In this paper, a two stage forecasting process is proposed for interval-valued time series viz. time series whose values are intervals instead of numbers. The forecasting of interval-valued time series is realized through predicting the centers and the radii of the intervals. The proposed model con sists of two functional modules: interval-valued threshold autoregression (ITAR) model followed by a granular fuzzy system. Fuzzy C-Means (FCM) method is used to determine the threshold parameters of the ITAR model while the least square error algorithm is used to estimate the values of its coefficients. To improve the forecasting accuracy, a granular fuzzy system is designed to further compensate for the series of residual errors. The proposed model can effectively capture the nonlinear feature of the original system. The piecewise compensation scheme can help to boost the prediction capability of the hybrid model. Some experiments demonstrate the performance of the model.
Posttraumatic thumb defects result in significant functional impairment. Multiple reconstructive procedures have been described for the management and improvement of function. Compared with no treatment, all reconstructive methods are beneficial. Each of the available procedures may be more applicable under certain conditions, can offer great benefits, and have its own downsides as well. With a thorough assessment and meticulous technique, the results of thumb reconstruction can be excellent. We present a review of the current reconstructive procedures for traumatic thumb amputation.
The study is focused on a development of a global structure in a family of distributed data realized on a basis of locally discovered structures. The local structures are revealed by running fuzzy clustering (Fuzzy C-Means), whereas building a global view is realized by forming global proximity matrices on a basis of the local proximity matrices implied by the partition matrices formed for the individual data sets. To capture the diversity of local structures, a global perspective at the structure of the data is captured in terms of a granular proximity matrix, which is built by invoking a principle of justifiable granularity with regard to the aggregation of individual proximity matrices. The three main scenarios are investigated: (a) designing a global structure among the data through building a granular proximity matrix, (b) refining a local structure (expressed in the form of a partition matrix) by engaging structural knowledge conveyed at the higher level of the hierarchy and provided in the form of the granular proximity matrix, (c) forming a consensus-building scheme and updating all local structures with the aid of the proximity dependences available at the upper layer of the hierarchy. While the first scenario delivers a passive approach to the development of the global structure, the two others are of an active nature by facilitating a structural feedback between the local and global level of the hierarchy of the developed structures. The study is illustrated through a series of experiments carried out for synthetic and publicly available data sets.
The learning abilities and high transparency are the two important and highly desirable features of any model of software quality. The transparency and user-centricity of quantitative models of software engineering are of paramount relevancy as they help us gain a better and more comprehensive insight into the revealed relationships characteristic to software quality and software processes. In this study, we are concerned with logic-driven architectures of logic models based on fuzzy multiplexers (fMUXs). Those constructs exhibit a clear and modular topology whose interpretation gives rise to a collection of straightforward logic expressions. The design of the logic models is based on the genetic optimization and genetic algorithms, in particular. Through the prudent usage of this optimization framework, we address the issues of structural and parametric optimization of the logic models. Experimental studies exploit software data that relates software metrics (measures) to the number of modifications made to software modules.
Abstract Given rapidly growing requirements for explainability, counterfactual explanations have gained interest in Machine Learning systems. This study investigates this timely problem in fuzzy relational systems described by fuzzy relational equations and develops a detailed solution to the counterfactual problems encountered in this setting. An underlying optimization problem is formulated, and its gradient-based solution is constructed. It is also demonstrated that the non-uniqueness of the derived solution is conveniently formalized and quantified by admitting a result coming in the form of information granules of a higher type, namely type-2 or interval-valued fuzzy set. The construction of the solution in this format is realized by invoking the principle of justifiable granularity. We also discuss ways of designing fuzzy relations and elaborate on methods of carrying out counterfactual explanation in rule-based models. Illustrative examples are included to present the performance of the method and interpret the obtained results.