Modeling and Prediction of the MXNUSD Exchange Rate Using Interval Singleton Type-2 Fuzzy Logic Systems

Parameter Prediction with Novel Enhanced Wagner Hagras Interval Type-3 Takagi–Sugeno–Kang Fuzzy System with Type-1 Non-Singleton Inputs

“…In the world of modern business, it is required to improve the performance and the quality of fuzzy systems when they are used to predict and control real-time nonlinear dynamical industrial processes. Among others, the processes of financial systems [1][2][3][4][5], industrial manufacturing processes [6][7][8], autonomous mobile robots [9][10][11][12][13], intelligent controllers [14][15][16][17][18][19][20][21][22][23][24][25][26], route selection [27,28], clustering systems [29,30], medical systems [31][32][33], vision and pattern recognition systems [34][35][36], granular computing and optimization [37,38], database and information systems [39,40], and plant monitoring and diagnostics [18,[41][42][43][44] are characterized by high uncertainty, nonlinearity, and time-varying behavior …”

Intersection and union of type-n fuzzy sets

“…Real world Manuscript applications often support Gaussian or Gaussian-like (e.g. truncated Gaussian) models of vagueness [2,3], which are parsimoniously specified by two parameters. As these examples illustrate, imposing a convexity constraint still allows flexibility in choice of membership form.…”

“…A fuzzy set on the unit interval is said to be convex if there is some fraction t for which its membership function does not decrease on the sub interval [ ] 0,t and does not increase on [ ] ,1 t . The most commonly employed forms of membership functions --interval, triangular, trapezoidal and Gaussian [2][3][4][5][6] --define convex fuzzy sets. When the memberships of convex fuzzy sets on the unit interval attain a peak value one at exactly one point, as with Gaussian or triangular functions, then the fuzzy sets are fuzzy numbers, which have long been the subject of investigation [7][8][9] While interval models of vagueness such as interval type-2 fuzzy sets reduce complexity, they are unnatural reflections of the real world because of the discontinuity between zero and full memberships at the interval endpoints.…”

Hybrid learning for interval type-2 fuzzy logic systems based on orthogonal least-squares and back-propagation methods

“…In the backward pass, the error propagates backward, and the antecedent parameters are tuned using the BP method. One of the hybrid algorithms proposed elsewhere [5,8,9] is based on an RLS method, and since then it has been a benchmark algorithm for parameter estimation and systems identification. It has been shown [5,8,9] that hybrid algorithms provide improved convergence compared with the BP method.…”

“…The processes of financial systems [5][6][7], hot strip mills [8,9], autonomous mobile robots [10], intelligent controllers [11][12][13], and plant monitoring and diagnostics [14][15][16] are characterized by high uncertainty, nonlinearity, and time-varying behavior [17]. Type-2 (T2) fuzzy sets let us model the effects of uncertainties and minimize them by optimizing the parameters of an IT2 fuzzy set during a learning process [18][19][20].…”