Fuzzy sets: Abstraction Axiom, Statistical Interpretation, Observations of Fuzzy Sets

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities.

Basic Structure of the General Information Theory

The basic structure of the General Information Theory (GIT) is presented in the paper. The main divisions of the GIT are outlined. Some new results are pointed.

On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem

Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube [0, ∞)d . The elements of J(χ) can be distinguished among all W -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of both characteristics is a consequence of S-MT, and is equivalent to a result of Williamson. Pólya’s theorem can be obtained from the above identity by the specialization χ = 1W , where 1W is the unit character of W.

Neural Networks for Modelling of Large Social Systems. Approaches for Mentality, Anticipating and Multivaluedness Accounting

It is consider the new global models for society of neuronet type. The hierarchical structure of society and mentality of individual are considered. The way for incorporating in model anticipatory (prognostic) ability of individual is considered. Some implementations of approach for real task and further research problems are described. Multivaluedness of models and solutions is discussed. Sensory-motor systems analogy also is discussed. New problems for theory and applications of neural networks are described.

Formal Definition of the Concept “Infos”

The concept INFOS is very important for understanding the information phenomena. Because of this, it is basic for the General Information Theory. The more precise formal definition of this concept is given in the paper.

Extended Networks of Evolutionary Processors

This paper presents an extended behavior of networks of evolutionary processors. Usually, such nets are able to solve NP-complete problems working with symbolic information. Information can evolve applying rules and can be communicated though the net provided some constraints are verified. These nets are based on biological behavior of membrane systems, but transformed into a suitable computational model. Only symbolic information is communicated. This paper proposes to communicate evolution rules as well as symbolic information. This idea arises from the DNA structure in living cells, such DNA codes information and operations and it can be sent to other cells. Extended nets could be considered as a superset of networks of evolutionary processors since permitting and forbidden constraints can be written in order to deny rules communication.

Systemological Bases of Business Intelligence

Sustainable development support, balanced scorecard development and business process modeling are viewed from the position of systemology. Extensional, intentional and potential properties of a system are considered as necessary to satisfy functional requirements of a meta-system. The correspondence between extensional, intentional and potential properties of a system and sustainable, unsustainable, crisis and catastrophic states of a system is determined. The inaccessibility cause of the system mission is uncovered. The correspondence between extensional, intentional and potential properties of a system and balanced scorecard perspectives is showed. The IDEF0 function modeling method is checked against balanced scorecard perspectives. The correspondence between balanced scorecard perspectives and IDEF0 notations is considered.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.