Parallel Interval Type-2 Subsethood Neural Fuzzy Inference System

Fuzzy logic (FL) has been regarded as a useful methodology in modelling. The modeling performance of FL heavily relies on the modeling capability of a fuzzy set (FS). However, the MF of a FS cannot be arbitrarily accurate in practice and thus the centroid as a measure of a FS cannot be accurate to any degree. In face of inaccurate MF, the sensitivity of the centroid of a FS to the deviation of its MF from the ideal MF determines the accuracy of the centroid. To evaluate the modeling capability of a type-1 (T1) FS and an interval type-2 (IT2) FS, this paper will present a comparative study of the sensitivity of the centroid of a T1 FS and an IT2 FS to the deviation of their MFs from the ideal MFs. In this paper, equations relating the amount that the centroid of a T1 FS and an IT2 FS vary with the deviation of their MFs from the ideal MFs were established. Based on the derived equations, it was found that an IT2 FS is able to provide an additional design freedom to vary the sensitivity of its centroid compared to a T1 FS. This unique characteristic may enable an IT2 FS to minimize the sensitivity of the centroid and thus to achieve higher modeling accuracy. Furthermore, guidelines for designing an IT2 FS were provided.

In this paper, a new method for fuzzy inference system optimization is presented. The proposed method performs type-1, interval type-2 and general type-2 fuzzy inference systems design using a hierarchical genetic algorithm as optimization method. This method is an improvement of a fuzzy system optimization approach presented in previous works where only the optimization of type-1 and interval type-2 fuzzy inference systems was performed using a human recognition application. The human recognition is performed using three biometric measures namely iris, ear, and voice, where the main idea is to perform the combination of responses in the modular neural networks using an optimized fuzzy inference system to improve the final results without and with noisy conditions. The main contribution of the proposed method is an optimization able to select type of fuzzy logic, granulation of each fuzzy variable and fuzzy rules selection to design optimal fuzzy inference systems applied in combining modular neural networks responses. The results obtained show the effectiveness of the proposed method to design structures of fuzzy inference systems. Statistical comparisons are performed with previous results, where better results can be observed using the proposed method. The design of optimal structures of fuzzy inference systems include among other parameters; type of fuzzy logic (type-1, interval and general type-2 fuzzy logic), type of inference model (Mamdani model or Sugeno model), and consequents of the fuzzy if–then rules.

The application interval type-2 fuzzy inference systems (IT2FIS) has been attention for a short-term load forecasting problems solution. This paper present optimization membership function of antecedent (X,Y) and consequent (Z) interval type-2 Fuzzy Logic System using Big Bang – Big Crunch Algorithm for application short term load forecasting on national holiday. This method has implemented on the historical peak load data during 14 national holiday case study in South and Central Kalimantan – Indonesia electrical power system on year 2008. The Big Bang–Big Crunch (BB–BC) algorithm will applied to optimization interval footprint of uncertainty (FOU) membership functions of interval type-2 fuzzy logic system. BB-BC Algorithm is a global optimization algorithm and has a low computational cost and a high convergence speed, so very efficient in this research. The test result showed main absolute percentage error (MAPE) less than interval type-2 fuzzy inference system (FIS) and type-1 fuzzy inference system (FIS). Finally, this paper defined main absolute percentage error (MAPE) 0.58045% for type-1 FIS, 0.53906% for interval type-2 FIS, and 0.52421% for optimization interval type-2 FIS-Big Bang Big Crunch Algorithm.

The Wang-Mendel Approach (WMA) focuses on combining the numerical as well as linguistic information for achieving greater explainability for inference models. The standard WMA models the linguistic information using type-1 (T1) fuzzy sets (FSs), which have a reduced capability to model the semantics of linguistic information. Therefore, we propose a novel Enhanced WMA, which models the linguistic information using the type-2 (T2) FSs. Further, our Enhanced T2 FS-based WMA can be modified to reflect the use of interval type-2 (IT2) FSs, for modelling linguistic uncertainty. IT2 FSs are suitable when better uncertainty handling capabilities are required compared to T1 FSs, however, at a computational cost lesser than the T2 FSs. Performance of Enhanced WMA is demonstrated through a real-world crop-yield prediction problem in smart agriculture and an additional exemplar application on users’ satisfaction ratings. Further, we have compared our approach with the performance obtained from the T1 FS-based WMA and the original estimations given in the original data. We found that our Enhanced WMA provides more precise estimates than the other two with 95% confidence level. To the best of our knowledge, this is the first proposal of a T2 FSs method for enhancing the modeling of linguistic uncertainty in the WMA.

This article provides a high-level retrospective of type-2 fuzzy sets and fuzzy logic systems. It explains how type-2 fuzzy sets can be used to model membership function uncertainties, and how by doing this smoother performance can be obtained than by using type-1 fuzzy sets. It also summarizes the notation that should be used for type-2 fuzzy sets, describes four important mathematical representations for these fuzzy sets, explains the differences between type-1 and type-2 fuzzy logic systems and which of the four representations is most useful when designing an optimal type-2 fuzzy logic system, provides a very useful strategy for optimal designs of fuzzy logic systems – one that guarantees performance improvement as one goes from a type-1 fuzzy logic system to a type-2 fuzzy logic system design – , and describes four methods for simplifying the designs of type-2 fuzzy logic systems. Finally, it explains why type-2 fuzzy sets can capture two kinds of linguistic uncertainties simultaneously (the uncertainty of an individual and the uncertainties of a group about a word), whereas type-1 fuzzy sets cannot, and that such type-2 fuzzy set word models are what should be used to implement Zadeh’s Computing With Words paradigm.

Assessment method sends messages to students to define and priorities what is important to learn and ultimately how they spend their time leaning it. Traditional grading methods are largely based on human judgments, which tend to be subjective. In addition, it is based on sharp criteria instead of fuzzy criteria and suffers from erroneous scores assigned by indifferent or inexperienced examiners, which represent a rich source of uncertainties, which might impair the credibility of the system. In an attempt to reduce uncertainties and provide more objective, reliable, and precise grading, a sophisticated assessment approach based on type-2 fuzzy set theory is developed. In this paper, interval type-2 (IT2) fuzzy sets, which are a special case of the general T2 fuzzy sets, are used. The transparency and capabilities of type-2 fuzzy sets in handling uncertainties is expected to provide an evaluation system able to justify and raise the quality and consistency of assessment judgments. A simplified implementation of interval type-2 fuzzy system using the basic knowledge of type-1 fuzzy is presented. A comparison between the use of type-1, interval type-2 fuzzy systems and the simplified IT2 fuzzy systems in reducing uncertainties and providing more transparent and fair assessment that can reflect needs of individual students and foster development is presented.

Disaster management is one of the most important issues in service organizations, especially in healthcare sector. Due to the occurrences of natural or human-made incidents, requirements of assistance and rescue increase gradually. Hospitals have the vital role in addressing these requirements and therefore should enhance their skill to provide a punctual and appropriate response to these events. An important prerequisite for this level of responsiveness is agility. This study aims to introduce and implement a new approach in order to estimate the agility level of hospitals in disaster management. Founded on the four phases of disaster management, a hospital agility framework is established which showcases the relations between hospital agility factors and phases of disaster management. A new Flowsort-based approach is also introduced through the integration of the conventional Flowsort method with interval type-2 fuzzy sets. This approach is applied for a case study consisting of 30 hospitals seeking to improve their agility in disasters. We use upper and lower control limits (UCL and LCL) to define the categories of Flowsort method. The results show that 40% of the hospitals position in between the $$ \pm \,2\delta $$ and $$ \pm \,3\delta $$ limits, i.e., the best and the worst categories. Results also approve the ability of the proposed method in evaluation of hospitals based on their agility factors and represent a geographical observation on the hospitals. Some indications about required actions for hospitals of each category in order to increase or maintain their agility level in disaster management are also provided.

This paper presents the hybrid network of Interval Type-2 Subsethood Neural Fuzzy Inference System (IT2SuNFIS) [1] and Interval Type-2 Mutual Subsethood Neural Fuzzy Inference System (IT2MSFuNIS) [2] and it’s applications in the area of Mackey-Glass time-series (MGTS) prediction, chemical plant control and Hang function approximation. This model introduces the mutual subsethood measure [2] in IT2SuNFIS network [1]. Resulting hybrid network differs from IT2MSFuNIS in its consequent network structure and it is different from IT2SuNFIS as well; it uses mutual subsethood measure instead of subsethood measure for determining correlation between the interval type-2 fuzzy set (IT2 FS) inputs and IT2 FS antecedents. The inputs to the system are fuzzified using IT2 FSs with Gaussian primary membership function (GPMF) having identical mean but different variance. The signal aggregation of type-2 based activation is performed using product operator. This hybrid neuro-fuzzy system learns using different differential evolution (DE) strategies and Artificial Bee colony differential evolution (ABC-DE) framework [3]. Empirical studies are conducted on benchmark data sets of MGTS, a chemical plant and Hang function. Comparisons with other type-1 and type-2 neuro-fuzzy models and in particular with IT2SuNFIS [1], verify the excellent performance of the hybrid network.

This paper studies the continuity of the input-output mappings of fuzzy logic systems (FLSs), including both type-1 (T1) and interval type-2 (IT2) FLSs. We show that a T1 FLS being an universal approximator is equivalent to saying that a T1 FLS has a continuous input-output mapping. We also derive the condition under which a T1 FLS is discontinuous. For IT2 FLSs, we consider six type-reduction and defuzzification methods (the Karnik-Mendel method, the uncertainty bound method, the Wu-Tan method, the Nie-Tan method, the Du-Ying method, and the Begian-Melek-Mendel method) and derive the conditions under which continuous and discontinuous input-output mappings can be obtained. Guidelines for designing continuous IT2 FLSs are also given. This paper is to date the most comprehensive study on the continuity of FLSs. Our results will be very useful in the selection of the parameters of the membership functions to achieve a desired continuity (e.g., for most traditional modeling and control applications) or discontinuity (e.g., for hybrid and switched systems modeling and control).

The main reason of the extensive usage of the fuzzy systems in many branches of science is their approximation ability. In this paper, an interval type-3 fuzzy system (IT3FS) is proposed. The uncertainty modeling capability of the proposed IT3FS is improved in contrast to type-1 and type-2 fuzzy systems (T1FS and T2FS). Because in the proposed IT3FS, the membership is defined as an interval type-2 fuzzy set, whereas in T1FS and T2FS, the membership is crisp value and type-1 fuzzy set, respectively. An online fractional-order learning algorithm is given to optimize the consequent parameters of the IT3FS. The stability of the learning algorithm is proved by utilizing the Lyapunov method. The validity of the proposed fuzzy system is illustrated by both simulation and the experimental studies. It is shown that the proposed fuzzy system and associated learning algorithm result in better approximation performance in comparison with the other well-known approaches.

PurposeIn recent times, fuzzy logic is gaining more and more attention, and this is because of the capability of understanding the functioning of the system as per human knowledge-based system. The main contribution of the work is dynamically adapting the important parameters throughout the execution of the flower pollination algorithm (FPA) using concepts of fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.Design/methodology/approachThe fuzzy logic-based parameter adaptation in the FPA is proposed. In addition, type-2 fuzzy logic is used to design fuzzy inference system for dynamic parameter adaptation in metaheuristics, which can help in eliminating uncertainty and hence offers an attractive improvement in dynamic parameter adaption in metaheuristic method, and, in reality, the effectiveness of the interval type-2 fuzzy inference system (IT2 FIS) has shown to provide improved results as matched to type-1 fuzzy inference system (T1 FIS) in some latest work.FindingsOne case study is considered for testing the proposed approach in a fault tolerant control problem without faults and with partial loss of effectiveness of main actuator fault with abrupt and incipient nature. For comparison between the type-1 fuzzy FPA and interval type-2 fuzzy FPA is presented using statistical analysis which validates the advantages of the interval type-2 fuzzy FPA. The statistical Z-test is presented for comparison of efficiency between two fuzzy variants of the FPA optimization method.Originality/valueThe main contribution of the work is a dynamical adaptation of the important parameters throughout the execution of the flower pollination optimization algorithm using concepts of type-2 fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

Successful implementation of type-1 Fuzzy Systems (FS) in diverse application areas have been accomplished till date. Nonetheless type-1 FS are not able to handle significant amount of uncertainties present in dynamic real world applications. An improved performance against these uncertainties is achieved by type-2 FS. In this paper, a type-2 FS is proposed to remove variable gaussian noise from a number of images using multilevel two dimensional wavelet transform and multilevel soft threshold. We have displayed that the proposed type-2 FS achieve a good efficiency in removing the noise from the wavelet transformed images and also has a superior performance compared to type-1 FS.

An interval type-2 fuzzy logic system (IT2FLS) can function well with uncertain data, with which a type-1 fuzzy logic system (T1FLS) is ineffective because its membership function rests upon crisp values. However, similar to T1FLSs, there are challenges associated with IT2FLSs in selecting parameters, which can significantly affect the accuracy of the classification results with their relatively high sensitivity. This paper discusses and proposes a hybrid model based on IT2FLS and particle swarm optimization (PSO) for prediction problems. The main objective of this paper is to find the optimal solution for the unknown fuzzy systems using labelled data for training the fuzzy system. The PSO technique was used to find the optimal parameters of the Gaussian membership functions which utilized for IT2FLSs. The authors tested two data sets for each of the two prediction problems, namely: burnt forest area prediction and wine quality prediction. The predictive results were compared with other predictive methods including random forest (RF), support vector machines (SVM), artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS) and IT2FLS with parameters generated by using the fuzzy c-means algorithm (IT2FLS-FCM). Experiment results showed that the proposed method could significantly improve accuracy compared to several other predictive techniques.

The aim of this study was to explore relationships between the shape of the primary membership functions and the uncertainties obtained in the output sets for both non-stationary and interval type-2 fuzzy systems. The study was carried out on a fuzzy system implementing the standard XOR problem, in which either Gaussian or triangular membership functions were employed, using a range of input values and recording the size of the output intervals obtained. It can be observed that the shape of the surfaces of the output intervals are related to the primary membership function and that the surface is divided into four roughly symmetrical parts. Furthermore, it can be observed that there are complex differences between the surfaces produced by interval type-2 systems and various kinds of non-stationary systems. Detailed differences between the output surfaces of uniformly distributed non-stationary systems are examined and the implications are discussed.

In this paper, we develop the parametric graded mean integration representation (PGMIR) for the interval type 2 fuzzy sets (IT2FS). The PGMIR value can be served as the type reduced or defuzzification of an IT2FS. A set of IT2FSs can then be ordered by the corresponding PGMIR values. Firstly, the parametric representation of the embedded fuzzy sets is defined for the general IT2FS. The IT2FS is characterized by the set of embedded fuzzy sets induced from the parametric function. Then, the graded mean integration representation (GMIR) of a type 1 fuzzy set (T1FS) is extended to the IT2FS through the parametric form of an IT2FS. The GMIR of the parametric embedded T1FS is defined and is called the PGMIR. In this manner, the IT2FSs are defuzzified and can be ranked by sorting the PGMIR values. The average value of the PGMIR is used to determine IT2FS ranking. A numerical example is presented to show that the proposed approach is superior to the ranking method from IT2FS centroid.