A new efficiency evaluation approach with rough data: An application to Indian fertilizer

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.In the world of chaos, nothing is certain. In such an unpredictable world, measuring the efficiency of any individual is inevitable. In a conventional data envelopment analysis (DEA) model, exact input and output quantity data are needed to measure the relative efficiencies of homogeneous decision-making units (DMUs). However, in many real-world applications, the exact knowledge of data might not be available. The rough set theory allows for handling this type of situation. This paper tries to construct a rough DEA model by combining conventional DEA and rough set theory using optimistic and pessimistic confidence values of rough variables, all of which help provide a way to quantify uncertainty. In the proposed method, the same set of constraints (production possibility sets) is employed to build a unified production frontier for all DMUs that can be used to properly assess each DMU's performance in the presence of rough input and output data. Besides, a ranking system is presented based on the approaches that have been proposed. In the presence of uncertain conditions, this article investigates the efficiency of the Indian fertilizer supply chain for over a decade. The results of the proposed models are compared to the existing DEA models, demonstrating how decision-makers can increase the supply chain performance of Indian fertilizer industries

New rough set based maximum partitioning attribute algorithm for categorical data clustering

Clustering a set of data into homogeneous groups is a fundamental operation in data mining. Recently, consideration has been put on categorical data clustering, where the data set consists of non-numerical attributes. However, implementing several existing categorical clustering algorithms is challenging as some cannot handle uncertainty while others have stability issues. The Rough Set theory (RST) is a mathematical tool for dealing with categorical data and handling uncertainty. It is also used to identify cause-effect relationships in databases as a form of learning and data mining. Therefore, this study aims to address the issues of uncertainty and stability for categorical clustering, and it proposes an improved algorithm centred on RST. The proposed method employed the partitioning measure to calculate the information system's positive and boundary regions of attributes. Firstly, an attributes partitioning method called Positive Region-based Indiscernibility (PRI) was developed to address the uncertainty issue in attribute partitioning for categorical data. The PRI method requires the positive and boundary regions-based partitioning calculation method. Next, to address the computational complexity issue in the clustering process, a clustering attribute selection method called Maximum Mean Partitioning (MMP) is introduced by computing the mean. The MMP method selects the maximum degree of the mean attribute, and the attribute with the maximum mean partitioning value is chosen as the best clustering attribute. The integration of proposed PRI and MMP methods generated a new rough set hybrid clustering algorithm for categorical data clustering algorithm named Maximum Partitioning Attribute (MPA) algorithm. This hybrid algorithm is an all-inclusive solution for uncertainty, computational complexity, cluster purity, and higher accuracy in attribute partitioning and selecting a clustering attribute. The proposed MPA algorithm is compared against the baseline algorithms, namely Maximum Significance Attribute (MSA), Information-Theoretic Dependency Roughness (ITDR), Maximum Indiscernibility Attribute (MIA), and simple classical K-Mean. In addition, seven small data sets from previously utilized research cases and 21 UCI repository and benchmark datasets are used for validation. Finally, the results were presented in tabular and graphical form, showing the proposed MPA algorithm outperforms the baseline algorithms for all data sets. Furthermore, the results showed that the proposed MPA algorithm improves the rough accuracy against MSA, ITDR, and MIA by 54.42%. Hence, the MPA algorithm has reduced the computational complexity compared to MSA, ITDR, and MIA with 77.11% less time and 58.66% minimum iterations. Similarly, a significant percentage improvement, up to 97.35%, was observed for overall purity by the MPA algorithm against MSA, ITDR, and MIA. In addition, the increment up to 34.41% of the overall accuracy of simple K-means by MPA has been obtained. Hence, it is proven that the proposed MPA has given promising solutions to address the categorical data clustering problem

The Quantification of Perception Based Uncertainty Using R-fuzzy Sets and Grey Analysis

The nature of uncertainty cannot be generically defined as it is domain and context specific. With that being the case, there have been several proposed models, all of which have their own associated benefits and shortcomings. From these models, it was decided that an R-fuzzy approach would provide for the most ideal foundation from which to enhance and expand upon. An R-fuzzy set can be seen as a relatively new model, one which itself is an extension to fuzzy set theory. It makes use of a lower and upper approximation bounding from rough set theory, which allows for the membership function of an R-fuzzy set to be that of a rough set. An R-fuzzy approach provides the means for one to encapsulate uncertain fuzzy membership values, based on a given abstract concept. If using the voting method, any fuzzy membership value contained within the lower approximation can be treated as an absolute truth. The fuzzy membership values which are contained within the upper approximation, may be the result of a singleton, or the vast majority, but absolutely not all. This thesis has brought about the creation of a significance measure, based on a variation of Bayes' theorem. One which enables the quantification of any contained fuzzy membership value within an R-fuzzy set. Such is the pairing of the significance measure and an R-fuzzy set, an intermediary bridge linking to that of a generalised type-2 fuzzy set can be achieved. Simply by inferencing from the returned degrees of significance, one is able to ascertain the true significance of any uncertain fuzzy membership value, relative to other encapsulated uncertain values. As an extension to this enhancement, the thesis has also brought about the novel introduction of grey analysis. By utilising the absolute degree of grey incidence, it provides one with the means to measure and quantify the metric spaces between sequences, generated based on the returned degrees of significance for any given R-fuzzy set. As it will be shown, this framework is ideally suited to domains where perceptions are being modelled, which may also contain several varying clusters of cohorts based on any number of correlations. These clusters can then be compared and contrasted to allow for a more detailed understanding of the abstractions being modelled

Modelling potential movement in constrained travel environments using rough space-time prisms

The widespread adoption of location-aware technologies (LATs) has afforded analysts new opportunities for efficiently collecting trajectory data of moving individuals. These technologies enable measuring trajectories as a finite sample set of time-stamped locations. The uncertainty related to both finite sampling and measurement errors makes it often difficult to reconstruct and represent a trajectory followed by an individual in space-time. Time geography offers an interesting framework to deal with the potential path of an individual in between two sample locations. Although this potential path may be easily delineated for travels along networks, this will be less straightforward for more nonnetwork-constrained environments. Current models, however, have mostly concentrated on network environments on the one hand and do not account for the spatiotemporal uncertainties of input data on the other hand. This article simultaneously addresses both issues by developing a novel methodology to capture potential movement between uncertain space-time points in obstacle-constrained travel environments

Dealing with uncertain entities in ontology alignment using rough sets

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Ontology alignment facilitates exchange of knowledge among heterogeneous data sources. Many approaches to ontology alignment use multiple similarity measures to map entities between ontologies. However, it remains a key challenge in dealing with uncertain entities for which the employed ontology alignment measures produce conflicting results on similarity of the mapped entities. This paper presents OARS, a rough-set based approach to ontology alignment which achieves a high degree of accuracy in situations where uncertainty arises because of the conflicting results generated by different similarity measures. OARS employs a combinational approach and considers both lexical and structural similarity measures. OARS is extensively evaluated with the benchmark ontologies of the ontology alignment evaluation initiative (OAEI) 2010, and performs best in the aspect of recall in comparison with a number of alignment systems while generating a comparable performance in precision

Study of the neutron quantum states in the gravity field

We have studied neutron quantum states in the potential well formed by the earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in the two lowest quantum states correspond to expectations with an experimental accuracy. A position-sensitive neutron detector with an extra-high spatial resolution of ~2 microns was developed and tested for this particular experiment, to be used to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states. The present experiment can be used to set an upper limit for an additional short-range fundamental force. We studied methodological uncertainties as well as the feasibility of improving further the accuracy of this experiment