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The type-1 ordered weighted averaging (T1OWA) operator has demonstrated the capacity for directly aggregating multiple sources of linguistic information modelled by fuzzy sets rather than crisp values. Yager's OWA operators possess the properties of idempotence, monotonicity, compensativeness, and commutativity. This paper aims to address whether or not T1OWA operators possess these properties when the inputs and associated weights are fuzzy sets instead of crisp numbers. To this end, a partially ordered relation of fuzzy sets is defined based on the fuzzy maximum (join) and fuzzy minimum (meet) operators of fuzzy sets, and an alpha-equivalently-ordered relation of groups of fuzzy sets is proposed. Moreover, as the extension of orness and andness of an Yager's OWA operator, joinness and meetness of a T1OWA operator are formalised, respectively. Then, based on these concepts and the Representation Theorem of T1OWA operators, we prove that T1OWA operators hold the same properties as Yager's OWA operators possess, i.e.: idempotence, monotonicity, compensativeness, and commutativity. Various numerical examples and a case study of diabetes diagnosis are provided to validate the theoretical analyses of these properties in aggregating multiple sources of uncertain information and improving integrated diagnosis, respectively.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. The type-1 ordered weighted averaging (T1OWA) operator has demonstrated the capacity for directly aggregating multiple sources of linguistic information modelled by fuzzy sets rather than crisp values. Yager’s OWA operators possess the properties of idempotence, monotonicity, compensativeness, and commutativity. This paper aims to address whether or not T1OWA operators possess these properties when the inputs and associated weights are fuzzy sets instead of crisp numbers. To this end, a partially ordered relation of fuzzy sets is defined based on the fuzzy maximum (join) and fuzzy minimum (meet) operators of fuzzy sets, and an alpha-equivalently-ordered relation of groups of fuzzy sets is proposed. Moreover, as the extension of orness and andness of an Yager’s OWA operator, joinness and meetness of a T1OWA operator are formalised, respectively. Then, based on these concepts and the Representation Theorem of T1OWA operators, we prove that T1OWA operators hold the same properties as Yager’s OWA operators possess, i.e.: idempotence, monotonicity, compensativeness, and commutativity. Various numerical examples and a case study of diabetes diagnosis are provided to validate the theoretical analyses of these properties in aggregating multiple sources of uncertain information and improving integrated diagnosis, respectively.

Objectives Though an effective drug to treat heart failure and heart rhythm abnormalities, digoxin has side effects, such as confusion. Adverse drug events (ADEs) are major public health issues, but signal detection of ADEs is challenging for healthcare professionals. The objectives of this study is to evaluate if data-driven techniques can be used to detect ADEs, specifically examine the best method to detect the known event of confusion in patients prescribed digoxin from electronic primary care records and generate evidence for unknown ADEs. Approach In this study, we analysed 195,454 patients from a general practitioner (GP) database Wales, UK held in the SAIL (Secured Anonymised Information Linkage) databank with 51,920 patients prescribed digoxin and the rest acted as controls. All diagnostic events within 1 year after taking digoxin were considered. We used different data-driven analytic techniques - the proportional reporting ratio (PRR), the reporting odds ratio (ROR), the information component (IC), and the Yule’s Q (YULE) to detect signal of a statistical association between digoxin and associated adverse events. Results The YULE detected the highest number of 544 signals, the IC the lowest number of 117 signals, and they commonly identified 83 same signals. All ROR based signals were included in the YULE based signals. It detected that 8.09 people per 10,000 who took digoxin suffered from the side effect of confusion including acute confusional state of cerebrovascular origin and others. All 4 methods can detect the confusion event with the values of IC =5.35 (standard deviation =0.312), PRR=1407.2 (95% confidence interval=[993.72, 1992.71]), ROR== 2813.39 (95% confidence interval=[1692.443, 4676.776]), and YULE=0.99 (95% confidence interval=[0.9992892, , 0.9992895]) respectively. Also some unknown signals, such as “carcinoma in situ of rectum”, were identified by the 4 methods. One common signal detected which was not clearly mentioned in clinical guideline is “digoxin poisoning” with the values of IC =1.87 (standard deviation =0.0946), PRR=214.71 (95% confidence interval=[68.75, 670.56]), ROR=215.67(95% confidence interval=[69.05, 673.63]), and YULE=0.99 (95% confidence interval=[0.9907,0.9908]) respectively. This finding is consistent with the previous study that digoxin can sometimes have toxic effects, particularly at high blood concentrations, because it normally takes a long time to be broken down by the body. Conclusion Data-driven analytic methods are a valuable aid to signal detection of ADEs from large electronic health records for drug safety monitoring. This study finds the methods can detect known ADE and so could potentially be used to detect unknown ADE.

Objectives: 1) To use data-driven method to examine clinical codes (risk factors) of a medical condition in primary care electronic health records (EHRs) that can accurately predict a diagnosis of the condition in secondary care EHRs. 2) To develop and validate a disease phenotyping algorithm for rheumatoid arthritis using primary care EHRs. Methods: This study linked routine primary and secondary care EHRs in Wales, UK. A machine learning based scheme was used to identify patients with rheumatoid arthritis from primary care EHRs via the following steps: i) selection of variables by comparing relative frequencies of Read codes in the primary care dataset associated with disease case compared to non-disease control (disease/non-disease based on the secondary care diagnosis); ii) reduction of predictors/associated variables using a Random Forest method, iii) induction of decision rules from decision tree model. The proposed method was then extensively validated on an independent dataset, and compared for performance with two existing deterministic algorithms for RA which had been developed using expert clinical knowledge. Results: Primary care EHRs were available for 2,238,360 patients over the age of 16 and of these 20,667 were also linked in the secondary care rheumatology clinical system. In the linked dataset, 900 predictors (out of a total of 43,100 variables) in the primary care record were discovered more frequently in those with versus those without RA. These variables were reduced to 37 groups of related clinical codes, which were used to develop a decision tree model. The final algorithm identified 8 predictors related to diagnostic codes for RA, medication codes, such as those for disease modifying anti-rheumatic drugs, and absence of alternative diagnoses such as psoriatic arthritis. The proposed data-driven method performed as well as the expert clinical knowledge based methods. Conclusion: Data-driven scheme, such as ensemble machine learning methods, has the potential of identifying the most informative predictors in a cost-effective and rapid way to accurately and reliably classify rheumatoid arthritis or other complex medical conditions in primary care EHRs.

Objectives: 1) To use data-driven method to examine clinical codes (risk factors) of a medical condition in primary care electronic health records (EHRs) that can accurately predict a diagnosis of the condition in secondary care EHRs. 2) To develop and validate a disease phenotyping algorithm for rheumatoid arthritis using primary care EHRs. Methods: This study linked routine primary and secondary care EHRs in Wales, UK. A machine learning based scheme was used to identify patients with rheumatoid arthritis from primary care EHRs via the following steps: i) selection of variables by comparing relative frequencies of Read codes in the primary care dataset associated with disease case compared to non-disease control (disease/non-disease based on the secondary care diagnosis); ii) reduction of predictors/associated variables using a Random Forest method, iii) induction of decision rules from decision tree model. The proposed method was then extensively validated on an independent dataset, and compared for performance with two existing deterministic algorithms for RA which had been developed using expert clinical knowledge. Results: Primary care EHRs were available for 2,238,360 patients over the age of 16 and of these 20,667 were also linked in the secondary care rheumatology clinical system. In the linked dataset, 900 predictors (out of a total of 43,100 variables) in the primary care record were discovered more frequently in those with versus those without RA. These variables were reduced to 37 groups of related clinical codes, which were used to develop a decision tree model. The final algorithm identified 8 predictors related to diagnostic codes for RA, medication codes, such as those for disease modifying anti-rheumatic drugs, and absence of alternative diagnoses such as psoriatic arthritis. The proposed data-driven method performed as well as the expert clinical knowledge based methods. Conclusion: Data-driven scheme, such as ensemble machine learning methods, has the potential of identifying the most informative predictors in a cost-effective and rapid way to accurately and reliably classify rheumatoid arthritis or other complex medical conditions in primary care EHRs.

Other Research Group involved in the research: CCI For general type-2 fuzzy sets, the defuzzification process is very complex, and the exhaustive direct method of implementing type-reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type-2 fuzzy inferencing systems in real world applications. The present situation will not be expected to change, unless an efficient and fast method of deffuzzifying general type-2 fuzzy sets emerges. Type-1 Ordered Weighted Averaging (OWA) operators have been proposed to aggregate expert uncertain knowledge expressed by type-1 fuzzy sets in decision making. In particular, the recently developed Alpha-Level Approach to type-1 OWA operations has proven to be an effective tool for aggregating uncertain information with uncertain weights in real-time applications because its complexity is of linear order. In this paper, we prove that the mathematical representation of the type-reduced set (TRS) of a general type-2 fuzzy set is equivalent to that of a special case of type-1 OWA operator. This relationship opens up a new way of performing type-reduction of general type-2 fuzzy sets, allowing the use of the Alpha-Level Approach to type-1 OWA operations to compute the TRS of a general type-2 fuzzy set. As a result, a fast and efficient method of computing the centroid of general type-2 fuzzy sets is realised. The experimental results presented here illustrate the effectiveness of this method in conducting type-reduction of different general type-2 fuzzy sets.