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Interval type-2 fuzzy sets to model linguistic label perception in online services satisfaction

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Abstract

In this paper, we propose a novel two-phase methodology based on interval type-2 fuzzy sets (T2FSs) to model the human perceptions of the linguistic terms used to describe the online services satisfaction. In the first phase, a type-1 fuzzy set (T1FS) model of an individual’s perception of the terms used in rating user satisfaction is derived through a decomposition-based procedure. The analysis is carried out by using well-established metrics and results from the Social Sciences context. In the second phase, interval T2FS models of online user satisfaction are calculated using a similarity-based data mining procedure. The procedure selects an essential and informative subset of the initial T1FSs that is used to discard the outliers automatically. Resulting interval T2FSs, which are synthesized based on the selected subset of T1FSs only, exhibit reasonable shapes and interpretability.

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References

  • Akama JS, Kieti DM (2003) Measuring tourist satisfaction with Kenya’s wildlife safari: a case study of Tsavo West National Park. Tour Manag 24(1):73–81. doi:10.1016/S0261-5177(02)00044-4

    Article  Google Scholar 

  • Bailey JE, Pearson SW (1983) Development of a tool for measuring and analyzing computer user satisfaction. Manag Sci 29(5):530–545

    Article  Google Scholar 

  • Bajaj RK, Hooda D (2010) On some new generalized measures of fuzzy information. Proc World Acad Sci Eng Technol 62:642–648

    Google Scholar 

  • Bartlett MS (1937) Properties of sufficiency and statistical tests. R Soc Lond Proc Ser A 160:268–282

    Article  Google Scholar 

  • Coupland S, Mendel J, Wu D (2010) Enhanced interval approach for encoding words into interval type-2 fuzzy sets and convergence of the word FOUs. In: Proceedings of the IEEE international conference on fuzzy systems, pp 1–8. doi:10.1109/FUZZY.2010.5584725

  • Cronbach LJ, Shavelson RJ (2004) My current thoughts on coefficient alpha and successor procedures. Educ Psychol Meas 64(3):391–418. doi:10.1177/0013164404266386

    Article  MathSciNet  Google Scholar 

  • Del Vescovo G, Livi L, Frattale Mascioli M, Rizzi A (2014) On the problem of modeling structured data with the MinSOD representative. Int J Comput Theory Eng 6(1):9–14. doi:10.7763/IJCTE.2014.V6.827

    Article  Google Scholar 

  • Ding S, Shi Z, Xia S, Jin F (2007) Studies on fuzzy information measures. In: Proceedings of the fourth international conference on fuzzy systems and knowledge discovery, FSKD’07, vol 3, pp 376–380. IEEE Computer Society, Washington, DC. doi:10.1109/FSKD.2007.534.

  • Dubois D, Ostasiewicz W, Prade H (2000) Fuzzy sets: history and basic notions. In: Dubois D, Prade H (eds) Fundamentals of fuzzy sets, the handbooks of fuzzy sets series, vol 7, pp 21–124. Springer, US . doi:10.1007/978-1-4615-4429-6_2.

  • Kaiser H (1974) An index of factorial simplicity. Psychometrika 39:31–36. doi:10.1007/BF02291575

    Article  MATH  Google Scholar 

  • Liu F, Mendel J (2008) Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans Fuzzy Syst 16(6):1503–1521. doi:10.1109/TFUZZ.2008.2005002

    Article  Google Scholar 

  • Livi L, Rizzi A (2013) Graph ambiguity. Fuzzy Sets Syst 221:24–47. doi:10.1016/j.fss.2013.01.001

    Article  MATH  MathSciNet  Google Scholar 

  • Livi L, Tahayori H, Sadeghian A, Rizzi A (2014) Distinguishability of interval type-2 fuzzy sets data by analyzing upper and lower membership functions. Appl Soft Comput. doi:10.1016/j.asoc.2013.12.020

  • Luca AD, Termini S (1972) A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Control 20(4):301–312. doi:10.1016/S0019-9958(72)90199-4

    Article  MATH  Google Scholar 

  • Mendel J (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice Hall PTR, USA

  • Mendel J, John R (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127. doi:10.1109/91.995115

    Article  Google Scholar 

  • Mendel J, John R, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821. doi:10.1109/TFUZZ.2006.879986

    Article  Google Scholar 

  • Mendel JM (2007) Computing with words and its relationships with fuzzistics. Inf Sci 177(4):988–1006. doi:10.1016/j.ins.2006.06.008

    Article  MathSciNet  Google Scholar 

  • Mendel JM (2007) Computing with words: Zadeh, turing, popper occam. Comput Intell Mag 2(4):10–17. doi:10.1109/MCI.2007.9066897

    Article  MathSciNet  Google Scholar 

  • Moharrer M, Tahayori H (2007) Clustering e-satisfaction factors in tourism industry. In: Proceedings of the international conference on information society, pp 182–185

  • Moharrer M, Tahayori H (2007) Drivers of customer convenience in electronic tourism industry. In: Canadian conference on electrical and computer engineering, CCECE, pp 836–839. doi:10.1109/CCECE.2007.214.

  • Moharrer M, Tahayori H, Albadavi A, Zegordi S, Perzon H (2006) Satisfaction in e-tourism, a case of european online customers. In: Proceedings of the international conference e-commerce, pp 303–307

  • Moharrer M, Tahayori H, Sadeghian A (2010) Modeling linguistic label perception in tourism e-satisfaction with type-2 fuzzy sets. In: Annual meeting of the north american fuzzy information processing society (NAFIPS), pp 1–6. doi:10.1109/NAFIPS.2010.5548185

  • Montero J, Ruan D (2010) Modelling uncertainty. Inf Sci 180(6):799–802. doi:10.1016/j.ins.2009.11.026

    Article  Google Scholar 

  • Nunnally J, Bernstein I (1994) Psychometric theory. No. 972 in McGraw-Hill series in psychology. McGraw-Hill, Maidenheach

  • Pedrycz W (2010) Human centricity in computing with fuzzy sets: an interpretability quest for higher order granular constructs. J Ambient Intell Humaniz Comput 1:65–74. doi:10.1007/s12652-009-0008-0

    Article  Google Scholar 

  • Pedrycz W, Gomide F (1998) An introduction to fuzzy sets: analysis and design. Complex adaptive systems. Mit Press, USA

    Google Scholar 

  • Setnes M, Babuska R, Kaymak U, van Nauta Lemke H (1998) Similarity measures in fuzzy rule base simplification. IEEE Trans Syst Man Cybern Part B Cybern 28(3):376–386. doi:10.1109/3477.678632

    Article  Google Scholar 

  • Szymanski DM, Hise RT (2000) E-satisfaction: an initial examination. J Retail 76(3):309–322. doi:10.1016/S0022-4359(00)00035-X

    Article  Google Scholar 

  • Tahayori H, Antoni GD (2008) Operations on concavoconvex type-2 fuzzy sets. Int J Fuzzy Syst 10(4):276–286

    MathSciNet  Google Scholar 

  • Tahayori H, Livi L, Sadeghian A, Rizzi A (2013) Interval type-2 fuzzy sets reconstruction based on fuzzy information-theoretic kernels. To appear in IEEE-TFS. Manuscript ID: TFS-2013-0660.R1

  • Tahayori H, Sadeghian A (2012) Handling uncertainties of membership functions with shadowed fuzzy sets. World Autom Congr (WAC) 2012:1–5

    Google Scholar 

  • Tahayori H, Sadeghian A (2013) Median interval approach to model words with interval type-2 fuzzy sets. Int J Adv Intell Paradig 4(3):313–336

    Google Scholar 

  • Tahayori H, Sadeghian A (2013) Shadowed fuzzy sets: a framework with more freedom degrees for handling uncertainties than interval type-2 fuzzy sets and lower computational complexity than general type-2 fuzzy sets. In: Balas VE, Fodor J, Várkonyi-Kóczy AR (eds) New concepts and applications in soft computing, studies in computational intelligence, vol 417, pp 97–117. Springer, Heidelberg. doi:10.1007/978-3-642-28959-0_6

  • Tahayori H, Sadeghian A, Pedrycz W (2013) Induction of shadowed sets based on the gradual grade of fuzziness. IEEE Trans Fuzzy Syst 21(5):937–949. doi:10.1109/TFUZZ.2012.2236843

    Article  Google Scholar 

  • Tahayori H, Sadeghian A, Visconti A (2010a) Operations on type-2 fuzzy sets based on the set of pseudo-highest intersection points of convex fuzzy sets. In: Fuzzy information processing society (NAFIPS), annual meeting of the North American, pp 1–6. doi:10.1109/NAFIPS.2010.5548213

  • Tahayori H, Tettamanzi A, Degli Antoni G (2006) Approximated type-2 fuzzy set operations. In: Proceedings of the IEEE international conference on fuzzy systems, pp 1910–1917

  • Tahayori H, Tettamanzi A, Degli Antoni G, Visconti A, Moharrer M (2010) Concave type-2 fuzzy sets: properties and operations. Soft Comput Fusion Found Methodol Appl 14:749–756. doi:10.1007/s00500-009-0462-9

    MATH  Google Scholar 

  • Tahayori H, Tettamanzi AGB, Antoni GD, Visconti A (2009) On the calculation of extended max and min operations between convex fuzzy sets of the real line. Fuzzy Sets Syst 160(21):3103–3114. doi:10.1016/j.fss.2009.06.005

    Article  MATH  Google Scholar 

  • Tahayori H, Moharrer M, Sadeghian A, Reibe S (2014a) Modeling quality of life with interval type-2 fuzzy sets (ready to submit)

  • Tahayori H, Visconti A, Sadeghian A (2014b) Fuzzy disjointing difference operator to calculate union and intersection of type-2 fuzzy sets with respect to min t-norm and max t-conorm. Under review. Int J Approx Reason. Manuscript ID: IJA-D-13-00086, Elsevier

  • Tripathy B, Ray G (2012) On mixed fuzzy topological spaces and countability. Soft Comput 16(10):1691–1695. doi:10.1007/s00500-012-0853-1

    Article  MATH  Google Scholar 

  • Tripathy BC, Baruah A (2010) Nörlund and Riesz mean of sequences of fuzzy real numbers. Appl Math Lett 23(5):651–655

    Article  MATH  MathSciNet  Google Scholar 

  • Tripathy BC, Baruah A, Et M, Gungor M (2012) On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers. Ira J Sci Technol Trans A 2(36):147–155

    MathSciNet  Google Scholar 

  • Tripathy BC, Borgohain S (2011) Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function. Adv Fuzzy Syst 8:8–8:8. doi:10.1155/2011

    Google Scholar 

  • Tripathy BC, Das PC (2012) On convergence of series of fuzzy real numbers. Kuwait J Sci Eng 1A(39):57–70

    MathSciNet  Google Scholar 

  • Tripathy BC, Sarma B (2012) On I-convergent double sequences of fuzzy real numbers. Kyungpook Math J 2(52):189–200

    Article  MathSciNet  Google Scholar 

  • Walker CL, Walker EA (2005) The algebra of fuzzy truth values. Fuzzy Sets Syst 149(2):309–347. doi:10.1016/j.fss.2003.12.003

    Article  MATH  Google Scholar 

  • Wanous JP, Lawler EE (1972) Measurement and meaning of job satisfaction. J Appl Psychol 56(2):95–105

    Article  Google Scholar 

  • Wu D, Mendel JM, Coupland S (2012) Enhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis. IEEE Trans Fuzzy Syst 20(3):499–513

    Article  Google Scholar 

  • Zadeh L (1974) A fuzzy-algorithmic approach to the definition of complex or imprecise concepts. Memorandum (University of California, Berkeley, Electronics Research Laboratory). Electronics Research Laboratory, College of Engineering, University of California

  • Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning—I. Inf Sci 8(3):199–249. doi:10.1016/0020-0255(75)90036-5

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353. doi:10.1016/S0019-9958(65)90241-X

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, Canada

    Masoomeh Moharrer, Hooman Tahayori & Alireza Sadeghian

  2. Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 , Rome, Italy

    Lorenzo Livi & Antonello Rizzi

Authors
  1. Masoomeh Moharrer
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  2. Hooman Tahayori
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  3. Lorenzo Livi
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  4. Alireza Sadeghian
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  5. Antonello Rizzi
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Corresponding author

Correspondence to Lorenzo Livi.

Additional information

Communicated by V. Piuri.

Appendix A: Studying satisfaction with tourism websites

Appendix A: Studying satisfaction with tourism websites

Based on your experiences as an online customer of tourism websites, please consider the following set of questions related to your satisfaction on tourism websites. Read the questions 1–9 and compare your purchasing from tourism websites with the traditional travel agencies and circle a number between 1 and 5 [(1) Much worse than, (2) Worse than, (3) The same, (4) Better than, (5) Much better than].

  1. 1.

    How much are you satisfied with the time efficiency of purchasing from a tourist website comparing to going to traditional agencies?

  2. 2.

    How is shopping from a tourism website from home, office, etc. comparing with going to and shopping from travel agencies?

  3. 3.

    The convenience of 24/7 operating hours of tourism websites comparing to the limited working hours of traditional travel agencies.

  4. 4.

    How is the number of tourism services (airline tickets, hotels, etc.) offered on internet comparing to traditional travel agencies.

  5. 5.

    How is the variety of tourist services (airline tickets, hotels, etc.) offered on internet comparing with traditional travel agencies.

  6. 6.

    How is the quantity of information about airline flights, restaurants, shopping, transportation etc. in tourism website comparing to traditional travel agencies?

  7. 7.

    How is the quality of information about airline flights, restaurants, shopping, transportation etc. in tourism website comparing to traditional travel agencies?

  8. 8.

    Do you feel Safe in online transactions comparing with traditional travel agencies.

  9. 9.

    How is the availability of a formal privacy in tourist websites comparing with traditional travel agencies. Based on your experiences as an online customer of a tourism website, please consider the following set of statements relate to your satisfaction of the tourism websites. Read the statement 10 to 12 and tell how much you are satisfied with each statement in tourism websites. Circle a number between 1 and 5 [(1) Strongly Dissatisfied (SD),\(\ldots \), (5) Strongly Satisfied (SS)].

  10. 10.

    Friendliness and ease of use of the tourist web sites.

  11. 11.

    Attractive web site designed.

  12. 12.

    Interactive and helpfulness of the tourist websites.

  13. 13.

    How would you rate your overall satisfaction of your electronic tourism experience?

    $$\begin{aligned} \hbox {1-Very poor} \quad \hbox {2-Poor} \quad \hbox {3-Fair} \quad \hbox {4-Good} \quad \hbox {5-Very Good} \end{aligned}$$

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Moharrer, M., Tahayori, H., Livi, L. et al. Interval type-2 fuzzy sets to model linguistic label perception in online services satisfaction. Soft Comput 19, 237–250 (2015). https://doi.org/10.1007/s00500-014-1246-4

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