On noncommutative spherically symmetric spaces

Two families of noncommutative extensions are given of a general space-time metric with spherical symmetry, both based on the matrix truncation of the functions on the sphere of symmetry. The first family uses the truncation to foliate space as an infinite set of spheres, is of dimension four and necessarily time-dependent; the second can be time-dependent or static, is of dimension five and uses the truncation to foliate the internal space.Comment: 22 page

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if-then rules which is obtained as particular case of the general result

Fuzzy Dynamic Discrimination Algorithms for Distributed Knowledge Management Systems

A reduction of the algorithmic complexity of the fuzzy inference engine has the following property: the inputs (the fuzzy rules and the fuzzy facts) can be divided in two parts, one being relatively constant for a long a time (the fuzzy rule or the knowledge model) when it is compared to the second part (the fuzzy facts) for every inference cycle. The occurrence of certain transformations over the constant part makes sense, in order to decrease the solution procurement time, in the case that the second part varies, but it is known at certain moments in time. The transformations attained in advance are called pre-processing or knowledge compilation. The use of variables in a Business Rule Management System knowledge representation allows factorising knowledge, like in classical knowledge based systems. The language of the first-degree predicates facilitates the formulation of complex knowledge in a rigorous way, imposing appropriate reasoning techniques. It is, thus, necessary to define the description method of fuzzy knowledge, to justify the knowledge exploiting efficiency when the compiling technique is used, to present the inference engine and highlight the functional features of the pattern matching and the state space processes. This paper presents the main results of our project PR356 for designing a compiler for fuzzy knowledge, like Rete compiler, that comprises two main components: a static fuzzy discrimination structure (Fuzzy Unification Tree) and the Fuzzy Variables Linking Network. There are also presented the features of the elementary pattern matching process that is based on the compiled structure of fuzzy knowledge. We developed fuzzy discrimination algorithms for Distributed Knowledge Management Systems (DKMSs). The implementations have been elaborated in a prototype system FRCOM (Fuzzy Rule COMpiler).Fuzzy Unification Tree, Dynamic Discrimination of Fuzzy Sets, DKMS, FRCOM

Exploiting supplier capabilities to maximise product design opportunities in the fuzzy front end activities

This paper explores the Fuzzy Front-End (FFE), i.e. the first phase of the Product Design and Development process where a company formulates a product concept to be developed and decides whether or not to invest resources in the further development of an idea. Our goal is to understand how companies leverage supply chain capabilities to improve product design opportunities in order to obtain optimized product concepts in the FFE. From the analysis of our pilot study, the results suggest that FFE is organized differently depending on design requirements and supply chain capabilities and that matching design requirements with supplier capabilities during the FFE improves performance. Therefore, the findings indicate that the proposed Conceptual Framework has the potential to be used by companies to design their FFE and to enhance the use of supply chain capabilities in their product design activities

Designing Software Architectures As a Composition of Specializations of Knowledge Domains

This paper summarizes our experimental research and software development activities in designing robust, adaptable and reusable software architectures. Several years ago, based on our previous experiences in object-oriented software development, we made the following assumption: ‘A software architecture should be a composition of specializations of knowledge domains’. To verify this assumption we carried out three pilot projects. In addition to the application of some popular domain analysis techniques such as use cases, we identified the invariant compositional structures of the software architectures and the related knowledge domains. Knowledge domains define the boundaries of the adaptability and reusability capabilities of software systems. Next, knowledge domains were mapped to object-oriented concepts. We experienced that some aspects of knowledge could not be directly modeled in terms of object-oriented concepts. In this paper we describe our approach, the pilot projects, the experienced problems and the adopted solutions for realizing the software architectures. We conclude the paper with the lessons that we learned from this experience

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP