An overview and a derivation of interval type-2 fussy logic system (IT2 FLS), which can handle ruleâ€™s uncer-tainties on continuous domain, having good number of applications in real world. This work focused on the performance of an IT2 FLS that involves the operations of fuzzification, inference, and output processing. The output processing consists of Type-Reduction (TR) and defuzzification. This work made IT2 FLS much more accessible to FLS modelers, because it provides mathematical formulation for calculating the deriva-tives. Presenting extend to representation of T2 FSs on continuous domain and using it to derive formulas for operations, we developed and extended the derivation of the union of two IT2 FSs to the derivation of the intersection and union of N-IT2 FSs that is based on various concepts. The derivation of all the formulas that are related with an IT2 and these formulas depend on continuous domain with multiple rules. Each rule has multiple antecedents that are activated by a crisp number with T2 singleton fuzzification (SF). Then, we have shown how those results can be extended to T2 non-singleton fuzzification (NSF). We are derived the relationship between the consequent and the domain of uncertainty (DOU) of the T2 fired output FS. As well as, provide the derivation of the general form at continuous domain to calculate the different kinds of type-reduced. We have also applied an IT2 FLS to medical application of Heart Diseases (HDs) and an IT2 pro-vide rather modest performance improvements over the T1 predictor. Finally, we made a comparison of HDs result between IT2 FLS using the IT2FLS in MATLAB and the IT2 FLS in Visual C# models with T1 FISs (Mamda-ni, and Takagi-Sugeno).
Type-2 fuzzy sets, Interval type-2 membership functions, Footprint of uncertainties, set theoretic operations, Type-2 fuzzy logic system, Type-reduction, Heart diseases
- Castro J., Castillo O., Melin P., and DÃaz A., (2008), â€œBuilding fuzzy inference systems with a new interval type-2 fuzzy logic toolbox,â€ Trans. on Computer Science, vol. 50, pp. 104â€“114
- Karnik N., Mendel J., (2001), â€œCentroid of a type-2 fuzzy sets,â€ An International Journal of Information Sciences, vol. 132, pp. 195-220
- Karnik N., Mendel J., (2001), â€œOperations on type-2 fuzzy sets,â€ Fuzzy Sets and Systems, vol. 122, pp. 327â€“348.
- Karnik N., Mendel J., and Liang Q., (1999), â€œType-2 fuzzy logic systems,â€ IEEE Transactions on Fuzzy Systems, vol. 7, no. 6, PP. 643-658
- Karnik N., and Mendel J., (1998), â€œIntroduction to type-2 fuzzy logic systemsâ€, IEEE International Conference on Fuzzy Sys-tems Proceedings, pp. 915â€“920
- Liang Q. and Mendel J., (2000), â€œInterval type-2 fuzzy logic systems: theory and design,â€ IEEE Transactions on Fuzzy Systems, vol. 8, no. 5, pp. 535â€“550
- Morales O., Mendez J., and Devia J., (2012), â€œCentroid of an interval type-2 fuzzy set re-formulation of the problemâ€, Ap-plied Mathematical Sciences, vol. 6, no. 122, pp. 6081-6086
- Mendel J., Liu F., and Zhai D., (2009), â€œÎ±-plane representation for type-2 fuzzy sets: theory and applications,â€ IEEE Transac-tions on Fuzzy Systems, vol. 17, no. 5, pp. 1189-1207
- Mendel J., (2009), â€œOn answering the question â€˜Where do i start in order to solve a new problem involving interval type-2 fuzzy sets?â€™â€, International Journal of Information Sciences, vol. 179, pp. 3418â€“3431
- Mendel J., (2007), â€œtype-2 fuzzy sets and systems: an overview,â€ IEEE computation intelligence magazine, vol. 2, no. 1, pp. 20-29
- Mendel J., (2007), â€œAdvances in type-2 fuzzy sets and systems,â€ International Journal of Information Sciences, vol. 177, pp. 84-110
- Mendel J., John R. and Liu F., (2006), â€œInterval type-2 fuzzy logic systems made simple,â€ IEEE Transactions on Fuzzy Systems, vol. 14, no. 6, pp. 808-821
- Mendel J., (2004), â€œComputing derivatives in interval Type-2 fuzzy logic systemsâ€, IEEE Transactions on Fuzzy Systems, vol. 12, no. 1, pp. 84-98
- Melgarejo M., Reyes A., and Garcia A., (2004), â€œComputational model and architectural proposal for a hardware type-2 fuzzy systemâ€, Proc. IEEE FUZZ Conf., Budapest, Hungary
- Mendel J., (2002), â€œAn architecture for making judgments using computing with wordsâ€, International Journal of Applied Mathematics and Computer Science, vol. 12, no. 3, pp. 325â€“335
- Mendel J. and Bob-John R., (2002), â€œType-2 fuzzy sets made simple,â€ IEEE Transactions on Fuzzy Systems, vol. 10, no. 2, pp. 117- 127
- Mendel J., (2001), â€œUncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directionsâ€, Prentice-Hall, Upper Sad-dle River
- Salazar O., Serrano H. and Soriano J., (2011), â€œCentroid of an interval type-2 fuzzy set: continuous vs. discrete,â€ Ingenieria, Universidad Distrital Francisco JosÃ© De Caldas, vol. 16, no. 2, pp. 67-78
- Wu D., Mendel J. , and Coupland S., (2012), â€œEnhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis,â€ IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp. 499-513
- Wu H. and Mendel J., (2007), â€œClassification of battlefield ground vehicles using acoustic features and fuzzy logic rule-based classifiers,â€ IEEE Trans. Fuzzy Syst., vol. 15, no. 1, pp. 56â€“72
- Wu H. and Mendel J., (2002), â€œUncertainty bounds and their use in the design of interval type-2 fuzzy logic systemsâ€, IEEE Transactions on Fuzzy Systems, vol. 10, no. 5, pp. 622-639
- Zeng J., Xie L., Liu Z., (2008), â€Type-2 fuzzy Gaussian mixture models,â€ Journal of the Pattern Recognition Society, vol. 41, pp. 3636 â€“ 3643
Cite this Article:
International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.