2018 (vol. 28) - Number 4

*T. Kaczorek:*

A new method for computation of positive realizations of fractional linear continuous-time systems

*A. Biswas, A. Sarkar:*

Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multi-criteria group decision making

*L. Li, R. Zhang, J. Wang, X. Shang:*

Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making

*J. Duda:*

Lyapunov matrices approach to the parametric optimization of a system with two delays and a PD controller

*M. Lhous, M. Rachik, El M. Magri:*

Ideal observability for bilinear discrete-time systems with and without delays in observation

*P.T. Anh, A. Babiarz, A. Czornik, M. Niezabitowski:*

Variation of constant formulas for fractional difference equations

*K. Bingi, R. Ibrahim, M. Noh Karsiti, S. Miya Hassan, V. Rajah Harindran:*

A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems

ACS Abstract:

**1995 (Volume 4)**

Number 1/2

**The programmed grammars and automata as tools for a construction of analytic expert systems**

M.Flasiñski(Jagiellonian University, Poland) |

**Optimal control of discrete distributed systems with delays in the control: the finite horizon case**

Mostafa Rachik(Faculté des Sciences Ben M'sik, Morocco) | Jamila Karrakchou(Ecole Mahammadia d'Ingénieurs, Morocco) |

**keywords:** difference equation, diffusion system, discrete distributed systems, linear quadratic optimal control, optimal control.

**Multivariable nonlinear system identification by radial basis function neural networks**

Shaohua Tan(National University of Singapore, Singapore) | Jianbin Hao and Joos Vandewalle(Katholieke Universiteit Leuven, Belgium) |

**Repetitive regulator approximation**

Krzysztof Nowosad(Warsaw University of Technology, Poland) |

**Eigenvalue assignment and exponential stability in discrete-time systems**

Jerzy Tokarzewski(Military University of Technology, Poland) |

**A comparative study of ranking fuzzy sets deffined by a neural network algorithm - justification for a centroidal method**

Les M. Sztandera(Philadelphia College of Textiles and Science, USA) |

A recent breakthrough calls on a neural network algorithm, Fuzzy CID3 Algorithm, [109,111], which learns the needed membership functions from a set of training examples to differentiate between classes.

It is the purpose of this paper to evaluate and analyze the performance of available methods of ranking fuzzy subsets on a set of selected examples that cover possible situations we might encounter as defining fuzzy subsets at each node of a neural network. Through this analysis, suggestions as to which methods have better performance for utilization in neural network architectures, as well as criteria for choosing an appropriate method for ranking in corresponding fuzzy trees will be made.

**keywords:** fuzzy multi-attribute decision making, evaluation of fuzzy ranking methods, neural network architecture.

**Digital relaying in power system using fuzzy set theory**

Bogdan Kasztenny(Technical University of Wroc³aw, Poland) |

**Logical foundations for knowledge-based control systems. Part II: Representation of states, transformations and analysis of theoretical properties**

Antoni Ligêza(St. Staszic Technical University of Mining and Metallurgy, Poland) |

*generalization*among logical formulae is defined. A formal reasoning method, so-called

*backward dual resolution*, is introduced; the method is aimed at performing reasoning in an efficient manner and can be applied to reasoning about states and situations, checking if preconditions of transformation rules are satisfied, and to the verification of some theoretical properties of knowledge-based systems.

In this part, an application of the introduced formalism to knowledge-based representation of physical states of dynamic systems is proposed. A generic scheme of state transformation rules is outlined. Definitions of properties such as

*determinism*,

*completeness*,

*conservativity*, and other are introduced and an idea of

*potential correctness*of knowledge formalization is given. Due to general format of the proposed formalization, the class of potential applications is very large. The applications of specific interest of the proposed formalism include design and implementation of knowledge-based control systems and modelling the behaviour of certain complex relational systems having no analytical models in the form of differential/difference equations, as well as analysis of theoretical properties of knowledge-based dynamic systems. Simple application examples are enclosed.

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