Selecting the individual numerical scale and prioritization method in the analytic hierarchy process : a 2-tuple fuzzy linguistic approach

The validity of the priority vector used in the analytic hierarchy process (AHP) relies on two factors: the selection of a numerical scale and the selection of a prioritization method. The traditional AHP selects only one numerical scale (e.g., the Saaty scale) and one prioritization method (e.g., the eigenvector method) for each particular problem. For this traditional selection approach, there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector. In fact, the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the AHP decision makers. By defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices (LPCMs) of the priority vector and by using LPCMs to unify the format of the input and output of AHP, this paper extends the AHP prioritization process under the 2-tuple fuzzy linguistic model. Based on the extended AHP prioritization process, we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods. We also use the performance measure criteria to develop a 2-tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different LPCMs. In this paper, we call this type of selection the individual selection of the numerical scale and prioritization method. We also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection.

A guided rule reduction system for prioritization of failures in fuzzy FMEA

Traditional Failure Mode and Effect Analysis (FMEA) utilizes the Risk Priority Number (RPN) ranking system to evaluate the risk level of failures, to rank failures, and to prioritize actions. Although this method is simple, it suffers from several shortcomings. In this paper, use of fuzzy inference techniques for RPN determination in an attempt to overcome the weaknesses associated with the traditional RPN ranking system is investigated. However, the fuzzy RPN model, suffers from the combinatorial rule explosion problem. As a result, a generic rule reduction approach, i.e. the Guided Rule Reduction System (GRRS), is proposed to reduce the number of rules that need to be provided by users during the fuzzy RPN modeling process. The proposed approach is evaluated using real-world case studies pertaining to semiconductor manufacturing. The results are analyzed, and implications of the proposed approach are discussed.

Fuzzy rule base assessment models : theoretical analyses and a case study

An assessment model is usually a mathematical model that produces a measuring index, in the form of a numerical score to a situation/object, with respect to the subject of measure. To allow a valid and useful comparison among various situations/objects according to their associated numerical scores to be made, two important properties, i.e., the monotone output property and output resolution properties, are essential in fuzzy inference-based assessment problems. In this paper, the conditions for a fuzzy assessment model to fulfill the monotone output property is investigated using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to the input, whereby the derivative should be greater than a minimum resolution. Based on the derivative, improvements to the output resolution property by refining the fuzzy production rules are suggested. A case study on the Bowles fuzzy RPN model to demonstrate the effectiveness of the properties is also included.

Enhancing the failure mode and effect analysis methodology with fuzzy inference techniques

Traditional Failure Mode and Effect Analysis (FMEA) adopts the Risk Priority Number (RPN) ranking model to evaluate failure risks, to rank failures, as well as to prioritize actions. Although this approach is simple, it suffers from several shortcomings. In this paper, we investigate a number of fuzzy inference techniques for determining the RPN scores, in an attempt to overcome the weaknesses associated with the traditional RPN model. The main objective is to examine the possibility of using fuzzy rule interpolation and reduction techniques to design new fuzzy RPN models. The performance of the fuzzy RPN models is evaluated using a real-world case study pertaining to the test handler process in a semiconductor manufacturing plant. The FMEA procedure for the test handler is performed, and a fuzzy RPN model is developed. In addition, improvement to the fuzzy RPN model is proposed by refining the weights of the fuzzy production rules, hence a new weighted fuzzy RPN model. The ability of the weighted fuzzy RPN model in failure risk evaluation with a reduced rule base is also demonstrated.

Fuzzy FMEA with a guided rules reduction system for prioritization of failures

Purpose – To propose a generic method to simplify the fuzzy logic-based failure mode and effect analysis (FMEA) methodology by reducing the number of rules that needs to be provided by FMEA users for the fuzzy risk priority number (RPN) modeling process.

Design/methodology/approach – The fuzzy RPN approach typically requires a large number of rules, and it is a tedious task to obtain a full set of rules. The larger the number of rules provided by the users, the better the prediction accuracy of the fuzzy RPN model. As the number of rules required increases, ease of use of the model decreases since the users have to provide a lot of information/rules for the modeling process. A guided rules reduction system (GRRS) is thus proposed to regulate the number of rules required during the fuzzy RPN modeling process. The effectiveness of the proposed GRRS is investigated using three real-world case studies in a semiconductor manufacturing process.

Findings – In this paper, we argued that not all the rules are actually required in the fuzzy RPN model. Eliminating some of the rules does not necessarily lead to a significant change in the model output. However, some of the rules are vitally important and cannot be ignored. The proposed GRRS is able to provide guidelines to the users which rules are required and which can be eliminated. By employing the GRRS, the users do not need to provide all the rules, but only the important ones when constructing the fuzzy RPN model. The results obtained from the case studies demonstrate that the proposed GRRS is able to reduce the number of rules required and, at the same time, to maintain the ability of the Fuzzy RPN model to produce predictions that are in agreement with experts' knowledge in risk evaluation, ranking, and prioritization tasks.

Research limitations/implications – The proposed GRRS is limited to FMEA systems that utilize the fuzzy RPN model.

Practical implications – The proposed GRRS is able to simplify the fuzzy logic-based FMEA methodology and make it possible to be implemented in real environments.

Originality/value – The value of the current paper is on the proposal of a GRRS for rule reduction to enhance the practical use of the fuzzy RPN model in real environments.

On the use of fuzzy inference techniques in assessment models : part I — theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.

On the use of fuzzy inference techniques in assessment models : part II : industrial applications

In this paper, we study the applicability of the monotone output property and the output resolution property in fuzzy assessment models to two industrial Failure Mode and Effect Analysis (FMEA) problems. First, the effectiveness of the monotone output property in a single-input fuzzy assessment model is demonstrated with a proposed fuzzy occurrence model. Then, the usefulness of the two properties to a multi-input fuzzy assessment model, i.e., the Bowles fuzzy Risk Priority Number (RPN) model, is assessed. The experimental results indicate that both the fuzzy occurrence model and Bowles fuzzy RPN model are able to fulfill the monotone output property, with the derived conditions (in Part I) satisfied. In addition, the proposed rule refinement technique is able to improve the output resolution property of the Bowles fuzzy RPN model.

Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model

When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Mart´ınez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale.We find that the key of computational techniques
based on linguistic 2-tuples is to set suitable numerical scale with
the purpose of making transformations between linguistic 2-tuples
and numerical values. By defining the concept of the transitive
calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

On (TS,N)-fuzzy implications

This paper proposes a new class of fuzzy implications, built according to the well-known (S,N) scheme but in such a way that the t-conorm S is replaced with a compensatory TS function (an aggregation function combining a t-norm and a t-conorm). The basic properties of such implications are studied, and different examples are provided.

A robust learning control for SISO Nonlinear systems with T-S Fuzzy Model : C02-robust control

In this paper, a robust learning control is developed for a class of single input single output (SISO) nonlinear systems with T-S fuzzy model. It is seen that the proposed sliding mode learning control with the powerful Lipshitz-like condition can guarantee the stability, convergence and robustness of the closed-loop system without involving any assumptions on uncertain system dynamics. In addition, theconcept that the local system with the maximum membership function dominates the system dynamic behaviours helps to greatly simplify the control system design. It will be further seen that the continuous learning control ensures the advantage of chattering-free that may occur in conventional sliding mode systems. Simulation examples are presented to demonstrate the effectiveness of the proposed learning control through the comparison with the H-infinity control.

Enhancing an evolving tree-based text document visualization model with fuzzy c-Means clustering

An improved evolving model, i.e., Evolving Tree (ETree) with Fuzzy c-Means (FCM), is proposed for undertaking text document visualization problems in this study. ETree forms a hierarchical tree structure in which nodes (i.e., trunks) are allowed to grow and split into child nodes (i.e., leaves), and each node represents a cluster of documents. However, ETree adopts a relatively simple approach to split its nodes. Thus, FCM is adopted as an alternative to perform node splitting in ETree. An experimental study using articles from a flagship conference of Universiti Malaysia Sarawak (UNIMAS), i.e., Engineering Conference (ENCON), is conducted. The experimental results are analyzed and discussed, and the outcome shows that the proposed ETree-FCM model is effective for undertaking text document clustering and visualization problems.