scholarly journals Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

2019 ◽  
Vol 356 ◽  
pp. 44-62 ◽  
Author(s):  
Xiaozhan Yang ◽  
Hak-Keung Lam ◽  
Ligang Wu
Keyword(s):  
Fuzzy Systems ◽  
Stability Conditions ◽  
Interval Type

scholarly journals Optimal Design of Interval Type-2 Fuzzy Heart Rate Level Classification Systems Using the Bird Swarm Algorithm

Algorithms ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 206 ◽  
Author(s):  
Ivette Miramontes ◽  
Juan Guzman ◽  
Patricia Melin ◽  
German Prado-Arechiga
Keyword(s):  
Heart Rate ◽  
Fuzzy Systems ◽  
Membership Functions ◽  
Classification Rate ◽  
Heart Rate Level ◽  
Swarm Algorithm ◽  
Bird Swarm Algorithm ◽  
Interval Type

In this paper, the optimal designs of type-1 and interval type-2 fuzzy systems for the classification of the heart rate level are presented. The contribution of this work is a proposed approach for achieving the optimal design of interval type-2 fuzzy systems for the classification of the heart rate in patients. The fuzzy rule base was designed based on the knowledge of experts. Optimization of the membership functions of the fuzzy systems is done in order to improve the classification rate and provide a more accurate diagnosis, and for this goal the Bird Swarm Algorithm was used. Two different type-1 fuzzy systems are designed and optimized, the first one with trapezoidal membership functions and the second with Gaussian membership functions. Once the best type-1 fuzzy systems have been obtained, these are considered as a basis for designing the interval type-2 fuzzy systems, where the footprint of uncertainty was optimized to find the optimal representation of uncertainty. After performing different tests with patients and comparing the classification rate of each fuzzy system, it is concluded that fuzzy systems with Gaussian membership functions provide a better classification than those designed with trapezoidal membership functions. Additionally, tests were performed with the Crow Search Algorithm to carry out a performance comparison, with Bird Swarm Algorithm being the one with the best results.

scholarly journals Uncertainty in Interval Type-2 Fuzzy Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Sadegh Aminifar ◽  
Arjuna Marzuki
Keyword(s):  
Fuzzy Systems ◽  
System Response ◽  
Membership Functions ◽  
Degree Reduction ◽  
Word Meanings ◽  
Lower Complexity ◽  
Interval Type

This paper studies uncertainty and its effect on system response displacement. The paper also describes how IT2MFs (interval type-2 membership functions) differentiate from T1MFs (type-1 membership functions) by adding uncertainty. The effect of uncertainty is modeled clearly by introducing a technique that describes how uncertainty causes membership degree reduction and changing the fuzzy word meanings in fuzzy logic controllers (FLCs). Several criteria are discussed for the measurement of the imbalance rate of internal uncertainty and its effect on system behavior. Uncertainty removal is introduced to observe the effect of uncertainty on the output. The theorem of uncertainty avoidance is presented for describing the role of uncertainty in interval type-2 fuzzy systems (IT2FSs). Another objective of this paper is to derive a novel uncertainty measure for IT2MFs with lower complexity and clearer presentation. Finally, for proving the affectivity of novel interpretation of uncertainty in IT2FSs, several investigations are done.

Realizing Interval Type-2 Fuzzy Systems with Type-1 Fuzzy Systems

2012 ◽  
pp. 412-427
Author(s):  
Mamta Khosla ◽  
R K Sarin ◽  
Moin Uddin ◽  
Satvir Singh ◽  
Arun Khosla
Keyword(s):  
Time Series ◽  
Fuzzy Logic ◽  
Mean Square Error ◽  
Fuzzy Systems ◽  
Mean Square ◽  
Fuzzy Logic Systems ◽  
Interval Type

In this chapter, the authors have realized Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) with the average of two Type-1 Fuzzy Logic Systems (T1 FLSs). The authors have presented two case studies by applying this realization methodology on (i) an arbitrary system, where an IT2 FLS is considered, in which its footprint of uncertainty (FOU) is expressed using Principal T1 FS+FOU approach, and the second (ii) the Mackey-Glass time-series forecasting. In the second case study, T1 FLS is evolved using Particle Swarm Optimization (PSO) algorithm for the Mackey-Glass time-series data with added noise, and is then upgraded to IT2 FLS by adding FOU. Further, four experiments are conducted in this case study for four different noise levels. For each case study, a comparative study of the results of the average of two T1 FLSs and the corresponding IT2 FLS, obtained through computer simulations in MATLAB environment, is presented to demonstrate the effectiveness of the realization approach. Very low values of Mean Square Error (MSE) and Root Mean Square Error (RMSE) demonstrate that IT2 FLS performance is equivalent to the average of two T1 FLSs. This approach is helpful in the absence of the availability of development tools for T2 FLSs or because of complexity and difficulty in understanding T2 FLSs that makes the implementation difficult. It provides an easy route to the simulation/realization of IT2 FLSs and by following this approach, all existing tools/methodologies for the design, simulation and realization of T1 FLSs can be directly extended to T2 FLSs.

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