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Frontiers of Higher Order Fuzzy Sets pp 31–49Cite as

Fuzzy Sets of Higher Type and Higher Order in Fuzzy Modeling

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Abstract

Fuzzy sets of higher order and higher type form one of the interesting conceptual and methodological pursuits in the development of the fundamentals of fuzzy sets. The objective of this study is to investigate a role of these constructs in the realm of fuzzy modeling. Rather than venturing into detailed algorithmic developments, we highlight key motivating factors behind the use of type-2 and order-2 in fuzzy models, especially fuzzy rule-based models. Linkages between type-n fuzzy sets and hierarchical fuzzy models are discussed. An overall setting of the study concerns granular computing (GC) along with its two fundamental ideas of the principle of justifiable granularity and an optimal allocation of information granularity.

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References

  1. A. Bargiela, W. Pedrycz, Granular Computing: An Introduction (Kluwer Academic Publishers, London, 2003)

    Book  Google Scholar 

  2. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms (Plenum Press, New York, 1981)

    Book  MATH  Google Scholar 

  3. E. Czogala, W. Pedrycz, On the concept of fuzzy probabilistic controllers. Fuzzy Sets Syst. 10, 109–121 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Czogala, S. Gottwald, W. Pedrycz, Logical connectives of probabilistic sets. Fuzzy Sets Syst. 10, 299–308 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  5. K. Hirota, Concepts of probabilistic sets. Fuzzy Sets Syst. 5(1), 31–46 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  6. K. Hirota, W. Pedrycz, Characterization of fuzzy clustering algorithms in terms of entropy of probabilistic sets. Pattern Recognit. Lett. 2(4), 213–216 (1984)

    Article  MATH  Google Scholar 

  7. E. Hisdal, The IF THEN ELSE statement and interval-valued fuzzy sets of higher type. Int. J. Man–Machine Stud. 15, 385–455 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  8. N.M. Karnik, J. M. Mendel, Q. Liang, Type-2 fuzzy logic systems, IEEE Trans. Fuzzy Syst. 7, 643–658 (1999)

    Article  Google Scholar 

  9. J. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions (Prentice Hall, Upper Saddle River, 2001)

    Google Scholar 

  10. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data (Kluwer Academic Publishers, Dordrecht, 1991)

    Book  MATH  Google Scholar 

  11. W. Pedrycz, Shadowed sets: Representing and processing fuzzy sets, IEEE Trans. Syst. Man, Cybern. Part B 28, 103–109 (1998)

    Article  Google Scholar 

  12. W. Pedrycz, Knowledge-Based Clustering: From Data to Information Granules (John Wiley, Hoboken, 2005)

    Book  Google Scholar 

  13. W. Pedrycz, Allocation of information granularity in optimization and decision-making models: towards building the foundations of granular computing. Eur. J. Oper. Res. (2012, to appear)

    Google Scholar 

  14. W. Pedrycz, Granular Computing: Analysis and Design of Intelligent Systems (CRC Press/Francis Taylor, Boca Raton, 2013)

    Book  Google Scholar 

  15. W. Pedrycz, P. Rai, Collaborative clustering with the use of Fuzzy C-Means and its quantification. Fuzzy Sets Syst. 15, 2399–2427 (2008)

    Article  MathSciNet  Google Scholar 

  16. W. Pedrycz, M.L. Song, Analytic Hierarchy Process (AHP) in group decision making and its optimization with an allocation of information granularity, IEEE Trans. Fuzzy Syst. 19, 527–539 (2011)

    Article  Google Scholar 

  17. L.A. Zadeh, Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  18. L.A. Zadeh, Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90, 111–117 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. L.A. Zadeh, From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circuits Syst. 45, 105–119 (1999)

    Article  MathSciNet  Google Scholar 

  20. L.A. Zadeh, Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plan. Inference 105, 233–264 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  21. L.A. Zadeh, A note on Z-numbers. Inf. Sci. 181, 2923–2932 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of Alberta, T6R 2V4, Edmonton, AB, Canada

    Witold Pedrycz

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Witold Pedrycz

  3. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Witold Pedrycz

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  1. Witold Pedrycz
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Correspondence to Witold Pedrycz .

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Editors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    Alireza Sadeghian

  2. Ryerson University, Toronto, Ontario, Canada

    Hooman Tahayori

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Pedrycz, W. (2015). Fuzzy Sets of Higher Type and Higher Order in Fuzzy Modeling. In: Sadeghian, A., Tahayori, H. (eds) Frontiers of Higher Order Fuzzy Sets. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3442-9_3

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  • DOI: https://doi.org/10.1007/978-1-4614-3442-9_3

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-3441-2

  • Online ISBN: 978-1-4614-3442-9

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