Abstract-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. Keywords-Fuzzy inference system; monotonicity property; fuzzy rule relabeling; application frameworks, failure mode and effect analysis I. INTRODUCTION The importance of the monotonicity property in Fuzzy Inference System (FIS) modeling has been highlighted in a number of recent publications [1][2][3][4][5][6].To maintain the monotonicity property of an FIS model, a monotonically ordered and complete fuzzy rule base is necessary [1][2][3][4][5][6]. In order to maintain a monotonically ordered fuzzy rule base obtained from domain experts, a monotone fuzzy relabeling technique was introduced in our previous work [7]. It attempts to relabel a non-monotone fuzzy rule base gathered from domain experts. It searches for a new fuzzy rule base that is monotone (as the first priority), with the minimum number of relabeled rules (as the second priority), and with the minimum loss measure (as the third priority). A Genetic Algorithm (GA) was adopted in [7]. However, the use of the GA could not guarantee an optimal solution. It also might require a relatively high computation complexity.As a solution to these shortcomings, the first aim of this paper is to develop a new fuzzy rule relabeling technique.To maintain a monotonically ordered and complete fuzzy rule base, we also proposed an optimization based similarity reasoning (SR) scheme previously [7][8]. A search in the literature reveals that various SR schemes (e.g., analogical reasoning [9], fuzzy rule interpolation [10][11], and qualitative reasoning [12]) are available to allow the conclusion of an observation (in the form of a fuzzy set) to be deduced or predicted, based on a fuzzy rule base (database). Even though
Abstract-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.Index Terms-TSK Fuzzy Inference system, monotonicity property, fuzzy rules relabeling, Failure Mode and Effect Analysis
a b s t r a c tIn 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.
Abstract-In this paper, a new online updating framework for constructing monotonicity-preserving Fuzzy Inference Systems (FISs) is proposed.The framework encompasses an optimization-based Similarity Reasoning (SR) scheme and a new monotone fuzzy rule relabeling technique. A complete and monotonically-ordered fuzzy rule base is necessary to maintain the monotonicity property of an FIS model. The proposed framework attempts to allow a monotonicity-preserving FIS model to be constructed when the fuzzy rules are incomplete and not monotonically-ordered. An online feature is introduced to allow the FIS model to be updated from time to time. We further investigate three useful measures, i.e., the belief, plausibility, and evidential mass measures, which are inspired from the DempsterShafer theory of evidence, to analyze the proposed framework and to give an insight for the inferred outcomes from the FIS model.
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