Mao-Jiun J. Wang

Ranking fuzzy numbers with integral value

Abstract Ranking fuzzy numbers is important in decision making. Since very often the alternatives are evaluated by fuzzy numbers in a vague environment, a comparison between these fuzzy numbers is indeed a comparison between alternatives. This paper proposes a method of ranking fuzzy numbers with integral value. The method, which is independent of the type of membership functions used and the normality of the functions, can rank more than two fuzzy numbers simultaneously. It is relatively simple in computation, especially in ranking triangular and trapezoidal fuzzy numbers. Further, an index of optimism is used to reflect the decision makers optimistic attitude. Discussion on comparative advantages is included.

Image thresholding by minimizing the measures of fuzziness

Abstract This paper introduces a new image thresholding method based on minimizing the measures of fuzziness of an input image. The membership function in the thresholding method is used to denote the characteristic relationship between a pixel and its belonging region (the object or the background). In addition, based on the measure of fuzziness, a fuzzy range is defined to find the adequate threshold value within this range. The principle of the method is easy to understand and it can be directly extended to multilevel thresholding. The effectiveness of the new method is illustrated by using the test images of having various types of histograms. The experimental results indicate that the proposed method has demonstrated good performance in bilevel and trilevel thresholding.

A fuzzy multi-criteria decision-making method for facility site selection

Abstract In this paper, a facility site selection algorithm is proposed. The algorithm based on the concepts of fuzzy set theory and the hierarchical structure analysis to aggregate decision-makers’ linguistic assessments about criteria weightings and the suitability of facility sites versus various selection criteria to obtain fuzzy suitability indices. Then rank the suitability ratings to determine the best facility site selection. By utilizing this decision algorithm, the decision-makers’ fuzzy assessments with various rating attitudes and the trade-off among various selection criteria can be taken into account in the aggregation process to asssure more convincing and accurate decision-making.

A comprehensive framework for selecting an ERP system

Abstract This paper presents a comprehensive framework for combining objective data obtained from external professional reports and subjective data obtained from internal interviews with vendors to select a suitable Enterprise Resource Planning (ERP) project. A hierarchical attribute structure is proposed to evaluate ERP projects systematically. In addition, fuzzy set theory is used to aggregate the linguistic evaluation descriptions and weights. An actual example in Taiwan demonstrates the feasibility of applying the proposed framework.

Fuzzy weighted average: an improved algorithm

Abstract This paper suggests a modification on the fuzzy weighted average (FWA) method developed by Dong and Wong (1987). A steepest descend/ascend method is proposed to facilitate steps (3) and (4) of the FWA to find the minimum/maximum of f(x1,x2,…,xn,w1,w2,…,wn) = Σi=1n wixi/Σi=1n wi. An example used by Dong and Wong is again employed to illustrate the new method. The same results are obtained but the new method requires much less evaluations and computations. The advantages and disadvantages of the two algorithms are discussed. Also, several relevant theorems are stated and discussed in this paper, and the proofs of these theorems are listed in the Appendix.

Automated inspection of printed circuit boards through machine vision

Abstract This paper introduces the development of an automated visual inspection system for printed circuit boards (PCBs). It utilizes an elimination-subtraction method which directly subtracts the template image from the inspected image, and then conducts an elimination procedure to locate defects in the PCB. Each detected defect is subsequently classified into one of the seven defect types by three indices: the type of object detected, the difference in object numbers, and the difference in background numbers between the inspected image and the template. Finally, a 256 × 240 PCB image was tested to show the effectiveness of this system.

Usability evaluation of E-books

The objective of this study is to evaluate the usability of electronic books (E-books). An experiment was designed to compare the differences between reading an E-book and a conventional book (C-book) with objective measures. Twenty junior college students, ages sixteen to eighteen, participated in the study. Response measures included reading performance and critical flicker fusion (CFF). The results indicate that reading an E-book causes significantly higher eye fatigue than reading a C-book. Reading a C-book generated a higher level of reading performance than reading an E-book. In addition, females demonstrated better reading performance than males in reading either book.

A fuzzy set approach for event tree analysis

The traditional event tree analysis uses a single probability to represent each top event. However, it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has. The fuzzy set theory is universally applied to deal with this kind of phenomena. The main purpose of this study is to construct an easy method to evaluate human errors and integrate them into event tree analysis by using fuzzy concepts. A systematic fuzzy event tree analysis algorithm is developed to evaluate the risk of a large-scale system. A practical example in a nuclear power plant is used to demonstrate this procedure.

Relationship between maximum acceptable work time and physical workload

For safe job design, it is necessary to know the maximum acceptable work time (MAWT) for a given workload. The aim was to establish the relationship between MAWT and physical workload. Cycling tests at six different work rates relative to personal maximum working capacity were performed by 12 young adults in the laboratory. The oxygen uptake (VO2) in the per cent maximum aerobic capacity (%VO2max), relative heart rate (RHR) and relative oxygen uptake (RVO2) were collected throughout the test. MAWT was determined by observing the heart rate data during the test. The results showed that MAWT was negatively correlated with %VO2max, RHR and RVO2(p<0.01). Three exponential regression models were obtained and all their R2 >0.80. These models suggest that long-hour shifts (>10 h) should assign a lower work intensity than for an 8-h workday. It is also logical that the workload limit for a 4-h work shift could be set at about 10%VO2max higher than the suggested limit for an 8-h workday.

Hybrid fault tree analysis using fuzzy sets

Abstract In conventional fault tree analysis (FTA), the ambiguous and imprecise events such as human errors tend not to be handled effectively. To overcome this disadvantage, a hybrid approach employing fuzzy set evaluation and probabilistic estimation for FTA is proposed to evaluate abnormal events. The safety problem of unexpected robot motion in an aircraft wing drilling system was analyzed using the proposed method. The results indicated that the proposed approach is very effective in analyzing the reliability of a man-machine system.