Logical Reasoning for Forecasting in Mesopotamia

In this paper, I show that a kind of perfect logical competence is observed in the Babylonian tablets used for forecasting. In these documents, we see an intuition of some algebraic structures that are used for inferring prognoses as logical conclusions. The paper is based mainly on the omen series reconstructed by N. De Zorzi. It is shown that in composing these divination lists there was implicitly used the Boolean algebra.

Forwarding Table Entries in Software Defined Networks: Representation and Uses in Network Engineering

<p>Software Defined Networking (SDN) is an emerging architecture that decouples the network control and forwarding functions. In SDN, the functionality of static configuration and routing table in a traditional network has been replaced by forwarding table entries (FTEs). Thus a systematic research on FTE to better monitor traffic and manage networking resources becomes crucial in SDN. There are already some initial works on FTE representation from mathematical/logical perspective. However, they usually concentrate on the abstraction and expression of FTE rather than the applications in real network. Based on existing research, a controller is unable to monitor networking traffic and manage networking resources from a network-wide perspective. To address these challenges, Boolean algebra is chosen and extended in this thesis to examine the relations and manipulations among FTEs together with traffic statistics. Specifically, three SDN applications: i) equivalence evaluation during FTE deployment, ii) non-invasive traffic estimation and iii) anomaly detection, have been proposed and verified with the help of Boolean algebra. All of these applications rely on the mining of the FTEs and their associated statistics, thus no overhead will be introduced to the switch's original packet forwarding functionalities. They can be easily deployed in production networks due to the non-invasive strategy as well as the feasibility and flexibility in real networking scenarios.</p>

Forwarding Table Entries in Software Defined Networks: Representation and Uses in Network Engineering

<p>Software Defined Networking (SDN) is an emerging architecture that decouples the network control and forwarding functions. In SDN, the functionality of static configuration and routing table in a traditional network has been replaced by forwarding table entries (FTEs). Thus a systematic research on FTE to better monitor traffic and manage networking resources becomes crucial in SDN. There are already some initial works on FTE representation from mathematical/logical perspective. However, they usually concentrate on the abstraction and expression of FTE rather than the applications in real network. Based on existing research, a controller is unable to monitor networking traffic and manage networking resources from a network-wide perspective. To address these challenges, Boolean algebra is chosen and extended in this thesis to examine the relations and manipulations among FTEs together with traffic statistics. Specifically, three SDN applications: i) equivalence evaluation during FTE deployment, ii) non-invasive traffic estimation and iii) anomaly detection, have been proposed and verified with the help of Boolean algebra. All of these applications rely on the mining of the FTEs and their associated statistics, thus no overhead will be introduced to the switch's original packet forwarding functionalities. They can be easily deployed in production networks due to the non-invasive strategy as well as the feasibility and flexibility in real networking scenarios.</p>

Three-way Preconcept and Two Forms of Approximation Operators

Three-way decisions, as a better way than two-way decisions, has played an important role in many fields. As an extension of semiconcept, preconcept constitutes a new approach for data analysis. In contrast to preconcept, formal concept or semiconcept are too conservative about dealing with data. Hence, we want to further apply three-way decisions to preconcept. In this work, we introduce three-way preconcept by an example. This new notion combines preconcept with the assistant of three-way decisions. After that, we attain a generalized double Boolean algebra consisting of three-way preconcept. Furthermore, we give two form operators, approximation operators from lattice and set equivalence relation approximation operators, respectively. Finally, we present a conclusion with some summary and future issues that need to be addressed.

Fuzzy Annihilator Ideals of C -Algebra

In this paper, we introduce the concept of relative fuzzy annihilator ideals in C-algebras and investigate some its properties. We characterize relative fuzzy annihilators in terms of fuzzy points. It is proved that the class of fuzzy ideals of C-algebras forms Heything algebra. We observe that the class of all fuzzy annihilator ideals can be made as a complete Boolean algebra. Moreover, we study the concept of fuzzy annihilator preserving homomorphism. We provide a sufficient condition for a homomorphism to be a fuzzy annihilator preserving.

A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

One of the main issues in IFS theory are generalizations of intuitionistic fuzzy set (IFS) definition as well as IFS operations. In this paper, we present the LBIFS-IBA approach by applying operations based on interpolative Boolean algebra (IBA) on generalized IFS. Namely, LBIFS are defined as a special case of Liu’s generalized IFS with the maximal interpretational surface. By extending the interpretational surface, the descriptive power of the approach is enhanced, and therefore the problematic situations when μA+νA>1 can be modeled. In addition, IBA-based algebra secures Boolean properties of the proposed approach. Considerable attention is given to comprehension of uncertainty within LBIFS-IBA, i.e., we propose a novel manner of uncertainty interpretation by treating values from [−1,1] interval. In order to prove its importance, we compare LBIFS-IBA with several well-known IFS generalizations, showing that only our approach offers meaningful uncertainty interpretation is all selected cases. Additionally, we illustrate the practical benefits of LBIFS-IBA by applying it to an example of modeling Japanese candlesticks for price charting and paying special attention to uncertainty interpretation.

Rough Approximation Operators on a Complete Orthomodular Lattice

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.