving strategy driven by consensus measures are built to develop a group decision-making method. Finally, a case study to evaluate the SmartWatch design alternatives is provided to demonstrate the proposed approach, and the results of a comparative analysis verify the rationality and efficiency of the proposed operators.
Similar content being viewed by others
References
Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230
Yager RR, Alajlan N (2017) Approximate reasoning with generalized orthopair fuzzy sets. Inf Fusion 38:65–73
Yager RR, Alajlan N, Bazi Y (2018) Aspects of generalized orthopair fuzzy sets. Int J Intell Syst 33(11):2154–2174
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Yager RR (2013) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965
Wei G, Gao H, Wei Y (2018) Some \(q\)-Rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. Int J Intell Syst 33(7):1426–1458
Liu Z, Wang S, Liu P (2018a) Multiple attribute group decision making based on \(q\)-Rung orthopair fuzzy Heronian mean operators. Int J Intell Syst 33(12):2341–2363
Xing Y, Zhang R, Wang J, Bai K, Xue J (2020) A new multi-criteria group decision-making approach based on \(q\)-Rung orthopair fuzzy interaction Hamy mean operators. Neural Comput Appl 32:7465–7488
Liu P, Ali Z, Mahmood T (2019a) A method to multi-attribute group decision-making problem with complex \(q\)-rung orthopair linguistic information based on heronian mean operators. Int J Comput Intell Syst 12(2):1465–1496
Yang W, Pang Y (2019) New \(q\)-Rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making. Int J Intell Syst 34(3):439–476
Wei G, Wei C, Wang J, Gao H, Wei Y (2019) Some \(q\)-Rung orthopair fuzzy Maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. Int J Intell Syst 34(1):50–81
Liu P, Ali Z, Mahmood T, Hassan N (2020) Group decision-making using complex \(q\)-rung orthopair fuzzy Bonferroni mean. Int J Comput Intel Syst 13(1):822–851
Ju Y, Luo C, Ma J, Wang A (2019a) A novel multiple-attribute group decision-making method based on \(q\)-Rung orthopair fuzzy generalized power weighted aggregation operators. Int J Intell Syst 34(9):2077–2103
Du WS (2019a) Weighted power means of \(q\)-Rung orthopair fuzzy information and their applications in multiattribute decision making. Int J Intell Syst 34(11):2835–2862
Liu Z, Liu P, Liang X (2018b) Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under \(q\)-Rung orthopair fuzzy environment. Int J Intell Syst 33(9):1900–1928
Liu P, Wang P (2018) Some \(q\)-Rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280
Peng X, Dai J, Garg H (2018) Exponential operation and aggregation operator for \(q\)-Rung orthopair fuzzy set and their decision-making method with a new score function. Int J Intell Syst 33(11):2255–2282
Du WS (2018) Minkowski-type distance measures for generalized orthopair fuzzy sets. Int J Intell Syst 33(4):802–817
Liu D, Chen X, Peng D (2019b) Some cosine similarity measures and distance measures between \(q\)-Rung orthopair fuzzy sets. Int J Intell Syst 34(7):1572–1587
Peng X, Dai J (2019) Research on the assessment of classroom teaching quality with \(q\)-Rung orthopair fuzzy information based on multiparametric similarity measure and combinative distance-based assessment. Int J Intell Syst 34(7):1588–1630
Du WS (2019b) Correlation and correlation coefficient of generalized orthopair fuzzy sets. Int J Intell Syst 34(4):564–583
Peng X, Liu L (2019) Information measures for \(q\)-Rung orthopair fuzzy sets. Int J Intell Syst 34(8):1795–1834
Gao J, Liang Z, Shang J, Xu Z (2018) Continuities, derivatives, and differentials of \(q\)-rung orthopair fuzzy functions. IEEE Trans Fuzzy Syst 27(8):1687–1699
Gao J, Liang Z, Xu Z (2020) Additive integrals of \(q\)-Rung orthopair fuzzy functions. IEEE Trans Cybern 50(10):4406–4419
Ye J, Ai Z, Xu Z (2019) Single variable differential calculus under \(q\)-Rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application. Int J Intell Syst 34(7):1387–1415
Shu X, Ai Z, Xu Z, Ye J (2019) Integrations of \(q\)-Rung orthopair fuzzy continuous information. IEEE Trans Fuzzy Syst 27(10):1974–1985
Li H, Yin S, Yang Y (2019) Some preference relations based on \(q\)-Rung orthopair fuzzy sets. Int J Intell Syst 34(11):2920–2936
Zhang C, Liao H, Luo L (2019a) Additive consistency-based priority-generating method of \(q\)-Rung orthopair fuzzy preference relation. Int J Intell Syst 34(9):2151–2176
Banerjee D, Dutta B, Guha D, Martínez L (2020) SMAA-QUALIFLEX methodology to handle multicriteria decision-making problems based on \(q\)-rung fuzzy set with hierarchical structure of criteria using bipolar Choquet integral. Int J Intell Syst 35(3):401–431
Chen Z-S, Chin K-S, Tsui K-L (2019a) Constructing the geometric Bonferroni mean from the generalized Bonferroni mean with several extensions to linguistic 2-tuples for decision-making. Appl Soft Comput 78:595–613
Chen Z-S, Yang Y, Wang X-J, Chin K-S, Tsui K-L (2019b) Fostering linguistic decision-making under uncertainty: a proportional interval type-2 hesitant fuzzy TOPSIS approach based on Hamacher aggregation operators and andness optimization models. Inf Sci 500:229–258
Yang Y, Chen Z-S, Chen Y-H, Chin K-S (2018) Interval-valued Pythagorean fuzzy Frank power aggregation operators based on an isomorphic Frank dual triple. Int J Comput Intell Syst 11(1):1091–1110
Joshi BP, Singh A, Bhatt PK, Vaisla KS (2018) Interval valued \(q\)-Rung orthopair fuzzy sets and their properties. J Intell Fuzzy Syst 35(5):5225–5230
Ju Y, Luo C, Ma J, Gao H, Santibanez Gonzalez E D, Wang A (2019) Some interval-valued \(q\)-Rung orthopair weighted averaging operators and their applications to multiple-attribute decision making. Int J Intell Syst 34(10):2584–2606
Wang J, Wei G, Wang R, Alsaadi FE, Hayat T, Wei C, Zhang Y, Wu J (2019) Some \(q\)-Rung interval-valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making. Int J Intell Syst 34(11):2769–2806
Jan N, Mahmood T, Zedam L, Ullah K, Alcantud JCR, Davvaz B (2019) Analysis of social networks, communication networks and shortest path problems in the environment of interval-valued q-Rung orthopair fuzzy graphs. Int J Fuzzy Syst 21(6):1687–1708
Yager RR (2004a) OWA aggregation over a continuous interval argument with applications to decision making. IEEE Trans Syst Man Cybern Part B (Cybern) 34(5):1952–1963
Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190
Yager RR (1996) Quantifier guided aggregation using OWA operators. Int J Intell Syst 11(1):49–73
Chen H, Zhou L (2011) An approach to group decision making with interval fuzzy preference relations based on induced generalized continuous ordered weighted averaging operator. Expert Syst Appl 38(10):13432–13440
Zhou H, Ma X, Zhou L, Chen H, Ding W (2018) A novel approach to group decision-making with interval-valued intuitionistic fuzzy preference relations via shapley value. Int J Fuzzy Syst 20(4):1172–1187
Zhou L, Wu J, Chen H (2014a) Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making. Appl Soft Comput 25:266–276
Jin F, Ni Z, Chen H, Li Y, Zhou L (2016) Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Comput Ind Eng 101:103–115
Jin F, Pei L, Chen H, Zhou L (2014) Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making. Knowl-Based Syst 59:132–141
Wu J, Chiclana F (2014) A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions. Appl Soft Comput 22:272–286
Zhou L, Tao Z, Chen H, Liu J (2014b) Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making. Appl Math Model 38(7–8):2190–2205
Lin J, Zhang Q (2017) Note on continuous interval-valued intuitionistic fuzzy aggregation operator. Appl Math Model 43:670–677
Yang Y, Lv H-X, Li Y-L (2017) WIC-IVIFOWA operator based on standard negation and its application. Control Decis 32(11):2021–2033
Chen Z-S, Yu C, Chin K-S, Martínez L (2019c) An enhanced ordered weighted averaging operators generation algorithm with applications for multicriteria decision making. Appl Math Model 71:467–490
Liu J, Lin S, Chen H, Zhou L (2013) The continuous quasi-OWA operator and its application to group decision making. Group Decis Negot 22(4):715–738
Wang L, Li N (2019) Continuous interval-valued Pythagorean fuzzy aggregation operators for multiple attribute group decision making. J Intell Fuzzy Syst 36(6):6245–6263
Yager RR (2004b) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3(1):93–107
Yager RR (1979) On the measure of fuzziness and negation part I: membership in the unit interval. Int J Gener Syst 5:221–229
Yager RR (1980) On the measure of fuzziness and negation. II. Lattices. Inf Control 44(3):236–260
Beliakov G, Pradera A, Calvo T et al (2007) Aggregation functions: a guide for practitioners, vol 221. Springer, Berlin
Rodríguez RM, Labella Á, De Tré G, Martínez L (2018) A large scale consensus reaching process managing group hesitation. Knowl-Based Syst 159:86–97
Dutta B, Labella Á, Rodríguez RM, Martínez L (2019) Aggregating interrelated attributes in multi-attribute decision-making with ELICIT information based on Bonferroni mean and its variants. Int J Comput Intell Syst 12(2):1179–1196
Chen Z-S, Liu X-L, Rodríguez RM, Wang X-J, Chin K-S, Tsui K-L, Martínez L (2020) Identifying and prioritizing factors affecting in-cabin passenger comfort on high-speed rail in China: a fuzzy-based linguistic approach. Appl Soft Comput 95:106558
Chen Z-S, Liu X-L, Chin K-S, Pedrycz W, Tsui K-L, Skibniewski MJ (2021) Online-review analysis based large-scale group decision-making for determining passenger demands and evaluating passenger satisfaction: case study of high-speed rail system in China. Inf Fusion 69:22–39
Labella Á, Liu Y, Rodríguez R, Martínez L (2018) Analyzing the performance of classical consensus models in large scale group decision making: A comparative study. Appl Soft Comput 67:677–690
Zhang L, Li JT, Zhao YY, Tian ZQ (2019b) Evaluation method for product design based on users’ emotional needs. Oper Res Manag Sci 28(1):152–157
Yu C, Shao Y, Wang K, Zhang L (2019) A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment. Expert Syst Appl 121:1–17
Tao Z, Liu X, Chen H, Zhou L (2016) Using new version of extended \(t\)-norms and \(s\)-norms for aggregating interval linguistic labels. IEEE Trans Syst Man Cybern Syst 47(12):3284–3298
Tao Z, Shao Z, Liu J, Zhou L, Chen H (2020) Basic uncertain information soft set and its application to multi-criteria group decision making. Eng Appl Artif Intell 95:103871
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant nos. 71801175, 71871171, 71971182, and 72031009), The Ministry of Education of Humanities and Social Science Foundation of China (Grant no. 20YJCZH210), the Natural Science Foundation of Hunan Province, China (Grant no. 2020JJ5112), the Theme-based Research Projects of the Research Grants Council (Grant no. T32-101/15-R), the Spanish Ministry of Economy and Competitiveness through the Spanish National Research Project (Grant no. PGC2018-099402-B-I00) and the postdoctoral fellowship Ramón y Cajal (Grant no. RyC-2017-21978), the Ger/HKJRS project (Grant no. G-CityU103/17), and partly by the City University of Hong Kong SRG (Grant no. 7004969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yang, Y., Chen, ZS., Rodríguez, R.M. et al. Novel fusion strategies for continuous interval-valued q-rung orthopair fuzzy information: a case study in quality assessment of SmartWatch appearance design. Int. J. Mach. Learn. & Cyber. 13, 609–632 (2022). https://doi.org/10.1007/s13042-020-01269-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-020-01269-2