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

Abstract

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.

A Novel Fuzzy Monotone Relationship Method With its Application on Inclusion Degree

“…Edward [7] introduced the fuzzy monotone function, together with logic control applications. Many papers [8]- [21] have discussed the monotonicity property in the fuzzy inference system (FIS) including Mamdiani, TSK and etc. Some papers [8]- [19] discussed various useful mathematical conditions to satisfy the monotonicity property for different fuzzy inference systems' models; Some paper [21] discussed the data driven monotone fuzzy system.…”

“…Many papers [8]- [21] have discussed the monotonicity property in the fuzzy inference system (FIS) including Mamdiani, TSK and etc. Some papers [8]- [19] discussed various useful mathematical conditions to satisfy the monotonicity property for different fuzzy inference systems' models; Some paper [21] discussed the data driven monotone fuzzy system. And the monotonicity is also discussed as an important property in aggregation functions too [20].…”