Skip to main content
SpringerLink
Log in

Multi-attribute decision making application using hybridly modelled Gaussian Interval Type-2 Fuzzy sets with uncertain mean

  • 1215: Multimodal Interaction and IoT Applications
  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Perceptual computing (Per-C) is a branch of CWW (Computing with words) that assist people in making subjective decisions. Their applications take linguistic inputs (i.e., words) from the user and return a linguistic output (i.e., word). The perception of these linguistic inputs suffers from uncertainties, for which IT2FSs (Interval Type-2 Fuzzy Sets) are considered better than T1FSs (Type-1 Fuzzy Sets) to capture it. In these applications, the IT2FSs are constructed either by application developers or by consulting experts. Due to the manual introduction of biases, these methods cannot capture uncertainties appropriately, so constructing IT2FS using data intervals is a better approach. The Trapezoidal IT2FS is the only available through this approach, but it has a linear membership function. In real life, the distribution observed is primarily non-linear. The paper presents an experimental method to construct the GIT2FSUM (Gaussian IT2FSs with Uncertain Mean) following statistical (i.e. pruning) and heuristical (i.e. selection of underlying T1FS) steps on data intervals. In order to show its capability in capturing uncertainties, a MADM (Multi-attribute decision making) application following the Per-C framework is developed. The application recommends the suitability of the Online Study Platforms (OSP) to a student. LWA (Linguistic weighted average) operation is performed to obtain OWR (Output Word Representation) for selecting the recommendation word corresponding to an OSP. In this experiment, we compare our GIT2FSUM with the existing Trapezoidal IT2FS (i.e., also formed using data-interval). The average Jaccard similarity between OWR (using GIT2FSUM) and recommendation word is (0.67 ± 0.12), while for OWR (using Trapezoidal IT2FS) is (0.55 ± 0.11). It indicates that the GIT2FSUM is much better than Trapezoidal IT2FS in capturing uncertainties present in the perception of words. In addition, the number of parameters to model GIT2FSUM is comparatively less than Trapezoidal IT2FS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability

The data collected for the experiment from seven hundred students is made freely available at https://github.com/rohit129/G-IT2FS.

Code Availability

The source-code is built on MATLAB R2018b and is freely available at https://github.com/rohit129/G-IT2FS.

Notes

  1. Source code and data is available at: https://github.com/rohit129/G-IT2FS

  2. GATE (Graduate Aptitude Test in Engineering): A national level exam for admission in masters in Indian government engineering institute.

  3. It is used in calculating the tolerance interval from the samples.

  4. For details see Table A.7 of [32].

References

  1. Alonso JM (2018) From Zadeh’s computing with words towards explainable artificial intelligence. In: International workshop on fuzzy logic and applications, pp. 244–248. Springer

  2. Azar FS (2000) Multiattribute decision-making: use of three scoring methods to compare the performance of imaging techniques for breast cancer detection

  3. Chen SM, Hong JA (2014) Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets and the topsis method. IEEE Transactions on Systems, Man, and Cybernetics: Systems 44(12):1665–1673

    Article  Google Scholar 

  4. Dong W, Wong F (1987) Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets Syst 21(2):183–199

    Article  MATH  Google Scholar 

  5. Gao Y, Li DS, Zhong H (2020) A novel target threat assessment method based on three-way decisions under intuitionistic fuzzy multi-attribute decision making environment. Eng Appl Artif Intell 103276:87

    Google Scholar 

  6. Gupta PK, Muhuri PK (2019) Computing with words for student strategy evaluation in an examination. Granul Comput 4(2):167–184

    Article  Google Scholar 

  7. Kacprzyk J, Yager RR (2001) Linguistic summaries of data using fuzzy logic. Int J Gen Syst 30(2):133–154

    Article  MATH  Google Scholar 

  8. Kazmier LJ (2019) Theory and Problems of BUSINESS STATISTICS. McGraw-Hill Companies

  9. Liang D, Liu D, Pedrycz W, Hu P (2013) Triangular fuzzy decision-theoretic rough sets. Int J Approx Reason 54(8):1087–1106

    Article  MATH  Google Scholar 

  10. Liu F, Mendel JM (2007) An interval approach to fuzzistics for interval type-2 fuzzy sets. In: 2007 IEEE International fuzzy systems conference, pp. 1–6. IEEE

  11. Liu F, Mendel JM (2008) Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans Fuzzy Syst 16(6):1503–1521

    Article  Google Scholar 

  12. Lyon A (2014) Why are normal distributions normal? Br J Philos Sci 65(3):621–649

    Article  MATH  Google Scholar 

  13. Majumder D, Debnath J, Biswas A (2017) Interval type-2 mamdani fuzzy inference system for morningness assessment of individuals. In: Artificial intelligence and evolutionary computations in engineering systems, pp. 679–693. Springer

  14. Manna S, Basu TM, Mondal SK (2019) Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making. Granul Comput 4(3):585–599

    Article  Google Scholar 

  15. Mendel JM (1999) Computing with words, when words can mean different things to different people. In: Proceedings of third international ICSC symposium on fuzzy logic and applications, pp. 158–164

  16. Mendel JM (2003) Fuzzy sets for words: a new beginning. In: The 12th IEEE international conference on fuzzy systems, 2003. FUZZ’03., vol. 1, pp. 37–42. IEEE

  17. Mendel JM (2007) Computing with words and its relationships with fuzzistics. Inf Sci 177(4):988–1006

    Article  Google Scholar 

  18. Mendel JM (2018) The perceptual computer: The past, up to the present, and into the future. Informatik-Spektrum 41(1):15–26

    Article  Google Scholar 

  19. Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821

    Article  Google Scholar 

  20. Mendel JM, Wu H (2007) Type-2 fuzzistics for symmetric interval type-2 fuzzy sets: Part 2, inverse problems. IEEE Trans Fuzzy Syst 15(2):301–308

    Article  Google Scholar 

  21. Mendel JM, Wu D (2008) Perceptual reasoning for perceptual computing. IEEE Trans Fuzzy Syst 16(6):1550–1564

    Article  Google Scholar 

  22. Mendel J, Wu D (2010) Perceptual computing: aiding people in making subjective judgments, vol 13. Wiley, New York

    Book  Google Scholar 

  23. Mishra R, Barnwal SK, Malviya S, Singh V, Singh P, Singh S, Tiwary US (2019) Computing with words through interval type-2 fuzzy sets for decision making environment. In: International conference on intelligent human computer interaction, pp. 112–123. Springer

  24. Nguyen HT, Walker CL, Walker EA (2018) A first course in fuzzy logic CRC press

  25. Niewiadomski A, Ochelska J, Szczepaniak P (2006) Interval-valued linguistic summaries of databases. Control Cybern 35:415–443

    MATH  Google Scholar 

  26. O’Hagan A, Buck CE, Daneshkhah A, Eiser JR, Garthwaite PH, Jenkinson DJ, Oakley JE, Rakow T (2006) Uncertain judgements: eliciting experts’ probabilities

  27. Rao RV (2007) Introduction to multiple attribute decision-making (madm) methods. Decision Making in the Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods, pp. 27–41

  28. Runkler T, Coupland S, John R (2017) Interval type-2 fuzzy decision making. Int J Approx Reason 80:217–224

    Article  MATH  Google Scholar 

  29. Tan WW, Chua TW (2007) Uncertain rule-based fuzzy logic systems: introduction and new directions (mendel, jm; 2001)[book review]. IEEE Comput Intell Mag 2(1):72–73

    Article  Google Scholar 

  30. Vinogradova I (2019) Multi-attribute decision-making methods as a part of mathematical optimization. Mathematics 7(10):915

    Article  Google Scholar 

  31. Wallsten TS, Budescu DV (1995) A review of human linguistic probability processing: General principles and empirical evidence. Knowl Eng Rev 10 (1):43–62

    Article  Google Scholar 

  32. Walpole RE, Myers SL, Ye K, Myers RH (2007) Probability and statistics for engineers and scientists

  33. Wu D (2012) Twelve considerations in choosing between gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers. In: 2012 IEEE International conference on fuzzy systems, pp. 1–8. IEEE

  34. Wu H, Mendel JM (2002) Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 10(5):622–639

    Article  Google Scholar 

  35. Wu D, Mendel JM (2006) The linguistic weighted average. In: 2006 IEEE International conference on fuzzy systems, pp. 566–573. IEEE

  36. Wu D, Mendel JM (2007) Uncertainty measures for interval type-2 fuzzy sets. Inf Sci 177(23):5378–5393

    Article  MATH  Google Scholar 

  37. Wu D, Mendel JM (2007) Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Trans Fuzzy Syst 15(6):1145–1161

    Article  Google Scholar 

  38. Wu D, Mendel JM (2008) Corrections to “aggregation using the linguistic weighted average and interval type-2 fuzzy sets”. IEEE Trans Fuzzy Syst 16(6):1664–1666

    Article  Google Scholar 

  39. Wu D, Mendel JM (2008) A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets. Inf Sci 178(2):381–402

    Article  MATH  Google Scholar 

  40. Wu D, Mendel JM (2009) A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inf Sci 179(8):1169–1192

    Article  Google Scholar 

  41. Wu D, Mendel JM (2009) Enhanced karnik–mendel algorithms. IEEE Trans Fuzzy Syst 17(4):923–934

    Article  Google Scholar 

  42. Wu D, Mendel JM (2018) Similarity measures for closed general type-2 fuzzy sets: overview, comparisons, and a geometric approach. IEEE Trans Fuzzy Syst 27(3):515–526

    Article  Google Scholar 

  43. Wu D, Mendel JM (2019) Recommendations on designing practical interval type-2 fuzzy systems. Eng Appl Artif Intell 85:182–193

    Article  Google Scholar 

  44. Yager RR (1982) A new approach to the summarization of data. Inf Sci 28(1):69–86

    Article  MATH  Google Scholar 

  45. Yang YY, Liu XW, Liu F (2020) Trapezoidal interval type-2 fuzzy topsis using alpha-cuts. Int J Fuzzy Syst 22(1):293–309

    Article  Google Scholar 

  46. Zadeh LA (1988) Fuzzy logic. Computer 21(4):83–93

    Article  Google Scholar 

  47. Zadeh LA (1999) Fuzzy logic= computing with words. In: Computing with words in information/intelligent systems 1, pp. 3–23. Springer

  48. Zadeh LA (1999) From computing with numbers to computing with words. from manipulation of measurements to manipulation of perceptions. IEEE Trans Circuits Syst I Fundam Theor App 46(1):105–119

    Article  MATH  Google Scholar 

  49. Zadeh LA (2001) A new direction in ai: Toward a computational theory of perceptions. AI magazine 22(1):73–73

    MATH  Google Scholar 

  50. Zadeh LA (2008) Toward human level machine intelligence - is it achievable? the need for a paradigm shift. IEEE Comput Intell Mag, 3

  51. Zadeh L (2016) From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. ieee transa. Health Informatics Meets eHealth G Schreier others.(Eds.) 9

  52. Zhang Q, Chen JC, Chong PP (2004) Decision consolidation: criteria weight determination using multiple preference formats. Decis Support Syst 38 (2):247–258

    Article  Google Scholar 

  53. Zimmermann HJ (2011) Fuzzy set theory—and its applications Springer Science & Business Media

Download references

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

  1. Department of Information Technology, Indian Institute of Information Technology Allahabad, Prayagraj, India

    Rohit Mishra, Shrikant Malviya, Sumit Singh, Varsha Singh & Uma Shanker Tiwary

Authors
  1. Rohit Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shrikant Malviya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sumit Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Varsha Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Uma Shanker Tiwary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rohit Mishra.

Ethics declarations

Conflict of Interests

The authors declare that they have no conflict of interest, financial or otherwise.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, R., Malviya, S., Singh, S. et al. Multi-attribute decision making application using hybridly modelled Gaussian Interval Type-2 Fuzzy sets with uncertain mean. Multimed Tools Appl 82, 4913–4940 (2023). https://doi.org/10.1007/s11042-022-12172-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-022-12172-z

Keywords

Search

Navigation