L-Fuzzy Structured Query Language

Lattice valued fuzziness is more general than crispness or fuzziness based on the unit interval. In this work, we present a query language for a lattice based fuzzy database. We define a Lattice Fuzzy Structured Query Language (LFSQL) taking its membership values from an arbitrary lattice L. LFSQL can handle, manage and represent crisp values, linear ordered membership degrees and also allows membership degrees from lattices with non-comparable values. This gives richer membership degrees, and hence makes LFSQL more flexible than FSQL or SQL. In order to handle vagueness or imprecise information, every entry into an L-fuzzy database is an L-fuzzy set instead of crisp values. All of this makes LFSQL an ideal query language to handle imprecise data where some factors are non-comparable. After defining the syntax of the language formally, we provide its semantics using L-fuzzy sets and relations. The semantics can be used in future work to investigate concepts such as functional dependencies. Last but not least, we present a parser for LFSQL implemented in Haskell.

The micromorphology of Paleoseismic soft sediment deformation structures in glacial deposits from three sample sites in Scotland /

The nature of this research is to investigate paleoseismic deformation of glacial soft sediments from three sampling sites throughout the Scottish Highlands; Arrat's Mills, Meikleour and Glen Roy. The paleoseismic evidence investigated in this research will provide a basis for applying criteria to soft sediment deformation structures, and the trigger mechanisms that create these structures. Micromorphology is the tool used in this to investigate paleoseismic deformation structures in thin section. Thin section analysis, (micromorphology) of glacial sediments from the three sampling sites is used to determine microscale evidence of past earthquakes that can be correlated to modem-day events and possibly lead to a better understanding of the impact of earthquakes throughout a range of sediment types. The significance of the three sampling locations is their proximity to two major active fault zones that cross Scotland. The fault zones are the Highland Boundary Fault and the Great Glen Fault, these two major faults that parallel each other and divide the country in half Sims (1975) used a set of seven criteria that identified soft sediment deformation structures created by a magnitude six earthquake in Cahfomia. Using criteria set forth by Sims (1975), the paleoseismic evidence can be correlated to the magnitude of the deformation structures found in the glacial sediments. This research determined that the microstructures at Arrat's Mill, Meikleour and Glen Roy are consistent with a seismically induced origin. It has also been demonstrated that, even without the presence of macrostructures, the use of micromorphology techniques in detecting such activity within sediments is of immense value.

Improving the Scalability of Reduct Determination in Rough Sets

Rough Set Data Analysis (RSDA) is a non-invasive data analysis approach that solely relies on the data to find patterns and decision rules. Despite its noninvasive approach and ability to generate human readable rules, classical RSDA has not been successfully used in commercial data mining and rule generating engines. The reason is its scalability. Classical RSDA slows down a great deal with the larger data sets and takes much longer times to generate the rules. This research is aimed to address the issue of scalability in rough sets by improving the performance of the attribute reduction step of the classical RSDA - which is the root cause of its slow performance. We propose to move the entire attribute reduction process into the database. We defined a new schema to store the initial data set. We then defined SOL queries on this new schema to find the attribute reducts correctly and faster than the traditional RSDA approach. We tested our technique on two typical data sets and compared our results with the traditional RSDA approach for attribute reduction. In the end we also highlighted some of the issues with our proposed approach which could lead to future research.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.

Small, black, soft cover notebook which has “Niagara Historical Society” taped to the front cover

Small, black, soft cover notebook which has “Niagara Historical Society” taped to the front cover. It contains handwritten entries which include: names of early settlers; buildings; veterans at Queenston Heights, 1859; group of Indians; and list of people whose picture was taken in 1870[?] at Queenston, n.d.

Memoranda booklet (soft cover) compliments of the Canadian Bank of Commerce, St. Catharines Branch

Memoranda booklet (soft cover) compliments of the Canadian Bank of Commerce, St. Catharines Branch. Only one page has writing on it. It appears to be a shopping list, n.d.