Shih Chuan Cheng

The Association of Bone Mineral Density with Vitamin D Receptor Gene Polymorphisms

Abstract: A recent meta-analysis of 16 publications suggested that bone mineral density (BMD) is not associated with vitamin D receptor (VDR) gene polymorphism (VDRGP) at the 0.05 significance level when a study with genotyping mistakes is excluded. We wished to determine whether ‘positive’ findings supporting the BMD–VDRGP association may be explained by chance, and what factors affect the outcomes of these studies. Seventy-five articles and abstracts on the association of VDRGP with BMD and related skeletal phenotypes published before January 1997 were identified. Twenty-three of 67 (34.3%) studies on spinal BMD and 22 of 51 (43.1%) on femoral neck BMD had found a BMD–VDRGP association at p<0.05, significantly (p= 7 × 10–14 for spinal BMD, p= 9 × 10–16 for hip BMD) higher than the expected 5% false positive rate under the null hypothesis of ‘no association’. ‘Positive’ results were more frequently observed in studies on females before the menopause than those on females after the menopause (p<0.02) or on male and female subjects combined (p<0.05) when skeletal phenotypes at any bone sites were considered. The ‘positive rate’ among studies was also influenced by the age range of subjects studied and by the inclusion of subjects with osteoporosis. It is concluded that: (1) BMD is associated with VDRGP with high levels of confidence and (2) non-genetic factors and genetic heterogeneity interfere with the detection of the effects of VDRGP on bone phenotypes.

Statistical versus Fuzzy Measures of Variable Interaction in Patients with Stroke

Evidence-based medicine, founded in probability-based statistics, applies what is the case for the collective to the individual patient. An intuitive approach, however, would define structure in the (physiologic) system of interest, the human being, directly relevant to other systems (patients) composed of similar variables. A difference in measure of variable interaction in the patient from that in the collective would show how extrapolation of information from the latter to the single patient is counterintuitive. Methods: We compare statistical to ‘fuzzy’ measures of variable interaction. Three diagnostic variables are considered in 30 stroke patients who underwent the same diagnostic tests. ‘Fit’ (fuzzy information) values [0, 1] for degree of variable severity were expertly assigned by 2 blinded raters for real and fabricated patients. Fabricated patients were composed of real-patient ‘fit’ values after shuffling. Real and fabricated patients were each numerically represented as a set . Three groups of fabricated patients and the real patient group were studied. Statistical [Pearson’s product-moment (regression analysis) and Spearman’s rank correlation] and three different fuzzy measures of variable interaction were applied to patient data. Results: Interaction for blood-vessel measured strong in real patients, and weak after one shuffle, using all fuzzy measures. By comparison, the same interaction was found in real patients by only 1 rater (Rater 2) using 1 statistical technique (Spearman’s rank correlation) which, as did Pearson product-moment correlation, found a ‘significant’ interaction between blood-heart in fabricated patients. Conclusion: Our study suggests that the measure of variable interaction in nature – as combined in the individual (real) patient – is captured robustly by fuzzy measures and not so by standard statistical measures.

An application of fuzzy dynamic integrated judgment to cotton allocation

In the manufacturing process of yarns for the textile industry, often encountered is the problem of how to select a substitute (from the warehouse) for a brand of cotton in the cotton allocation that is currently in use but running out of the raw material. A model that uses fuzzy dynamic integrated judgment (FDIJ) provides a very useful tool in solving this problem. In view of several factors in cotton allocations, the FDIJ is made for cotton selection according to the data feedback from previous production runs. The main objective of this paper is to explain how the data feedback can be stored in a fuzzy dynamic relationship dictionary which generates a fuzzy dynamic relation to be used in the learning ability in the problem of cotton allocation.

Applications of fuzzy algebra in automata theory and coding theory

We apply fuzzy semigroup theory to show that (fuzzy) automata with fuzzy input are equivalent to (fuzzy) automata with crisp input. We use fuzzy group theory to show how abstract pattern recognition problems can be used to examine the faithfulness of a device which decodes messages transmitted across a noisy channel.

Vitamin D receptor gene polymorphism affects bone mineral density: An analysis by fuzzy mathematics

To find defects in genes that cause diseases, geneticists test whether a change or variation in a gene is associated with a disease or an increased susceptibility. Morrison first reported in 1994 that a slight variation in the vitamin D receptor gene (VDRGP) is associated with a significant change in our bone mineral density (BMD). By January of 1997, seventy-five independent investigations had been published, and no consensus had been reached as to whether BMD is really associated with VDRGP. We analyzed all the 75 publications using a fuzzy mathematics approach to address this issue. We use two methods, one based on preference relations, and the other based on p-values. Fifty-five studies on spinal BMD and 73 on hip BMD were analyzed. Results from method I found that VDRGP affects spinal BMD strongly among pre-menopausal populations, and moderately among post-menopausal populations, and populations with pre- and post-menopausal women combined. No relations were found in populations with males and females combined. VDRGP was associated with hip BMD among pre-menopausal, but not any other, populations. Using method II we found that VDRGP was associated with spinal BMD only in pre-menopausal women, and VDRGP was somewhat associated with hip BMD in all four types of populations. Conclusion: BMD is associated with VDRGP in certain populations, but not in others. Heterogeneity of populations studied seems to be responsible for the discrepancies among studies.

A Note on the Inverse Fuzzy Integrated Judgment

An application of fuzzy dynamic integrated judgment in cotton allocation can be found in Zhao, Peng, and Cheng [4]. Often applications in which the fuzzy integrated judgment has been successfully used were turned out to be quite effective. How to decide a fuzzy weight set is an inverse operation of fuzzy integrated judgment. Nonetheless, the fuzzy weight set that stands for the experience and the technology of experts plays a crucial role in applying the fuzzy integrated judgment. The success of fuzzy integrated judgment depends upon the choice of fuzzy weight set. Thus, an inverse process of fuzzy integrated judgment is an important practice; especially, in cotton allocation problem. Under certain conditions, the original image à (as a fuzzy weight set) is an important feasible solution to the fuzzy relation equation B̃ = à ￮ R̃. However, it is necessary to use the original image à as a fuzzy weight set unconditionally in some practical applications of fuzzy integrated judgment. Therefore, it is very crucial to create a practical approach of obtaining the optimal fuzzy weight set for building a model of fuzzy dynamic integrated judgment regardless of the existence of the exact original image.

Fuzzy confidence estimation of the parameter involving in the distribution of the total time on test for censored data

Data mining has captured the interest of researchers from many different as well as diverse fields of study such as data base systems, machine learning, statistics, cluster analysis, knowledge based systems. One of the major issues in data mining is the analysis of attribute relevance. The basic idea is to come up with a measure that can be effectively used to quantify the relevance of an attribute in identifying a class or a concept. One possible application is the total failure time of censored data. That is, the total time on test for censored data of a system with several components often plays an important role in the reliability theory. In some cases, all components of a system with several identical components may be put on test until an r-th smallest failure time occurs and the total time on test is subsequently calculated. The total time on test for censored data from exponentially distributed censored data has been proved to be an adequate statistic by Nair and Cheng in light of the works by Skibinsky, Cheng and Mordeson, and others. The test may be repeated for many times. As a result, since the total time on test until the r-th ordered failure time is observed will be recorded for each test, several total time on test (for censored data) for the same system are available for use in analyzing the reliability of the system. Fuzzy set theory was formalized by Zadeh. Some fuzzy statistical techniques can be found in (J. J. Buckley 2004, H. J. Zimmerma 1990). In this proposal, we are investigating the fuzzy estimation of the parameter of underlying probability distribution for total failure time of censored data.

Risk of falling in older women

We propose a weighted average approach to measure the risk of falling in older women. We consider four causal variables of falling, namely serum 25-OHD levels, medication use, fracture, and age. We use five methods to derive linear equations with these four factors as independent variables in the linear equations with risk of falling as the dependent variable.

Knowledge presentation according to the linkage intensity

The objective of this paper is to study methods of knowledge representation, such as frame approaches, production systems, semantic network, and symbolic logic, can be found in literatures. In this paper, we study the notions of similar relation of sets and linkage sets that can be used in not only the characterization of the relation, but also the knowledge representation system and pattern recognition.