Search results

The purpose of this paper is to state new formulation of the programme‐styled framework of pansystems research and related expansions.

Pansystems‐generalized extremum principle (0**: (dy/dx=0)**) is presented with recognitions to various logoi of philosophy, mathematics, technology, systems, cybernetics, informatics, relativity, biology, society, resource, communications and related topics: logic, history, humanities, aesthetics, journalism, IT, AI, TGBZ* <truth*goodness*beauty*Zen*>, etc. including recent rediscoveries of 50 or so pansystems logoi.

A keynote of the paper is to develop the deep logoi of the analytic mathematics, analytic mechanics, variational principles, Hilbert's sixth/23rd problems, pan‐axiomatization to encyclopedic principles and various applications. The 0**‐universal connections embody the transfield internet‐styled academic tendency of pansystems exploration.

The paper includes topics: history megawave, pansystems sublation‐modes, pan‐metaphysics, pansystems dialogs with logoi of 100 thinkers or so, and pansystems‐sublation for a series of logoi concerning the substructure of encyclopedic dialogs such as systems, derivative, extremum, quantification, variational principle, equation, symmetry, OR, optimization, approximation, yinyang, combination, normality‐abnormality, framework, modeling, simulation, relativity, recognition, practice, methodology, mathematics, operations and transformations, quotientization, product, clustering, Banach completeness theorem, Weierstrass approximation theorem, Jackson approximation theorem, Taylor theorem, approximation transformation theorems due to Walsh‐Sewell mathematical school, Hilbert problems, Cauchy theorem, theorems of equation stability, function theory, logic, paradox, axiomatization, cybernetics, dialectics, multistep decision, computer, synergy, vitality and the basic logoi for history, ethics, economics, society OR, aesthetics, journalism, institution, resource and traffics, AI, IT, etc.

This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules. The applications of rough sets are discussed in pattern recognition, information processing, business and finance, industry, environment engineering, medical diagnosis and medical data analysis, system fault diagnosis and monitoring and intelligent control systems. Development trends and future efforts are outlined. An extensive list of references is also provided to encourage interested readers to pursue further investigations.

The purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.

The uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if‐part fuzzy sets in the case of single‐input and single‐output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.

The since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.

From the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.

For engineers, the sinc‐shaped membership function is a good choice to improve their fuzzy systems in real applications.

The uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.

The purpose of this paper is to present an academic programme of pansystems research with a lot of new concepts, principles, methods. Universal consideration of philosophy‐mathematics‐technology is set forth with mega‐combination. The emphasis on the transfield internet‐like investigations is developed. Many theory‐methods of pansystems get further concise optimization.

The concrete contents of the paper include: historical megawave, philosophical stratagems, meta‐mathematics, meta‐methodology, technological realistic principles, unification and differentiation of encyclopedic branches, systems science, information theory, cybernetics, biosystems, generalized vitality, computer and IT, thinking science, logic, OR, AI, PR, DM, modernization of yinyang analysis combining dialectics, sociology, economics, meta‐relativity, generalized quantification and scale theory, general process of birth‐growth‐ageing‐disease‐death, the inheritance and development of 300 scholars' researches, etc.

All of the topics concerned with are reduced to the actualizations of PVOR – pansystems variational OR: V−d(xy)=^*0^*/PRR′P′/0^**, which is an integrated synthesis of 20‐PanStemCells of PanConcepts and PanMethod, and embodies a specific pansystems summarization for the core of the true and the good. Furthermore, the formula “Pansystems Researches=^*(PVOR/0^**/Pan54787721/Everything)+^*0^*=^*Pan–netlike connections of thoughts and methods” is expanded with concrete applications.

Provides information on pansystems research.

A new expression of the philosophy framework of pansystems theory is stated. Some generalized quantification formulae are developed. Concrete contents include: new forms of panderivative and pansymmetry, meta‐equation, eight‐counter methodology, pansystems relativity, dialectical logic, panbox principle, complex systems, systems engineering, analytic hierarchy process, general living systems, economy‐sociology, clustering, topology, morphology, master equation, approximation‐transforming theory, equivalence theory of dynamics of electromagnetic media, etc.

Rough set theory is a simple and potential methodology in extracting and minimizing rules from decision tables. Its concepts are core, reduct and discovering knowledge in the form of rules. The decision rules explain the decision state to predict and support the new situation. Initially it was proposed as a useful tool for analysis of decision states. This approach produces a set of decision rules involves two types namely certain and possible rules based on approximation. The prediction may highly be affected if the data size varies in larger numbers. Application of Rough set theory towards this direction has not been considered yet. Hence the main objective of this paper is to study the influence of data size and the number of rules generated by rough set methods. The performance of these methods is presented through the metric like accuracy and quality of classification. The results obtained show the range of performance and first of its kind in current research trend.

To study and to analyze a second order finite‐element boundary‐flux approximation using isoparametric numerical integration.

The numerical finite‐element integration is the main method used in this research. Since a domain with curved boundary is considered we apply an isoparametric approach. The lumped flux formulation is another method of approach in this paper.

This research study presents a careful analysis of the combined effect of the numerical integration and isoparametric FEM on the boundary‐flux error. Some L₂‐norm estimates are proved for the approximate solutions of the problem under consideration.

The authors offer a general study within the framework of the boundary‐flux approximation theory, which completes the results of published works in this scientific field of research.

A useful application is to employ appropriate quadrature formulae without violating the precision of the boundary‐flux FEM. The lumped mass approximation is also an important practical approach to the problem in question.

The paper presents an entire investigation in FE boundary‐flux approximation theory, in particular, elements of arbitrary degree and domains with curved boundaries. The work is addressed to the possible related fields of interest of postgraduate students and specialists in fluid mechanics and numerical analysis.

Some new and powerful resources for cybernetics and system theory are explored, stemming from number theory, chronotopology, and the cybernetics of history — a field previously not considered.

This paper presents a closed form analytic solution for the impulse response of an optimum FIR deconvolution filter intended for a pair of discrete pulses of arbitrary amplitude and sign, subject to the minimisation of Chebyshev maximum norm for the approximation error. The tradeoff between the approximation error and the degradation of signal‐to‐noise ratio, is examined.