The Monotonicity And Sub-Additivity Properties Of Fuzzy Inference Systems And Their Applications

The Fuzzy Inference System (FIS) is a popular computing paradigm for undertaking modelling, control, and decision-making problems. In this thesis, the focus of investigation is on two theoretical properties of an FIS model, i.e., the monotonicity and sub-additivity properties. These properties are defined, and their applicability to tackling real-world problems is discussed. This research contributes to formulating a systematic procedure that is based on a mathematical foundation (i.e., the sufficient conditions) to develop monotonicity-preserving FIS models. A method to improve the sub-additivity property is also proposed

On fuzzy inference system based failure mode and effect analysis (FMEA) methodology

Failure Mode and Effect Analysis (FMEA) is a popular problem prevention methodology. It utilizes a Risk Priority Number (RPN) model to evaluate the risk associated to each failure mode. The conventional RPN model is simple, but, its accuracy is argued. A fuzzy RPN model is proposed as an alternative to the conventional RPN. The fuzzy RPN model allows the relation between the RPN score and Severity, Occurrence and Detect ratings to be of non-linear relationship, and it maybe a more realistic representation. In this paper, the efficiency of the fuzzy RPN model in order to allow valid and meaningful comparisons among different failure modes in FMEA to be made is investigated. It is suggested that the fuzzy RPN should be subjected to certain theoretical properties of a length function e.g. monotonicity, sub-additivity and etc. In this paper, focus is on the monotonicity property. The monotonicity property for the fuzzy RPN is firstly defined, and a sufficient condition for a FIS to be monotone is applied to the fuzzy RPN model. This is an easy and reliable guideline to construct the fuzzy RPN in practice. Case studies relating to semiconductor industry are then presented

A perceptual computing-based approach for peer assessment

Peer assessment is useful for assessing an individual's contribution in a collaborative learning task. It is commonly used in institutions of higher education as normally each class has a large number of students. Peer assessment allows students to assess their group members' contributions. It also helps the instructor to arrive at an assessment that reflects individual's effort in a collaborative learning task. In this paper, a perceptual computing (Per-C)-based peer assessment procedure is investigated. The assessment adopts vague and imprecise words in the evaluation process. Per-C is selected because it allows uncertainties of words to be considered in the decision making process. A real case study is conducted to demonstrate the effectiveness of the proposed method. The results show that the use of Per-C in peer assessment is important

Application of self-organizing map to failure modes and effects analysis methodology

In this paper, a self-organizing map (SOM) neural network is used to visualize corrective actions of failure modes and effects analysis (FMEA). SOM is a popular unsupervised neural network model that aims to produce a low-dimensional map (typically a two-dimensional map) for visualizing high-dimensional data. With regards to FMEA, it is a popular methodology to identify potential failure modes for a product or a process, to assess the risk associated with those failure modes, also, to identify and carry out corrective actions to address the most serious concerns. Despite the popularity of FMEA in a wide range of industries, two well-known shortcomings are the complexity of the FMEA worksheet and its intricacy of use. To the best of our knowledge, the use of computation techniques for solving the aforementioned shortcomings is limited. The use of SOM in FMEA is new. In this paper, corrective actions in FMEA are described in their severity, occurrence and detect scores. SOM is then used as a visualization aid for FMEA users to see the relationship among corrective actions via a map. Color information from the SOM map is then included to the FMEA worksheet for better visualization. In addition, a Risk Priority Number Interval is used to allow corrective actions to be evaluated and ordered in groups. Such approach provides a quick and easily understandable framework to elucidate important information from a complex FMEA worksheet; therefore facilitating the decision-making tasks by FMEA users. The significance of this study is two-fold, viz., the use of SOM as an effective neural network learning paradigm to facilitate FMEA implementations, and the use of a computational visualization approach to tackle the two well-known shortcomings of FMEA

Clustering and visualization of failure modes using an evolving tree

Despite the popularity of Failure Mode and Effect Analysis (FMEA) in a wide range of industries, two well-known shortcomings are the complexity of the FMEA worksheet and its intricacy of use. To the best of our knowledge, the use of computation techniques for solving the aforementioned shortcomings is limited. As such, the idea of clustering and visualization pertaining to the failure modes in FMEA is proposed in this paper. A neural network visualization model with an incremental learning feature, i.e., the evolving tree (ETree), is adopted to allow the failure modes in FMEA to be clustered and visualized as a tree structure. In addition, the ideas of risk interval and risk ordering for different groups of failure modes are proposed to allow the failure modes to be ordered, analyzed, and evaluated in groups. The main advantages of the proposed method lie in its ability to transform failure modes in a complex FMEA worksheet to a tree structure for better visualization, while maintaining the risk evaluation and ordering features. It can be applied to the conventional FMEA methodology without requiring additional information or data. A real world case study in the edible bird nest industry in Sarawak (Borneo Island) is used to evaluate the usefulness of the proposed method. The experiments show that the failure modes in FMEA can be effectively visualized through the tree structure. A discussion with FMEA users engaged in the case study indicates that such visualization is helpful in comprehending and analyzing the respective failure modes, as compared with those in an FMEA table. The resulting tree structure, together with risk interval and risk ordering, provides a quick and easily understandable framework to elucidate important information from complex FMEA forms; therefore facilitating the decision-making tasks by FMEA users. The significance of this study is twofold, viz., the use of a computational visualization approach to tackling two well-known shortcomings of FMEA; and the use of ETree as an effective neural network learning paradigm to facilitate FMEA implementations. These findings aim to spearhead the potential adoption of FMEA as a useful and usable risk evaluation and management tool by the wider community. © 2015 Elsevier Ltd. All rights reserved

A New Framework With Similarity Reasoning and Monotone Fuzzy Rule Relabeling for Fuzzy Inference Systems

A complete and monotonically-ordered fuzzy rule base is necessary to maintain the monotonicity property of a Fuzzy Inference System (FIS). In this paper, a new monotone fuzzy rule relabeling technique to relabel a non-monotone fuzzy rule base provided by domain experts is proposed. Even though the Genetic Algorithm (GA)-based monotone fuzzy rule relabeling technique has been investigated in our previous work [7], the optimality of the approach could not be guaranteed. The new fuzzy rule relabeling technique adopts a simple brute force search, and it can produce an optimal result. We also formulate a new two-stage framework that encompasses a GA-based rule selection scheme, the optimization based-Similarity Reasoning (SR) scheme, and the proposed monotone fuzzy rule relabeling technique for preserving the monotonicity property of the FIS model. Applicability of the two-stage framework to a real world problem, i.e., failure mode and effect analysis, is further demonstrated. The results clearly demonstrate the usefulness of the proposed framework

Monotone Fuzzy Rule Relabeling for the Zero-Order TSK Fuzzy Inference System

To maintain the monotonicity property of a fuzzy inference system, a monotonically-ordered and complete set of fuzzy rules is necessary. However, monotonically-ordered fuzzy rules are not always available, e.g. errors in human judgements lead to non-monotone fuzzy rules. The focus of this paper is on a new monotone fuzzy rule relabeling (MFRR) method that is able to relabel a set of non-monotone fuzzy rules to meet the monotonicity property with reduced computation. Unlike the brute-force approach, which is susceptible to the combinatorial explosion problem, the proposed MFRR method explores within a reduced search space to find the solutions; therefore decreasing the computational requirements. The usefulness of the proposed method in undertaking Failure Mode and Effect Analysis problems is demonstrated using publicly available information. The results indicate that the MFRR method can produce optimal solutions with reduced computational time

A New Evolving Tree-Based Model with Local Re-learning for Document Clustering and Visualization

The Evolving tree (ETree) is a hierarchical clustering and visualization model that allows the number of clusters to grow and evolve with new data samples in an online learning manner. While many hierarchical clustering models are available in the literature, ETree stands out because of its visualization capability. It is an enhancement of the Self-Organizing Map, a famous and useful clustering and visualization model. ETree organises the trained data samples in the form of a tree structure for better presentation and visualization especially for high-dimensional data samples. Even though ETree has been used in a number of applications, its use in textual document clustering and visualization is limited. In this paper, ETree is modified and deployed as a useful model for undertaking textual documents clustering and visualization problems. We introduce a new local re-learning procedure that allows the tree structure to grow and adapt to new features, i.e., new words from new textual documents. The performance of the proposed ETree model is evaluated with two (one benchmark and one real) document data sets. A number of key aspects of the proposed ETree model, which include its topology representation, learning time, as well as recall and precision rates, are evaluated. The results show that the proposed local re-learning procedure is useful for handling increasing number of features incrementally. In summary, this study contributes towards a modified ETree model and its use in a new domain, i.e., textual document clustering and visualization

Monotone Data Samples Do Not Always Generate Monotone Fuzzy If-Then Rules

The Wang–Mendel (WM) method is one of the earliest methods to learn fuzzy If-Then rules from data. In this article, the WM method is used to generate fuzzy If-Then rules for a zero-order Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) from a set of multi-attribute monotone data. Convex and normal trapezoid fuzzy sets are used as fuzzy membership functions. Besides that, a strong fuzzy partition strategy is used. Our empirical analysis shows that a set of multi-attribute monotone data may lead to non-monotone fuzzy If-Then rules. The same observation can be made, empirically, using adaptive neuro-fuzzy inference system (ANFIS), a well-known and popular FIS model with neural learning capability. This finding is important for the modeling of a monotone FIS model, because it shows that even with a “clean” data set pertaining to a monotone system, the generated fuzzy If-Then rules may need to be preprocessed, before being used for FIS modeling. In short, it is imperative to develop methods for preprocessing non-monotone fuzzy rules from data, e.g., monotone fuzzy rules relabeling, or removing non-monotone fuzzy rules, is important (and is potentially necessary) during the course of developing data-driven FIS models

A New Monotone Fuzzy Rule Relabeling Framework With Application to Failure Mode and Effect Analysis Methodology

A monotone fuzzy rule relabeling (MFRR) algorithm has been introduced previously for tackling the issue of a non-monotone fuzzy rule base in the Takagi-Sugeno-Kang (TSK) Fuzzy Inference System (FIS). In this paper, we further propose a new three-stage framework to develop a computationally efficient MFRR algorithm. The first stage determines the combinations of fuzzy rules to be relabeled by exploiting the prior information derived from a given non-monotone fuzzy rule base. This prior information includes the minimum number of fuzzy rules to be relabeled (denoted as k), as well as the states of fuzzy rules that must be, must not be, or may be relabeled. The second stage relabels the consequent parts of multiple sets of k noisy fuzzy rules obtained from the first stage, such that a monotone fuzzy rule base is produced. The third stage selects the most suitable relabeled fuzzy rule base among the potential monotone fuzzy rule bases obtained from the second stage, either objectively or subjectively. We provide insights into MFRR and discuss its practical implementation. In addition, a network flow method is fused with the proposed MFRR framework, resulting in an efficient computation scheme. The MFRR framework is applied to Failure Mode and Effect Analysis (FMEA) problems related to a sewage treatment plant and a public hospital. It is also evaluated with real FMEA information from a semiconductor plant. The results are analyzed and discussed, which positively demonstrate the effectiveness of the proposed MFRR framework in formulating a monotone TSK-FIS model for undertaking FMEA problems