Enhancing fuzzy inference system based criterion-referenced assessment with an application

An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets, and fuzzy rules. The aim of this paper is to demonstrate how an additional qualitative information, i.e., monotonicity property, can be exploited and extended to be part of an FIS designing procedure (i.e., fuzzy sets and fuzzy rules design). In this paper, the FIS is employed as an alternative to the use of addition in aggregating the scores from test items/tasks in a Criterion-Referenced Assessment (CRA) model. In order to preserve the monotonicity property, the sufficient conditions of the FIS is proposed. Our proposed FIS based CRA procedure can be viewed as an enhancement for the FIS based CRA procedure, where monotonicity property is preserved. We demonstrate the applicability of the proposed approach with a case study related to a laboratory project assessment task at a university, and the results indicate the usefulness of the proposed approach in the CRA domain.

Hydrological modelling with a dynamic neural fuzzy inference system

Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) is a Takagi-Sugeno-type fuzzy inference system for online learning which can be applied for dynamic time series prediction. Data from Heshui catchment (2,275 km2) which is rural catchment in China, comprising daily time series of rainfall and discharge from January 1, 1990 to January 21, 2006 were analyzed. Rainfall and discharge antecedents were the inputs used for the DENFIS and ANFIS models and the output was discharge at the present time. DENFIS model results were compared with the results obtained from the physically-based University Regina Hydrologic Model (URHM) and an Adaptive Network-based Fuzzy Inference System (ANFIS) which employs offline learning. Our analysis shows that DENFIS results are better or at least comparable to URHM, but almost identical to ANFIS.

Dynamic evolving neural-fuzzy inference system for rainfall-runoff (R-R) modelling

Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) is a Takagi-Sugeno-type fuzzy inference system for online learning which can be applied for dynamic time series prediction. To the best of our knowledge, this is the first time that DENFIS has been used for rainfall-runoff (R-R) modeling. DENFIS model results were compared to the results obtained from the physically-based Storm Water Management Model (SWMM) and an Adaptive Network-based Fuzzy Inference System (ANFIS) which employs offline learning. Data from a small (5.6 km2) catchment in Singapore, comprising 11 separated storm events were analyzed. Rainfall was the only input used for the DENFIS and ANFIS models and the output was discharge at the present time. It is concluded that DENFIS results are better or at least comparable to SWMM, but similar to ANFIS. These results indicate a strong potential for DENFIS to be used in R-R modeling.

A new fuzzy ratio and its application to the single input rule modules connected fuzzy inference system

The principle of ratios has been applied to many real world problems, e.g. the part-to-part and part-to-whole ratio formulations. As it is difficult for humans to provide an exact ratio in many real situations, we introduce a fuzzy ratio in this paper. We use some notions from fuzzy arithmetic to analyze fuzzy ratios captured from humans. An application of the formulated fuzzy ratio to a Single Input Rule Modules connected Fuzzy Inference System (SIRMs-FIS) is demonstrated. Instead of using a precise weight, fuzzy sets are employed to represent the relative importance of each rule module. The resulting fuzzy weights are explained as a fuzzy ratio on a weight domain. In addition, a new SIRMs-FIS model with fuzzy weights and part-to-whole fuzzy ratio is devised. A simulated example is presented to clarify the proposed SIRM-FIS model.

A new two-stage fuzzy inference system-based approach to prioritize failures in failure mode and effect analysis

This paper presents a new Fuzzy Inference System (FIS)-based Risk Priority Number (RPN) model for the prioritization of failures in Failure Mode and Effect Analysis (FMEA). In FMEA, the monotonicity property of the RPN scores is important. To maintain the monotonicity property of an FIS-based RPN model, a complete and monotonically-ordered fuzzy rule base is necessary. However, it is impractical to gather all (potentially a large number of) fuzzy rules from FMEA users. In this paper, we introduce a new two-stage approach to reduce the number of fuzzy rules that needs to be gathered, and to satisfy the monotonicity property. In stage-1, a Genetic Algorithm (GA) is used to search for a small set of fuzzy rules to be gathered from FMEA users. In stage-2, the remaining fuzzy rules are deduced approximately by a monotonicity-preserving similarity reasoning scheme. The monotonicity property is exploited as additional qualitative information for constructing the FIS-based RPN model. To assess the effectiveness of the proposed approach, a real case study with information collected from a semiconductor manufacturing plant is conducted. The outcomes indicate that the proposed approach is effective in developing an FIS-based RPN model with only a small set of fuzzy rules, which is able to satisfy the monotonicity property for prioritization of failures in FMEA.

Rainfall-runoff modeling using dynamic evolving neural fuzzy inference system with online learning

This is an open access article under the CC BY-NC-ND license.Neuro-Fuzzy Systems (NFS) are computational intelligence tools that have recently been employed in hydrological modeling. In many of the common NFS the learning algorithms used are based on batch learning where all the parameters of the fuzzy system are optimized off-line. Although these models have frequently been used, there is a criticism on such learning process as the number of rules are needed to be predefined by the user. This will reduce the flexibility of the NFS architecture while dealing with different data with different level of complexity. On the other hand, online or local learning evolves through local adjustments in the model as new data is introduced in sequence. In this study, dynamic evolving neural fuzzy inference system (DENFIS) is used in which an evolving, online clustering algorithm called the Evolving Clustering Method (ECM) is implemented. ECM is an online, maximum distance-based clustering method which is able to estimate the number of clusters in a data set and find their current centers in the input space through its fast, one-pass algorithm. The 10-minutes rainfall-runoff time series from a small (23.22 km2) tropical catchment named Sungai Kayu Ara in Selangor, Malaysia, was used in this study. Out of the 40 major events, 12 were used for training and 28 for testing. Results obtained by DENFIS were then compared with the ones obtained by physically-based rainfall-runoff model HEC-HMS and a regression model ARX. It was concluded that DENFIS results were comparable to HEC-HMS and superior to ARX model. This indicates a strong potential for DENFIS to be used in rainfall-runoff modeling.

A non-linear programming-based similarity reasoning scheme for modelling of monotonicity-preserving multi-input fuzzy inference systems

In this paper, the zero-order Sugeno Fuzzy Inference System (FIS) that preserves the monotonicity property is studied. The sufficient conditions for the zero-order Sugeno FIS model to satisfy the monotonicity property are exploited as a set of useful governing equations to facilitate the FIS modelling process. The sufficient conditions suggest a fuzzy partition (at the rule antecedent part) and a monotonically-ordered rule base (at the rule consequent part) that can preserve the monotonicity property. The investigation focuses on the use of two Similarity Reasoning (SR)-based methods, i.e., Analogical Reasoning (AR) and Fuzzy Rule Interpolation (FRI), to deduce each conclusion separately. It is shown that AR and FRI may not be a direct solution to modelling of a multi-input FIS model that fulfils the monotonicity property, owing to the difficulty in getting a set of monotonically-ordered conclusions. As such, a Non-Linear Programming (NLP)-based SR scheme for constructing a monotonicity-preserving multi-input FIS model is proposed. In the proposed scheme, AR or FRI is first used to predict the rule conclusion of each observation. Then, a search algorithm is adopted to look for a set of consequents with minimized root means square errors as compared with the predicted conclusions. A constraint imposed by the sufficient conditions is also included in the search process. Applicability of the proposed scheme to undertaking fuzzy Failure Mode and Effect Analysis (FMEA) tasks is demonstrated. The results indicate that the proposed NLP-based SR scheme is useful for preserving the monotonicity property for building a multi-input FIS model with an incomplete rule base.

Optimization of gaussian fuzzy membership functions and evaluation of the monotonicity property of fuzzy inference systems

In this paper, two issues relating to modeling of a monotonicity-preserving Fuzzy Inference System (FIS) are examined. The first is on designing or tuning of Gaussian Membership Functions (MFs) for a monotonic FIS. Designing Gaussian MFs for an FIS is difficult because of its spreading and curvature characteristics. In this study, the sufficient conditions are exploited, and the procedure of designing Gaussian MFs is formulated as a constrained optimization problem. The second issue is on the testing procedure for a monotonic FIS. As such, a testing procedure for a monotonic FIS model is proposed. Applicability of the proposed approach is demonstrated with a real world industrial application, i.e., Failure Mode and Effect Analysis. The results obtained are analysis and discussed. The outcomes show that the proposed approach is useful in designing a monotonicity-preserving FIS model.

Building monotonicity-preserving fuzzy inference models with optimization-based similarity reasoning and a monotonicity index

In this paper, a novel approach to building a Fuzzy Inference System (FIS) that preserves the monotonicity property is proposed. A new fuzzy re-labeling technique to re-label the consequents of fuzzy rules in the database (before the Similarity Reasoning process) and a monotonicity index for use in FIS modeling are introduced. The proposed approach is able to overcome several restrictions in our previous work that uses mathematical conditions in building monotonicity-preserving FIS models. Here, we show that the proposed approach is applicable to different FIS models, which include the zero-order Sugeno FIS and Mamdani models. Besides, the proposed approach can be extended to undertake problems related to the local monotonicity property of FIS models. A number of examples to demonstrate the usefulness of the proposed approach are presented. The results indicate the usefulness of the proposed approach in constructing monotonicity-preserving FIS models.

Enhancing the failure mode and effect analysis methodology with fuzzy inference techniques

Traditional Failure Mode and Effect Analysis (FMEA) adopts the Risk Priority Number (RPN) ranking model to evaluate failure risks, to rank failures, as well as to prioritize actions. Although this approach is simple, it suffers from several shortcomings. In this paper, we investigate a number of fuzzy inference techniques for determining the RPN scores, in an attempt to overcome the weaknesses associated with the traditional RPN model. The main objective is to examine the possibility of using fuzzy rule interpolation and reduction techniques to design new fuzzy RPN models. The performance of the fuzzy RPN models is evaluated using a real-world case study pertaining to the test handler process in a semiconductor manufacturing plant. The FMEA procedure for the test handler is performed, and a fuzzy RPN model is developed. In addition, improvement to the fuzzy RPN model is proposed by refining the weights of the fuzzy production rules, hence a new weighted fuzzy RPN model. The ability of the weighted fuzzy RPN model in failure risk evaluation with a reduced rule base is also demonstrated.

On monotonic sufficient conditions of fuzzy inference systems and their applications

An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets and fuzzy rules. In this paper, two useful qualitative properties of the FIS model, i.e., the monotonicity and sub-additivity properties, are studied. The monotonic sufficient conditions of the FIS model with Gaussian membership functions are further analyzed. The aim is to incorporate the sufficient conditions into the FIS modeling process, which serves as a simple (which can be easily understood by domain users), easy-to-use (which can be easily applied to or can be a part of the FIS model), and yet reliable (which has a sound mathematical foundation) method to preserve the monotonicity property of the FIS model. Another aim of this paper is to demonstrate how these additional qualitative information can be exploited and extended to be part of the FIS designing procedure (i.e., for fuzzy sets and fuzzy rules design) via the sufficient conditions (which act as a set of useful governing equations for designing the FIS model). The proposed approach is able to avoid the "trial and error" procedure in obtaining a monotonic FIS model. To assess the applicability of the proposed approach, two practical problems are examined. The first is an FIS-based model for water level control, while the second is an FIS-based Risk Priority Number (RPN) model in Failure Mode and Effect Analysis (FMEA). To further illustrate the importance of the sufficient conditions as the governing equations, an analysis on the consequences of violating the sufficient conditions of the FIS-based RPN model is presented.