Abstract
Fuzzy approaches that are proposed to describe uncertain, impressive or vague concepts, are based on the construction of membership function (MF), which reflects what is known about the linguistic variables in the application domain. However, a non-trivial problem exists in how to construct the most appropriate MF that has the best-fit representation of the analysed problem. Therefore, many authors propose their own ways to construct MF using a certain technique in a particular application domain. Consequently, the need for a general approach for constructing MF led us to systematise and to generalise the analysed approaches into a general methodological framework (GMF) of constructing MF. The novelty of this paper is that the proposed GMF is general, domain independent and free of a chosen understanding of fuzziness (i.e., similarity (imprecision), preference (vagueness), and uncertainty). To verify the proposed GMF, it was applied for the enterprise business service quality (QoSEBS) planning problem. The obtained results showed that a semi-automatic MF construction for QoSEBS planning was more sensitive, less subjective and more precise than a manual construction. Moreover, illustrative examples showed that our proposed GMF is applicable and implementable. The reliability of the results was assessed using experts and users’ experience, which is based on general guidelines of the “acceptable” response time limits for various activities.
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References
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Medasani, S., Kim, J., Krishnapuram, R.: An overview of membership function generation techniques for pattern recognition. Int. J. Approx. Reason. 19(3–4), 391–417 (1998)
dos Santos Schwaab, A.A., Nassar, S.M., de Freitas Filho, P.J.: Automatic methods for generation of type-1 and interval type-2 fuzzy membership functions. J. Comput. Sci. 11(9), 976–987 (2015)
Dubois, D., Ostasiewicz, W., Prade, H.: Fuzzy sets: history and basic notions. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets, pp. 21–124. Springer, Boston (2000)
Amini, A., Nikraz, N.: A method for constructing non-isosceles triangular fuzzy numbers using frequency histogram and statistical parameters. Soft Comput. Civil Eng. 1(1), 65–85 (2017)
Yadav, H.B., Yadav, D.K.: Construction of membership function for software metrics. Proc. Comput. Sci. 46, 933–940 (2015)
Pazhoumand-Dar, H., Lam, C., Masek, M.: Automatic generation of fuzzy membership functions using adaptive mean-shift and robust statistics. In: Proc. of the 8th international conference on agents and artificial intelligence, pp. 160–171 (2016)
Ferreyra, E., Hagras, H., Mohamed, A., Owusu, G.: A type-2 fuzzy logic system for engineers estimation in the workforce allocation domain. In Proc. of the 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE), pp. 1–6. IEEE, Naples (2017, July)
Nguyen, T., Khosravi, A., Creighton, D., Nahavandi, S.: Medical data classification using interval type-2 fuzzy logic system and wavelets. Appl. Soft Comput. 30, 812–822 (2015)
Wang, H., Yu, C., Wang, L., Yu, Q.: Effective bigdata-space service selection over trust and heterogeneous QoS preferences. IEEE Trans. Serv. Comput. 11(4), 644–657 (2018)
Si, G., Liao, H., Yu, D., Llopis-Albert, C.: Interval-valued 2-tuple hesitant fuzzy linguistic term set and its application in multiple attribute decision making. J. Intell. Fuzzy Syst. 34(6), 4225–4236 (2018)
Jusoh, A., Mardani, A., Omar, R., Štreimikienė, D., Khalifah, Z., Sharifara, A.: Application of MCDM approach to evaluate the critical success factors of total quality management in the hospitality industry. J. Bus. Econ. Manage. 19(2), 399–416 (2018)
Ghorabaee, M., Zavadskas, E., Amiri, M., Esmaeili, A.: Multi-criteria evaluation of green suppliers using an extended WASPAS method with interval type-2 fuzzy sets. J. Clean. Prod. 137, 213–229 (2016)
Litake, S., Prachi, M.: Fuzzification of context parameters for network selection in heterogeneous wireless environment. In: Smys, S., Bestak, R., Chen, J.Z., Kotuliak, I. (eds.), International conference on computer networks and communication technologies. LNDECT 15. pp. 907–921. Springer, Singapore (2019)
Arun, N., Mohan, B.: Mathematical modelling of the simplest fuzzy two-input two-output proportional integral or proportional derivative controller via Larsen product inference. Int. J. Autom. Control 10(1), 34–51 (2016)
Bigand, A., Colot, O.: Membership function construction for interval-valued fuzzy sets with application to Gaussian noise reduction. Fuzzy Sets Syst. 286, 66–85 (2016)
Rhimi, F., Yahia, S.B., Ahmed, S.B. Balancing between local and global optimization of web services composition by a fuzzy transactional-aware approach. ICSOFT-PT, 75–82 (2016)
Wang, P., Chao, K., Lo, C.: Satisfaction-based Web service discovery and selection scheme utilizing vague sets theory. Inf. Syst. Front. 17(4), 827–844 (2015)
Choi, B., Rhee, F.: Interval type-2 fuzzy memberships function generation methods for pattern recognition. Inf. Sci. 179(13), 2102–2122 (2009)
Liao, H., Wu, X., Keikha, A., Hafezalkotob, A.: Power average-based score function and extension rule of hesitant fuzzy set and the hesitant power average operators. J. Intell. Fuzzy Syst. 35(3), 3873–3882 (2018)
Mardani, A., Nilashi, M., Zavadskas, E., Awang, S., Zare, H., Jamal, N.: Decision making methods based on fuzzy aggregation operators: three decades review from 1986 to 2017. Int. J. Inf. Technol. Decis. Mak. 17(2), 391–466 (2018)
Krishankumar, R., Ravichandran, K., Premaladha, J., Kar, S., Zavadskas, E., Antucheviciene, J.: A decision framework under a linguistic hesitant fuzzy set for solving multi-criteria group decision making problems. Sustainability 10(8), 2608 (2018)
Mardani, A., Nilashi, M., Zavadskas, E.K., Awang, S.R., Zare, H., Jamal, N.M.: Decision making methods based on fuzzy aggregation operators: three decades review from 1986 to 2017. Int. J. Inf. Technol. Decis. Mak. 17(02), 391–466 (2018)
Vaidya, A., Metkewar, P., Naik, S.: A new paradigm for generation of fuzzy membership function. In Proc. of the 2018 IEEE 8th international advance computing conference (IACC), pp. 1–6. IEEE (2019, April)
Ghorabaee, M., Amiri, M., Zavadskas, E.K., Antucheviciene, J.: A new hybrid fuzzy MCDM approach for evaluation of construction equipment with sustainability considerations. Arch. Civil Mech. Eng. 18(1), 32–49 (2018)
Keshavarz-Ghorabaee, M., Amiri, M., Zavadskas, E.K., Turskis, Z., Antucheviciene, J.: A dynamic fuzzy approach based on the EDAS method for multi-criteria subcontractor evaluation. Information 9(3), 68 (2018)
Luo, W., Zhang, D., Jiang, H., Ni, L., Hu, Y.: Local community detection with the dynamic membership function. IEEE Trans. Fuzzy Syst. 26(5), 3136–3150 (2018)
Tripathy, A.K., Tripathy, P.K.: Fuzzy QoS requirement-aware dynamic service discovery and adaptation. Appl. Soft Comput. 68, 136–146 (2018)
Zheng, H., Feng, Y., Tan, J.: A fuzzy QoS-aware resource service selection considering design preference in cloud manufacturing system. Int. J. Adv. Manuf. Technol. 84(1–4), 371–379 (2016)
Georgieva, O., Petrova-Antonova, D.: Web service selection based on integrated QoS assesment. The ICCGI 2015: tenth international multi-conference on computing in the global information technology, pp. 114–118. IARIA (2015)
Wang, C., Qu, A.: The applications of vague soft sets and generalized. Acta Mathematicae Applicatae Sinica, English Series 31(4), 977–990 (2015)
Paul, A. K., Shill, P. C., Rabin, M. R., Kundu, A. M.: Fuzzy membership function generation using DMS-PSO for the diagnosis of heart disease. In: Proc. of the 18th international conference on computer and information technology (ICCIT), pp. 456–461. IEEE (2015, December)
Liao, H., Xu, Z., Zeng, X.J., Xu, D.L.: An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations. Inf. Sci. 329, 274–286 (2016)
Maheswari, S., Karpagam, G.R.: Enhancing fuzzy topsis for web service selection. Int. J. Comput. Appl. Technol. 51(4), 344–351 (2015)
Kumar, R.R., Mishra, S., Kumar, C.: Prioritizing the solution of cloud service selection using integrated MCDM methods under fuzzy environment. J. Supercomput. 73(11), 4652–4682 (2017)
Bagga, P., Joshi, A., Hans, R.: QoS based web service selection and multi-criteria decision making methods. Int. J. Interact. Multimed. Artif. Intell. 5(4), 113–121 (2019)
Miliauskaitė, J.: Some methodological issues related to preliminary QoS. Balt. J. Mod. Comput. 3(3), 149–163 (2015)
Chouiref, Z., Belkhir, A., Benouaret, K., Hadjali, A.: A fuzzy framework for efficient user-centric web service selection. Appl. Soft Comput. 41, 51–65 (2016)
Xu, J., Guo, L., Zhang, R., Hu, H., Wang, F., Pei, Z.: QoS-aware service composition using fuzzy set theory and genetic algorithm. Wireless Pers. Commun. 102(2), 1009–1028 (2018)
Zhang, S., Xu, Y., Zhang, W., Yu, D.: A new fuzzy QoS-aware manufacture service composition method using extended flower pollination algorithm. J. Intell. Manuf. 30(5), 2069–2083 (2019)
Lupeikienė, A., Miliauskaitė, J., Čaplinskas, A.: A model of view-based enterprise business service quality evaluation framework. Informatica 24(4), 543–560 (2013)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3):199–249(I) (1975); 8(4):301–357(II) (1975); 9(1):43–80 (1975)
Zimmermann, H.J.: Fuzzy set theory—and its applications. Springer Science & Business Media, Berlin (2011)
Zanotelli, R., Reiser, R., Bedregal, B.: n-dimensional intervals and fuzzy S-implications. In Proc. of the 2018 IEEE international conference on fuzzy systems (FUZZ-IEEE), pp. 1-8. IEEE (2018, July)
Hatzimichailidis, A., Papakostas, G., Kaburlasos, V.: On constructing distance and similarity measures based on fuzzy implications. In: Papakotas, G., Hatzimichailidis, A., Kaburlasos, V. (eds.) Handbook of fuzzy sets comparison—theory, algorithms and applications, 6th edn, pp. 1–21. Science Gate Publishing, Xanthi (2016)
Mohibullah, M., Hossain, M., Hasan, M.: Comparison of Euclidean distance function and Manhattan distance function using k-mediods. Int. J. Comput. Sci. Inf. Secur. 13(10), 61 (2015)
Kaufmann, M., Meier, A., Stoffel, K.: IFC-filter: membership function generation for inductive fuzzy classification. Expert Syst. Appl. 42(21), 8369–8379 (2015)
Bilgiç, T., Türkşen, I.: Measurement of membership functions: theoretical and empirical work. In: Dubois, D., Prade, H. (eds.) Fundamentals of fuzzy sets, 7th edn, pp. 195–227. Springer, Berlin (2000)
Bilgiç, T., Turksen, I.: Elicitation of Membership Functions: How far can theory take us? In Proc. of the Sixth IEEE international conference on fuzzy systems, 3, pp. 1321–1325. Barcelona (1997)
Klir, G., Yuan, B.: Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall, Upper Saddle River (1995)
Hasuike, T., Katagiri, H.: Construction of an appropriate membership function based on size of fuzzy set and mathematical programming. In: Proc. of the international multiconference of engineers and computer scientists, 2 (2016)
Schuerz, M., Adlassnig, K.-P., Lagor, C., Schneider, B., Grabner, G.: Definition of fuzzy sets representing medical concepts and acquisition of fuzzy relationships between them by semi-automatic procedures. (Electronic Newsletter) Fuzzy Soft Comput Digest 1(2) (1999)
Richardson, J.: The concepts and methods of phenomenographic research. Rev. Educ. Res. 69(1), 53–82 (1999)
Vafaei, N., Ribeiro, R.A., Camarinha-Matos, L.M.: Normalization techniques for multi-criteria decision making: analytical hierarchy process case study. In: Doctoral conference on computing, electrical and industrial systems, pp. 261–269. Springer, Cham (2016, April)
Deza, M., Deza, E.: Encyclopedia of distances. Springer, Berlin (2009)
Nielsen, J.: Usability engineering. Elsevier, New York (1994)
Taylor, B., Dey, A., Siewiorek, D., Smailagic, A.: Using crowd sourcing to measure the effects of system response delays on user engagement. In: Proc. of the 2016 CHI conference on human factors in computing systems, pp. 4413–4422. ACM (2016, May)
Wu, D.: Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans Fuzzy Syst 21(1), 80–99 (2013)
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Miliauskaitė, J., Kalibatiene, D. On General Framework of Type-1 Membership Function Construction: Case Study in QoS Planning. Int. J. Fuzzy Syst. 22, 504–521 (2020). https://doi.org/10.1007/s40815-019-00753-4
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DOI: https://doi.org/10.1007/s40815-019-00753-4