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Chee Peng Lim - One of the best experts on this subject based on the ideXlab platform.

  • On the Monotonicity Property of the TSK Fuzzy Inference System: The Necessity of the Sufficient Conditions and the Monotonicity Test
    International Journal of Fuzzy Systems, 2018
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    The sufficient conditions for satisfying the Monotonicity Property of the Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) have shown to be useful in many different applications. However, the related sufficient and necessary conditions are still unknown. As such, even when the sufficient conditions are violated, the TSK FIS model may still able to satisfy the Monotonicity Property. Therefore, the Monotonicity test is used as an approximated method to determine the validness of the Monotonicity Property. To the best of our knowledge, the use of the Monotonicity test in FIS is new. In this paper, we focus on single-input zero-order TSK FIS with Gaussian fuzzy membership functions. An algorithm to test the Monotonicity Property, either accepting or rejecting an TSK FIS model of being monotone, is devised and analyzed. The relationship between TSK FIS and its capability of satisfying the Monotonicity Property, along with the sufficient conditions and the outcome of the Monotonicity test, is established through a Monte Carlo simulation. The Monte Carlo simulation is a useful necessity test for the sufficient conditions. We define a necessity measure of the sufficient conditions (NMSC) as the probability that a randomly generated monotone TSK FIS model (evaluated based on the Monotonicity test algorithm) satisfies the sufficient conditions. We empirically show that the NMSC score reduces with increasing number of fuzzy rules. In addition, an application of the TSK FIS model to failure modes and effects analysis is demonstrated. As compared with the sufficient conditions, a better FIS-based model with a lower error measure can be obtained using the Monotonicity test. The outcome indicates the effectiveness of the Monotonicity test for designing low-dimensional TSK FIS models with large numbers of fuzzy rules.

  • monotone fuzzy rule relabeling for the zero order tsk fuzzy inference system
    IEEE Transactions on Fuzzy Systems, 2016
    Co-Authors: Lie Meng Pang, Kai Meng Tay, Chee Peng Lim
    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 judgments lead to nonmonotone 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 nonmonotone 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 Single Input Rule Modules Connected Fuzzy FMEA Methodology for Edible Bird Nest Processing
    Advances in Intelligent Systems and Computing, 2013
    Co-Authors: Chian Haur Jong, Kai Meng Tay, Chee Peng Lim
    Abstract:

    Despite of the popularity of the fuzzy Failure Mode and Effects Analysis (FMEA) methodology, there are several limitations in combining the Fuzzy Inference System (FIS) and the Risk Priority Number (RPN) model. Two main limitations are: (1) it is difficult and impractical to form a complete fuzzy rule base when the number of required rules is large; and (2) fulfillment of the Monotonicity Property is a difficult problem. In this paper, a new fuzzy FMEA methodology with a zero-order Single Input Rule Modules (SIRMs) connected FIS-based RPN model is proposed. An SIRMs connected FIS is adopted as an alternative to the traditional FIS to reduce the number of fuzzy rules required in the modeling process. To preserve the Monotonicity Property of the SIRMs-connected FIS-based RPN model, a number of theorems in the literature are simplified and adopted as the governing equations for the proposed fuzzy FMEA methodology. A case study relating to edible bird nest (EBN) processing in Sarawak (together with Sabah, known as the world’s number two source area of bird nest after Indonesia) is reported. In short, the findings in this paper contribute towards building a new fuzzy FMEA methodology using the SIRM s connected FIS-based RPN model. Besides that, the usefulness of the simplified theorems in a practical FMEA application is demonstrated.

  • interval based and fuzzy set based approaches to modeling of fuzzy inference systems with the local Monotonicity Property
    IEEE International Conference on Fuzzy Systems, 2013
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    Even though the importance of the local Monotonicity Property for function approximation problems is well established, there are relative few investigations addressing issues related to the fulfillment of the local Monotonicity Property in Fuzzy Inference System (FIS) modeling. We have previously conducted a preliminary study on the local Monotonicity Property of FIS models, with the assumption that the extrema point(s) (i.e., the maximum and/or minimum point(s)) is either known precisely or totally unknown. However, in some practical situations, the extrema point(s) can be known imprecisely (as an interval or a fuzzy set). In this paper, the imprecise information is exploited to construct an FIS model that fulfills the local Monotonicity Property. A procedure to estimate the extrema point(s) of a function is devised. Applicability of the findings to a data-driven modeling problem is further demonstrated.

  • a new framework with similarity reasoning and monotone fuzzy rule relabeling for fuzzy inference systems
    IEEE International Conference on Fuzzy Systems, 2013
    Co-Authors: Kai Meng Tay, Lie Meng Pang, Tze Ling Jee, Chee Peng Lim
    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.

Kai Meng Tay - One of the best experts on this subject based on the ideXlab platform.

  • On the Monotonicity Property of the TSK Fuzzy Inference System: The Necessity of the Sufficient Conditions and the Monotonicity Test
    International Journal of Fuzzy Systems, 2018
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    The sufficient conditions for satisfying the Monotonicity Property of the Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) have shown to be useful in many different applications. However, the related sufficient and necessary conditions are still unknown. As such, even when the sufficient conditions are violated, the TSK FIS model may still able to satisfy the Monotonicity Property. Therefore, the Monotonicity test is used as an approximated method to determine the validness of the Monotonicity Property. To the best of our knowledge, the use of the Monotonicity test in FIS is new. In this paper, we focus on single-input zero-order TSK FIS with Gaussian fuzzy membership functions. An algorithm to test the Monotonicity Property, either accepting or rejecting an TSK FIS model of being monotone, is devised and analyzed. The relationship between TSK FIS and its capability of satisfying the Monotonicity Property, along with the sufficient conditions and the outcome of the Monotonicity test, is established through a Monte Carlo simulation. The Monte Carlo simulation is a useful necessity test for the sufficient conditions. We define a necessity measure of the sufficient conditions (NMSC) as the probability that a randomly generated monotone TSK FIS model (evaluated based on the Monotonicity test algorithm) satisfies the sufficient conditions. We empirically show that the NMSC score reduces with increasing number of fuzzy rules. In addition, an application of the TSK FIS model to failure modes and effects analysis is demonstrated. As compared with the sufficient conditions, a better FIS-based model with a lower error measure can be obtained using the Monotonicity test. The outcome indicates the effectiveness of the Monotonicity test for designing low-dimensional TSK FIS models with large numbers of fuzzy rules.

  • monotone fuzzy rule relabeling for the zero order tsk fuzzy inference system
    IEEE Transactions on Fuzzy Systems, 2016
    Co-Authors: Lie Meng Pang, Kai Meng Tay, Chee Peng Lim
    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 judgments lead to nonmonotone 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 nonmonotone 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 Single Input Rule Modules Connected Fuzzy FMEA Methodology for Edible Bird Nest Processing
    Advances in Intelligent Systems and Computing, 2013
    Co-Authors: Chian Haur Jong, Kai Meng Tay, Chee Peng Lim
    Abstract:

    Despite of the popularity of the fuzzy Failure Mode and Effects Analysis (FMEA) methodology, there are several limitations in combining the Fuzzy Inference System (FIS) and the Risk Priority Number (RPN) model. Two main limitations are: (1) it is difficult and impractical to form a complete fuzzy rule base when the number of required rules is large; and (2) fulfillment of the Monotonicity Property is a difficult problem. In this paper, a new fuzzy FMEA methodology with a zero-order Single Input Rule Modules (SIRMs) connected FIS-based RPN model is proposed. An SIRMs connected FIS is adopted as an alternative to the traditional FIS to reduce the number of fuzzy rules required in the modeling process. To preserve the Monotonicity Property of the SIRMs-connected FIS-based RPN model, a number of theorems in the literature are simplified and adopted as the governing equations for the proposed fuzzy FMEA methodology. A case study relating to edible bird nest (EBN) processing in Sarawak (together with Sabah, known as the world’s number two source area of bird nest after Indonesia) is reported. In short, the findings in this paper contribute towards building a new fuzzy FMEA methodology using the SIRM s connected FIS-based RPN model. Besides that, the usefulness of the simplified theorems in a practical FMEA application is demonstrated.

  • interval based and fuzzy set based approaches to modeling of fuzzy inference systems with the local Monotonicity Property
    IEEE International Conference on Fuzzy Systems, 2013
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    Even though the importance of the local Monotonicity Property for function approximation problems is well established, there are relative few investigations addressing issues related to the fulfillment of the local Monotonicity Property in Fuzzy Inference System (FIS) modeling. We have previously conducted a preliminary study on the local Monotonicity Property of FIS models, with the assumption that the extrema point(s) (i.e., the maximum and/or minimum point(s)) is either known precisely or totally unknown. However, in some practical situations, the extrema point(s) can be known imprecisely (as an interval or a fuzzy set). In this paper, the imprecise information is exploited to construct an FIS model that fulfills the local Monotonicity Property. A procedure to estimate the extrema point(s) of a function is devised. Applicability of the findings to a data-driven modeling problem is further demonstrated.

  • a new framework with similarity reasoning and monotone fuzzy rule relabeling for fuzzy inference systems
    IEEE International Conference on Fuzzy Systems, 2013
    Co-Authors: Kai Meng Tay, Lie Meng Pang, Tze Ling Jee, Chee Peng Lim
    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.

John Haigh - One of the best experts on this subject based on the ideXlab platform.

  • further counterexamples to the Monotonicity Property of t step maintainable structures
    Journal of Applied Probability, 1992
    Co-Authors: John Haigh
    Abstract:

    Until Guerry's (1990) counterexample to a conjecture of Davies about three-state hierarchical organisations kept at constant size via annual promotion, wastage and recruitment, it was easy to believe that such structures maintainable in t steps would also be maintainable in t + 1 steps. Here we present further counterexamples, which show that t-step maintainability does not imply (t + 1)-step maintainability, for astonishingly large values of t.

Marie-anne Guerry - One of the best experts on this subject based on the ideXlab platform.

Chin Ying Teh - One of the best experts on this subject based on the ideXlab platform.

  • On the Monotonicity Property of the TSK Fuzzy Inference System: The Necessity of the Sufficient Conditions and the Monotonicity Test
    International Journal of Fuzzy Systems, 2018
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    The sufficient conditions for satisfying the Monotonicity Property of the Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) have shown to be useful in many different applications. However, the related sufficient and necessary conditions are still unknown. As such, even when the sufficient conditions are violated, the TSK FIS model may still able to satisfy the Monotonicity Property. Therefore, the Monotonicity test is used as an approximated method to determine the validness of the Monotonicity Property. To the best of our knowledge, the use of the Monotonicity test in FIS is new. In this paper, we focus on single-input zero-order TSK FIS with Gaussian fuzzy membership functions. An algorithm to test the Monotonicity Property, either accepting or rejecting an TSK FIS model of being monotone, is devised and analyzed. The relationship between TSK FIS and its capability of satisfying the Monotonicity Property, along with the sufficient conditions and the outcome of the Monotonicity test, is established through a Monte Carlo simulation. The Monte Carlo simulation is a useful necessity test for the sufficient conditions. We define a necessity measure of the sufficient conditions (NMSC) as the probability that a randomly generated monotone TSK FIS model (evaluated based on the Monotonicity test algorithm) satisfies the sufficient conditions. We empirically show that the NMSC score reduces with increasing number of fuzzy rules. In addition, an application of the TSK FIS model to failure modes and effects analysis is demonstrated. As compared with the sufficient conditions, a better FIS-based model with a lower error measure can be obtained using the Monotonicity test. The outcome indicates the effectiveness of the Monotonicity test for designing low-dimensional TSK FIS models with large numbers of fuzzy rules.

  • interval based and fuzzy set based approaches to modeling of fuzzy inference systems with the local Monotonicity Property
    IEEE International Conference on Fuzzy Systems, 2013
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    Even though the importance of the local Monotonicity Property for function approximation problems is well established, there are relative few investigations addressing issues related to the fulfillment of the local Monotonicity Property in Fuzzy Inference System (FIS) modeling. We have previously conducted a preliminary study on the local Monotonicity Property of FIS models, with the assumption that the extrema point(s) (i.e., the maximum and/or minimum point(s)) is either known precisely or totally unknown. However, in some practical situations, the extrema point(s) can be known imprecisely (as an interval or a fuzzy set). In this paper, the imprecise information is exploited to construct an FIS model that fulfills the local Monotonicity Property. A procedure to estimate the extrema point(s) of a function is devised. Applicability of the findings to a data-driven modeling problem is further demonstrated.

  • FUZZ-IEEE - Interval-based and fuzzy set-based approaches to modeling of fuzzy inference systems with the local Monotonicity Property
    2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2013
    Co-Authors: Chin Ying Teh, Kai Meng Tay, Chee Peng Lim
    Abstract:

    Even though the importance of the local Monotonicity Property for function approximation problems is well established, there are relative few investigations addressing issues related to the fulfillment of the local Monotonicity Property in Fuzzy Inference System (FIS) modeling. We have previously conducted a preliminary study on the local Monotonicity Property of FIS models, with the assumption that the extrema point(s) (i.e., the maximum and/or minimum point(s)) is either known precisely or totally unknown. However, in some practical situations, the extrema point(s) can be known imprecisely (as an interval or a fuzzy set). In this paper, the imprecise information is exploited to construct an FIS model that fulfills the local Monotonicity Property. A procedure to estimate the extrema point(s) of a function is devised. Applicability of the findings to a data-driven modeling problem is further demonstrated.