Top

Quality & Quantity

Published in:

12-02-2015

Intuitionistic fuzzy sets in questionnaire analysis

Authors: Donata Marasini, Piero Quatto, Enrico Ripamonti

Published in: Quality & Quantity | Issue 2/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Fuzzy sets represent an extension of the concept of set, used to mathematically model veiled and indefinite concepts, such as those of youth, poverty, customer satisfaction and so on. Fuzzy theory introduces a membership function, expressing the degree of membership of the elements to a set. Intuitionistic fuzzy sets and hesitant fuzzy sets are two extensions of the theory of fuzzy sets, in which non-membership degrees and hesitations expressed by a set of experts are, respectively, introduced. In this paper, we apply intuitionistic fuzzy sets to questionnaire analysis, with a focus on the construction of membership, non-membership and uncertainty functions. We also suggest the possibility of considering intuitionistic hesitant fuzzy sets as a valuable theoretical framework. We apply these models to the evaluation of a Public Administration and we assess our results through a sensitivity analysis.

previous article Telehealth services evaluation: a combination of SERVQUAL model and importance-performance analysis

next article Heterogeneous economic returns to higher education: evidence from Italy

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

In order to avoid any conflict of notation, we employed p and \( \omega \) instead of \( (1 - \xi ) \) and \( (1 - \pi ) \) adopted by Iannario and Piccolo (2012).

Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Set Syst 20(2), 87–96 (1986)CrossRef

Atanassov, K.T.: On Intuitionistic Fuzzy Sets Theory. Springer, New York (2012)CrossRef

Bede, B.: Mathematics of Fuzzy Sets and Fuzzy Logic. Springer, New York (2013)CrossRef

Beliakov, G., Bustince, H., Goswami, D.P., Mukherjee, U.K., Pal, N.R.: On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inform Sciences 181(6), 1116–1124 (2011)CrossRef

Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), B-141 (1970)CrossRef

Betti, G., Cheli, B., Lemmi, A., Verma, V.: On the construction of fuzzy measures for the analysis of poverty and social exclusion. Stat. Appl. Inf. Sci. IV(2), 23–26 (2006)

Betti, G., D’Agostino, A., Neri, L.: Educational mismatch of graduates: a multidimensional and fuzzy indicator. Soc. Indic. Res. 103(3), 465–480 (2011)CrossRef

Biswas, R.: An application of fuzzy sets in students’ evaluation. Fuzzy Set Syst 74(2), 187–194 (1995)CrossRef

Black, M.: Vagueness. An exercise in logical analysis. Philos. Sci. 4(4), 427–455 (1937)CrossRef

Castillo, C., Lorenzana, T.: Evaluation of business scenarios by means of composite indicators. Fuzzy Econ. Rev. 15(2), 3–20 (2010)

Cerioli, A., Zani, S.: A fuzzy approach to the measurement of poverty. In: Dagum, C., Zenga, M. (eds.) Income and wealth distribution, inequality and poverty. Studies in Contemporary Economics, pp. 272–284. Springer, Berlin (1990)CrossRef

Cheli, B.: Totally fuzzy and relative measures of poverty in dynamic context. Metron 53, 83–205 (1995)

Cheli, B., Lemmi, A.: A “Totally” fuzzy and relative approach to the multidimensional analysis of poverty. Econ. Notes 24, 115–134 (1995)

Chen, S.-M., Lee, C.-H.: New methods for students’ evaluation using fuzzy sets. Fuzzy Set Syst 104(2), 209–218 (1999)CrossRef

Chien, C.-J., Tsai, H.-H.: Using fuzzy numbers to evaluate perceived service quality. Fuzzy Sets Syst. 116(2), 289–300 (2000)CrossRef

Chung, S., Choi, H., Lee, S.S.Y.: Measuring social capital in the Republic of Korea with mixed methods: application of factor analysis and fuzzy-set ideal type approach. Soc. Indic. Res. 117(1), 45–64 (2014)CrossRef

Crocetta, C., Delvecchio, G.: A fuzzy measure of satisfaction for university education as a key for employment. In: Fabbris, L. (ed.) Effectiveness of University Education in Italy, pp. 11–27. Springer, Berlin (2007)

Cugnata, F., Salini, S.: Model-based approach for importance—performance analysis. Qual. Quant. 48(6), 3053–3064 (2013)CrossRef

Darestani, A.Y., Jahromi, A.E.: Measuring customer satisfaction using a fuzzy inference system. J. Appl. Sci. 9(3), 469–478 (2009)CrossRef

da Silva, C.F.D., de Araújo Batista, D., de Medeiros, D.D.: A proposed method to evaluate the quality of services using Fuzzy sets theory. Qual. Quant. 48(2), 871–885 (2014)CrossRef

Delgado, M., Ruiz, D., Sanchez, D., Vila, A.: Fuzzy quantification: a state of the art. Fuzzy Set Syst. 242, 1–30 (2014)CrossRef

D’Elia, A., Piccolo, D.: A mixture model for preferences data analysis. Comput. Stat. Data Anal. 49(3), 917–934 (2005)CrossRef

Despi, I., Opris, D., Yalcin, E.: Generalised Atanassov intuitionistic fuzzy sets. In eKNOW 2013, The Fifth International Conference on Information, Process, and Knowledge Management (pp. 51–56) (2013)

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, New York (2000)CrossRef

Goldstein, H., Rasbash, J., Browne, W., Woodhouse, G., Poulain, M.: Multilevel models in the study of dynamic household structures. Eur. J. Popul. 16(4), 373–387 (2000)CrossRef

Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18(2), 145–174 (1967)CrossRef

Kwong, C.K., Bai, H.: A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment. J. Intell. Manuf. 13(5), 367–377 (2002)CrossRef

Iannario, M., Piccolo, D.: CUB models: Statistical methods and empirical evidence. In: Kennet, R., Salini, S. (eds.) Modern Analysis of Customer Surveys: With Applications using R, pp. 231–258. Wiley, Chichester (2012)

Lalla, M., Facchinetti, G., Mastroleo, G.: Ordinal scales and fuzzy set systems to measure agreement: an application to the evaluation of teaching activity. Qual. Quant. 38(5), 577–601 (2005)CrossRef

Li, D.-F.: Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, vol. 308. Springer, New York (2014)

Manton, K.G., Tolley, H.D., Woodbury, M.A.: Statistical Applications Using Fuzzy Sets. Wiley, New York (1994)

Marasini, D., Quatto, P.: Descriptive Analysis of student ratings. J. Appl. Quant. Methods 6(4), 125–133 (2011)

Piccolo, D., D’Elia, A.: A new approach for modelling consumers’ preferences. Food Qual. Prefer. 19, 247–259 (2008)CrossRef

Qian, G., Wang, H., Feng, X.: Generalized hesitant fuzzy sets and their application in decision support system. Knowl.-Based Syst. 37, 357–365 (2013)CrossRef

Rodríguez, R.M., Martínez, L., Torra, V., Xu, Z.S., Herrera, F.: Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst. 29, 495–524 (2014)CrossRef

Smithson, M., Verkuilen, J.: Fuzzy Set Theory: Applications in the Social Sciences. Sage, London (2006)

Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

Xia, M., Xu, Z., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot. 22(2), 259–279 (2013)CrossRef

Xu, Z.: Hesitant Fuzzy Sets Theory, vol. 314. Springer, New York (2014a)

Xu, Z.: Hesitant fuzzy Aggregation Operators and Their Applications. Hesitant Fuzzy Sets Theory. Springer, New York (2014b)CrossRef

Xu, Z.: Intuitionistic Preference and Interactive Decision Making. Springer, New York (2014c)CrossRef

Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRef

Zani, S., Milioli, M.A., Morlini, I.: Fuzzy methods and satisfaction indices. In: Kennet, R., Salini, S. (eds.) Modern Analysis of Customer Surveys: With Applications Using R, pp. 439–455. Wiley, Chichester (2012)

Zani, S., Milioli, M.A., Morlini, I.: Fuzzy composite indicators: an application for measuring customer satisfaction. Advances in Theoretical and Applied Statistics, pp. 243–253. Springer, New York (2013)CrossRef

Zhu, B., Xu, Z., Xia, M.: Dual hesitant fuzzy sets. J. Appl. Math. (2012). doi:10.1155/2012/879629

Zimmermann, H.J.: Fuzzy set theory. Wiley Interdiscip. Rev. 2(3), 317–332 (2010)CrossRef

Title: Intuitionistic fuzzy sets in questionnaire analysis
Authors: Donata Marasini
Piero Quatto
Enrico Ripamonti
Publication date: 12-02-2015
Publisher: Springer Netherlands
Published in: Quality & Quantity / Issue 2/2016
Print ISSN: 0033-5177
Electronic ISSN: 1573-7845
DOI: https://doi.org/10.1007/s11135-015-0175-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 2/2016

Erratum to: Publication bias in the German social sciences: an application of the caliper test to three top-tier German social science journals

The influence of negative response style on survey-based household inflation expectations

Recessions, expectations, and labor supply dynamics

Publication bias in the German social sciences: an application of the caliper test to three top-tier German social science journals

The determinants of working capital management and firms performance of textile sector in pakistan

Telehealth services evaluation: a combination of SERVQUAL model and importance-performance analysis