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The set of fuzzy threshold functions is defined to be a fuzzy set over the set of functions. All threshold functions have full memberships in this fuzzy set. Defines and investigates a distance measure between a non‐linearly separable function and the set of all threshold functions. Defines an explicit expression for the membership function of a fuzzy threshold function through the use of this distance measure and finds three upper bounds for this measure. Presents a general method to compute the distance, an algorithm to generate the representation automatically, and a procedure to determine the proper weights and thresholds automatically. Presents the relationships among threshold gate networks, artificial neural networks and fuzzy neural networks. The results may have useful applications in logic design, pattern recognition, fuzzy logic, multi‐objective fuzzy optimization and related areas.

A fuzzy symmetric threshold (ST) function is defined to be a fuzzy set over the set of functions. All ST functions have full memberships in this fuzzy set. For n variables, there are (2n+2) ST functions. A distance measure between a nonsymmetric threshold function and the set of all ST functions is defined and investigated. An explicit expression for the membership function of a fuzzy ST function is defined through the use of this distance measure. An algorithm for obtaining this distance measure is presented with illustrative examples. It is also shown that any function and its complement always have the same grade of membership in the class of fuzzy ST functions. Applications to concise function representation and simple function implementation are also presented with examples. In addition, most inseparable unsymmetric functions are defined and investigated. Fuzzy ST functions are relevant to the development of practical applications of fuzzy methods and might contribute to the state of the art in the implementations of fuzzy methods in the areas requiring utilization of ST functions.

In real working condition, signal is highly disturbed and even drowned by noise, which extremely interferes in detecting results. Therefore, this paper aims to provide an effective de-noising method for the debris particle in lubricant so that the ultrasonic technique can be applied to the online debris particle detection.

For completing the online ultrasonic monitoring of oil wear debris, the research is made on some selected wear debris signals. It applies morphology component analysis (MCA) theory to de-noise signals. To overcome the potential weakness of MCA threshold process, it proposes fuzzy morphology component analysis (FMCA) by fuzzy threshold function.

According to simulated and experimental results, it eliminates most of the wear debris signal noises by using FMCA through the signal comparison. According to the comparison of simulation evaluation index, it has highest signal noise ratio, smallest root mean square error and largest similarity factor.

The rapid movement of the debris particles, as well as the lubricant temperature, may influence the measuring signals. Researchers are encouraged to solve these problems further.

This paper includes implications for the improvement in the online debris detection and the development of the ultrasonic technique applied in online debris detection.

This paper provides a promising way of applying the MCA theory to de-noise signals. To avoid the potential weakness of the MCA threshold process, it proposes FMCA through fuzzy threshold function. The FMCA method has great obvious advantage in de-noising wear debris signals. It lays the foundation for online ultrasonic monitoring of lubrication wear debris.

The grade of membership function for fuzzy monotone functions is defined and investigated. An algorithm for finding the membership value is presented. A minterm even function and minterm odd function are defined and studied. It is found that these two functions are the two most alternation functions. The relationships with threshold functions are also presented. In addition, three ways to implement a fuzzy monotone increasing function are investigated. Applications to function representation, data compression and error detection are illustrated. The results have useful applications in fuzzy logic, expert systems, fuzzy expert systems, and also management of uncertainty.

This paper aims to improve operational efficiency and minimize accident frequency in cold storage facilities through adopting an effective occupational safety and health program. The hidden knowledge can be extracted from the warehousing operations to create the comfortable and safe workplace environment.

A fuzzy association rule-based knowledge management system is developed by integrating fuzzy association rule mining (FARM) and rule-based expert system (RES). FARM is used to extract hidden knowledge from real operations to establish the relationship between safety measurement, personal constitution and key performance index measurement. The extracted knowledge is then stored and adopted in the RES to establish an effective occupational and safety program. Afterwards, a case study is conducted to validate the performance of the proposed system.

The results indicate that the aforementioned relationship can be built in the form of IF-THEN rules. An appropriate safety and health program can be developed and applied to all workers, so that they can follow instructions to prevent cold induced injuries and also improve the productivity.

Because of the increasing public consciousness of occupational safety and health, it is important for the workers in cold storage facilities where the ambient temperature is at/below 10°C. The proposed system can address the social problem and promote the importance of occupational safety and health in the society.

This study contributes to the knowledge management system for improving the occupational safety and operational efficiency in the cold storage facilities.

Gray code is a code with the property that there is one and only one bit‐change between any two neighboring numbers. An algorithm for generating gray codes is presented. It turns out that there are other codes which have the same characteristics as gray codes. We call this class of codes generalized gray code (GGC). More precisely, a GGC is a code which has both the reflective property and the unit distance property. Algorithms for generating n‐bit GGC from the (n – 1)‐bit GGC are presented with illustrative examples. It is found that the number of n‐bit GGC is equal to 2n times the number of (n – 1)‐bit GGC. GGC generation trees are used to find GGC. Shows that GGC may be used in the two cases: where 1: gray code cannot be used, and as 2: member of the GGC is better suited than the gray code. Deduces that through the use of GGC, we have more choices than using just gray codes, and that we may obtain better results in terms of fan‐in, fan‐out, propagation delays, power consumption, or other related constraints in designing digital systems. The results obtained in this paper may also have useful applications in implementing special logic functions such as fuzzy threshold functions or fuzzy symmetric functions.

Line‐oriented two‐dimensional grammars (LOTDGs), region‐oriented two‐dimensional grammars (ROTDGs) and parallel productions are introduced. The relationships between LOTDGs and ROTDGs are stated. Examples of LOTDGS for generating all possible 45° right‐angled triangles, all possible squares, all possible 45° isosceles trapezoids, and all possible 45° parallelograms using parallel productions are presented. A new concise representation of a derivation chain is also introduced and illustrated by examples. LOTDGs and ROTDGs are compared. Generally speaking, LOTDGs require less terminal variables and non‐terminal variables, require less storage space, and require less derivation steps. Seven challenging problems for future research are also included. In addition, parallel production is an effective tool to model parallel computers as well as parallel processing. The results have useful applications in robot vision interpretation, robot pictorial communication, artificial intelligence, visual languages, software engineering, medical expert systems, and fuzzy logic functions.

Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a challenge to treatment effect identification. This chapter provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.

The emergence of the fast fashion trend has exerted a great pressure on fashion designers who are urged to consider customers’ preferences in their designs and develop new products in an efficient manner. The purpose of this paper is to develop a fuzzy association rule mining (FARM) approach for improving the efficiency and effectiveness of new product development (NPD) in fast fashion.

The FARM identifies the hidden relationships between product styles and customer preferences. The knowledge discovered help the fashion industry design new products which are not only fashionable, but are also saleable in the market.

To evaluate the proposed approach, a case study is conducted in a Hong Kong-based fashion company in which a real-set of data are tested to generate fuzzy association rules. The results reveal that the FARM approach can provide knowledge support to the fashion industry during NPD, shorten the NPD cycle time, and increase customer satisfaction.

Compared with traditional association rule mining, the proposed FARM approach takes the fuzziness of data into consideration and the knowledge represented in the fuzzy rules is in a more human-understandable structure. It captures the voice of the customer into fashion product development and provides a specific solution to deal with the challenges brought by fast fashion. In addition, it helps increase the innovation and technological capability of the fashion industry.