Abstract
In fuzzy theory, modalities (like possibly and necessarily) and hedges (like quite, very, and extremely) are the most commonly examined unary operators. Here, we introduce two reasonable approaches for defining these unaries; by repeating the arguments of many-variable operators and by using compositions of negations. This way, hedges and also modalities can be viewed as a part of a logical system. We show that membership functions, which play a substantial role in the overall performance of fuzzy representation, can also be defined using a generator function. In the literature, the membership functions are usually chosen independently of the logical operators of the system. Parameters are normally fine-tuned based on pure experimental results. Now, we make a suggestion of how modifiers and membership functions can be linked to the logical operators of the system. This unified framework will be useful and aid better interpretability of neural computations in Chap. 9.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Banks, W.: Mixing crisp and fuzzy logic in applications. In: Idea/Microelectronics, WESCON/1994, pp. 94–97 (1994). https://doi.org/10.1109/WESCON.1994.403621
De Cock, M., Bodenhofer, U., Kerre, E.E.: Modelling linguistic expressions using fuzzy relations. In: Proceedings of 6th International Conference on Soft Computing (IIZUKA 2000), 2(Iizuka 2000), pp. 353–360 (2000)
Huynh, V.N., Ho, T.B., Nakamori, Y.: A parametric representation of linguistic hedges in Zadeh’s fuzzy logic. Int. J. Approx. Reason. 30(3), 203–223 (2002). https://doi.org/10.1016/S0888-613X(02)00075-0. ISSN 0888-613X
Jang, J., Sun, C., Mizutani, E.: Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review] (1997). http://ieeexplore.ieee.org/document/633847/. ISSN 0018-9286
Türkşen, I.B.: A foundation for CWW: meta-linguistic axioms. In: Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, vol. 1, pp. 395–400 (2004). https://doi.org/10.1109/nafips.2004.1336315. http://www.scopus.com/inward/record.url?eid=2-s2.0-4544223298&partnerID=40&md5=8c2c1dcce750e5d0721542ecb9f09883
Zadeh, L.: The concept of a linguistic variable and its applications to approximate reasoning II. Inf. Sci. 8(4), 199–249 (1975)
Zadeh, L.: The concept of a linguistic variable and its applications to approximate reasoning III. Inf. Sci. 8(4), 199–249 (1975)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning I. Inf. Sci. 8(3), 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5. ISSN 0020-0255
Dombi, J., Csiszár, O.: Operator-dependent modifiers in nilpotent logical systems. In: Proceedings of the 10th International Joint Conference on Computational Intelligence - vol. 1: IJCCI, pp. 126–134. INSTICC, SciTePress (2018)
Liu, B.-D., Member, S., Chen, C.-Y., Member, S., Tsao, J.-Y.: Design of adaptive fuzzy logic controller based on linguistic-hedge concepts and genetic algorithms. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 31(1), 32–53 (2001)
Csiszár, O., Dombi, J.: Generator-based modifiers and membership functions in nilpotent operator systems. In: IEEE International Work Conference on Bioinspired Intelligence (iwobi 2019), pp. 99–106 (2019)
Zadeh, L.A.: A fuzzy-set-theoretic interpretation of linguistic hedges. J. Cybern. 2(3), 4–34 (1972)
Zadeh, L.A.: Quantitative fuzzy semantics. Inf. Sci. 3, 159–176 (1971)
Dombi, J., Csiszár, O.: The general nilpotent operator system. Fuzzy Sets Syst. 261, 1–19 (2015)
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Dombi, J., Csiszár, O. (2021). Modifiers and Membership Functions in Fuzzy Sets. In: Explainable Neural Networks Based on Fuzzy Logic and Multi-criteria Decision Tools. Studies in Fuzziness and Soft Computing, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-030-72280-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-72280-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-72279-1
Online ISBN: 978-3-030-72280-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)