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Abstract-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.Index Terms-Failure mode and effect analysis, fuzzy inference system, similarity reasoning, monotonicity property, fuzzy rule reduction.

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-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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