Showing papers in "International Journal of General Systems in 1986"
TL;DR: The bag structure as a set-like object in which repeated elements are significant and the operation of selecting elements from a bag based upon their membership in a set is introduced.
Abstract: We introduce the bag structure as a set-like object in which repeated elements are significant. We discuss operations on bags such as intersection, union and addition. We introduce the operation of selecting elements from a bag based upon their membership in a set. We show the usefulness of the bag structure in relational data bases. We provide a definition for fuzzy bags. In these fuzzy bags the count of the number of elements itself becomes a crisp bags. We investigate a calculus for fuzzy bags.
695 citations
TL;DR: The algebraic structure of bodies of evidence on a set is studied, based on extended set union, intersection and complementation, and it is pointed out that a body of evidence can account for conjunctive as well as a disjunctive information.
Abstract: A body of evidence in the sense of Shafer can be viewed as an extension of a probability measure, but as a generalized set as well. In this paper we adopt the second point of view and study the algebraic structure of bodies of evidence on a set, based on extended set union, intersection and complementation. Several notions of inclusion are exhibited and compared to each other. Inclusion is used to compare a body of evidence to the product of its projections. Lastly, approximations of a body of evidence under the form of fuzzy sets are derived, in order to squeeze plausibility values between two grades of possibility. Through all the paper, it is pointed out that a body of evidence can account for conjunctive as well as a disjunctive information, i.e. the focal elements can be viewed either as sets of actual values or as restrictions on the (unique) value of a variable.
421 citations
TL;DR: It has been shown that the normalized measures of a given probability distribution are much closer to one another than the corresponding absolute measures of entropy.
Abstract: A number of “normalized” measures of entropy have been obtained to measure the “intrinsic” uncertainty of a probability distribution. Their graphs have been drawn and it has been shown that the normalized measures of a given probability distribution are much closer to one another than the corresponding absolute measures of entropy.
52 citations
TL;DR: In this paper, generalized proteromorphisms and amphimorphisms, forward and backward compatibility of relations, as well as other new useful concepts are introduced for solving relational equalions, investigation of compatibility of systems and data structures, and examining faithfulness of representations of knowledge structures in knowledge-based systems.
Abstract: Many diverse problems of compatibility of structures can be unified by generalizing tjie concept of a homomorphism. The paper introduces generalized proteromorphisms and amphimorphisms, forward and backward compatibility of relations, as well as other new useful concepts. These generalizations find application in solving relational equalions, investigation of compatibility of systems and data structures, in examining faithfulness of representations of knowledge structures in knowledge-based systems, in semiotics and elsewhere.
39 citations
TL;DR: Applications of entropy minimax are summarized in three major areas: meteorology, engineering/ materials science, and medicine/biology, and continuous patterns employing concepts of potential functions and fuzzy entropies.
Abstract: Applications of entropy minimax are summarized in three major areas: meteorology, engineering/ materials science, and medicine/biology. The applications cover both discrete patterns in multidimensional spaces of mixed quantitative and qualitative variables, and continuous patterns employing concepts of potential functions and fuzzy entropies. Major achievements of entropy minimax modeling include the first long range weather forecasting models with statistical reliability significantly above chance verified on independent data, the first models of fission gas release and nuclear fuel failure under commercial operating conditions with significant and independently verified statistical reliability, and the first prognosis models in coronary artery disease and in non-Hodgkin's lymphoma with significant predictability verified on independent data. In addition, applications of entropy minimization and maximization separately are reviewed, including feature selection, unsupervised classification, probability es...
35 citations
TL;DR: This paper gives a first account of GSLT, of its foundation, its main features, and most obvious applications, showing thus its versatility and usefulness.
Abstract: The General System Logical Theory (GSLT) is obtained by combining Resconi's logical theory of systems with Jessel's theory of secondary sources. In the present paper we give a first account of GSLT, of its foundation, its main features, and most obvious applications. GSLT is defined by its aims and concretized by a new specific concept, that of an Elementary Logical System (ELS). ELS may be connected with Lie algebras. The systems formerly dealt with by Resconi's and Jessel's separate theories are identified as particular ELS. Subsequently are built up various networks of ELS, leading thus to natural and powerful extensions of the classical feedback theory. Finally GSLT is applied to three very different topics: wave propagations (or any physical nature), Riemann geometries and chemical controls, showing thus its versatility and usefulness.
33 citations
TL;DR: It is shown that although maximally constrained mechanical systems seem thereby extremely limited in their possible behaviors, they can be programmed to introduce a limitless plasticity in their behavior without breaking their constraints.
Abstract: We present some formal and empirical evidence to support the proposition that maximally constrained mechanical systems exhibit some of the basic properties of organisms and of machines. We show further that although such maximally constrained systems seem thereby extremely limited in their possible behaviors, they can be programmed to introduce a limitless plasticity in their behavior without breaking their constraints. We then turn to the ambiguities inherent in the word “machine”, and show that programming, in the above sense, introduces a new relation among machines; namely simulation of one machine by another. This simulation relation has none of the nice properties familiar from mathematical machine theory, basically because the causal structure in the simulator is completely different from the corresponding structure in what is being simulated. A few general implications of this state of affairs, mostly to biological problems, are discussed.
33 citations
TL;DR: For a long time, people have been trying to characterize or define the notion of system, and the results so far have been contradictory and unsatisfactory as mentioned in this paper, leading many to conclude that there is no such thing as a "system" and hence to deny that System Theory is about anything.
Abstract: For a long time, people have been trying to characterize or define the notion of system. After all, “systems” are supposed to be what System Theory is about. The results so far have been contradictory and unsatisfactory. This confusion at the foundations has led many to conclude that there is no such thing as a “system” and hence to deny that System Theory is about anything.1,3 Even those most sympathetic to the notion have difficulties at this level. The very founders of System Theory did not try to say what a system was; and as for System Theory, they characterized it only obliquely, by saying it comprised all studies of interest to more than one discipline.5 They thereby begged the entire question.
27 citations
TL;DR: It is shown here that K-systems analysis can be used to solve problems in classical multivariate analysis, and solve them more effectively than existing methods.
Abstract: K-systems exist in general systems theory for the study of the relationships between parts and wholes. We show here that K-systems analysis can be used to solve problems in classical multivariate analysis, and solve them more effectively than existing methods. To demonstrate this, we take on “the analysis of variance” in this paper. The analysis of variance is the most important and powerful technique in the field of statistical inference (quoted from Probability and Statistics by Hines and Montgomery). We apply K-systems analysis to the analysis of variance problem, and we compare the two techniques. We see that K-systems analysis can provide more information. But the major difference is that the analysis of variance guesses a model for the data whereas K-systems analysis uses “the” model that is true and correct for the data. Further, K-systems theory delivers a surprising and important insight: it is generally incorrect to use any model where effects and interactions are represented statically over sub...
25 citations
TL;DR: In this paper, a method to estimate a given possibility distribution from the associated observations is derived based on the one-to-one correspondence between possibility distributions and their basic probability assignments, and it is shown that in this estimation the possibility value for a state is proportional to the frequency of the state in the observations which are drawn from nested state subsets.
Abstract: This paper is a theoretical contribution to reconstructability analysis of possibilistic systems. A method to estimate a given possibility distribution from the associated observations is derived based on the one-to-one correspondence between possibility distributions and their basic probability assignments. It is shown that in this estimation the possibility value for a state is proportional to the frequency of the state in the observations which are drawn from nested state subsets. The order preservation relationship between a given (true) possibility distribution and its estimation is derived. Based on this preservation property, it is shown that the order in the distance from an original possibilistic overall system of their unbiased reconstructions from two alternative reconstruction hypotheses (structures) is preserved in the estimated systems domain. Particularly, it is proved that systems conceptualized in terms of possibility theory possess an important property: if a possibilistic system is perf...
14 citations
TL;DR: Normalized measures of directed divergence, all of which lie between 0 and 1 and as such are comparable with one another, are discussed.
Abstract: In a recent paper, we discussed normalized measures of entropy,13 i.e. measures of entropy all of which lie between 0 and 1. This leads to standardized measures which can be compared with one another. In the present paper, we discuss normalized measures of directed divergence, all of which lie between 0 and 1 and as such are comparable with one another.
TL;DR: In this, the First part of a two part work, a general model of spatial organization is introduced and it is demonstrated via simulation that the resulting aspatial model of internal relations has a corresponding spatial interpretation (and therefore, in theory, that sensible space structures can be supported by...
Abstract: In this, the First part of a two part work, a general model of spatial organization is introduced. Following a brief synopsis of some of Spinoza's and Leibniz's views regarding natural structure, an extension of the Spinozian model is presented in which the attribute spatial extension is portrayed as a relational system that implicitly underlies the differentiation of sensible space into “modifications” (“natural systems”) and the latter's subdifferentiation into “modes” On the basis of this model, all instances of modal differentiation are understood to take place in a manner explained by this relational structure, the existence (but not the specific characteristics) of which is initially assumed. The nature of the structure is then deduced according to a “most-probable-state” kind of logic; next, it is demonstrated via simulation that the resulting aspatial model of internal relations has a corresponding spatial interpretation (and therefore, in theory, that sensible space structures can be supported by...
TL;DR: New refinements of homomorphisms that are needed in order to deal with partial algebraic systems, namely, weak, strong and Very strong homomorphism and the laws of their compositions are presented.
Abstract: The paper presents new refinements of homomorphisms that are needed in order to deal with partial algebraic systems; namely, weak, strong and Very strong homomorphisms and the laws of their compositions. Further, it describes loose and tight congruences and the canonical factorization of various kinds of homomorphisms. The results have important applications in cognitive modelling, general systems relational models, knowledge representation schemes in Expert Systems and formal methods of Software Engineering,
TL;DR: In this paper, the emergence and development of a self-reflexive contingent structure is depicted as a threshold condition which produces a set of properties not available to systems of lower complexity and which increases the variety available to the system through structural reformulation in the face of envi...
Abstract: Niklas Luhmann has provided a view of social theory from the perspective of contemporary systems theory which highlights a large number of social mechanisms that tend to be overlooked in the more traditional approaches. Using a complex hierarchical approach to social structure, I demonstrate the kinds of social change which Luhmann brings out in a way that avoids his own functionalist teleology while at the same time emphasizes his unique description of the role of contingency in the evolution of social systems. Finally, from Luhmann's approach toward social theory I suggest a theory of development and change in social structures which is unique to the level of complexity where social activities are found. This theory depicts the emergence and development of a self-reflexive contingent structure as a threshold condition which produces a set of properties not available to systems of lower complexity and which increases the variety available to the system through structural reformulation in the face of envi...
TL;DR: In this paper, the authors formalized the key concepts for describing the relationship between a goal seeking system and its relevant environment and developed a formal discussion on the relationship in the framework of mathematical general systems theory.
Abstract: The purpose of this paper is, first, to formalize the key concepts for describing the relationship between a goal seeking system and its relevant environment and, then, mainly based on Ashby's Law of Requisite Variety, to develop a formal discussion on the relationship in the framework of mathematical general systems theory. The law, one of the most well-known laws in the general systems theory, intuitively claims that “only the variety can destroy the variety”. Although the claim is so simple and has attracted more and more attention from organization theory, organizational cybernetics and control theory, the concepts involved are used quite loosely. By defining the concepts of the varieties in terms of equivalence relations, we will formulate the basic logic explaining the relationship between a goal seeking system and its relevant environment and explore its meaning and significance. In this process we will also reveal the meaning of the internal model principle, which says that in order to control the...
TL;DR: In this paper, a set of basic scaling equations for the self-similar hierarchical cosmological model is established for stellar and galactic scale systems using two of Mandelbrot's general equations.
Abstract: Using two of Mandelbrot's general equations for self-similar systems, a set of basic scaling equations is established for the Self-Similar Hierarchical Cosmology. Given the known properties of atomic scale systems and the proposed scaling rules, it is demonstrated that stellar and galactic scale systems conform to the self-similar model quantitatively. Definitive predictions for future tests of the cosmological model are presented.
TL;DR: It is suggested that this interpretation of Spencer Brown's Laws of Form is closer to his original ideas than the interpretation with three-valued logic given by Francisco Varela.
Abstract: G. Spencer Brown's book Laws of Form informally presents three distinct logical systems. The third system is interpreted here through Alonzo Church's restricted recursive arithmetic. Restricted recursive arithmetic was introduced by Church in 1955 as the first formal system capturing finite automata. It is suggested that this interpretation is closer to Spencer Brown's original ideas than the interpretation with three-valued logic given by Francisco Varela.
TL;DR: In this paper, a review of anticipatory systems is presented, based on the paper "ANTICIPATORY Systems" by Robert Rosen, Pergamon Press, Oxford, 1985, X + 436pp.
Abstract: (1986). A review of: “ANTICIPATORY SYSTEMS”, by Robert Rosen, Pergamon Press, Oxford, 1985, X + 436pp. International Journal of General Systems: Vol. 12, No. 4, pp. 405-409.
TL;DR: It is hypothesized that classifications involving more than five classes will be associated with township distribution patterns that conflict with Central Place Theory, and this is shown to be clearly so.
Abstract: The emphasis in this work is on the practical application of ideas set forth in Part I. Two studies involving spatial distribution are discussed: the distribution of human population in the Indianapolis, Indiana Region, and the world distribution of mammals. In the first, populations over the period 1890–1980 of Ihe 393 townships making up the study area are used to produce classifications involving various numbers of classes of township types. A test of the theoretical structure posed in Part I is then detailed. On the theory that the underlying relations involved cannot sustain a real world structure involving more than five functional classes, it is hypothesized that classifications involving more than five classes will be associated with township distribution patterns that conflict with Central Place Theory. This is shown to be clearly so. In the second study, the derivation of a five region partitioning of world mammalian distribution patterns is described. Discussion includes the introduction of a w...
TL;DR: In this article, the authors compared the radii, velocity distribution, rotation periods and masses of galaxies with predictions derived from a self-similar cosmological model, and predicted the existence of an undiscovered class of stellar objects that may account for the enigmatic "dark matter", which is known to be the dominant constituent of galaxies.
Abstract: Empirical estimates for the radii, velocity distribution, rotation periods and masses of galaxies are compared with predictions derived from a self-similar cosmological model previously presented by the author. This model also predicts the existence of an undiscovered class of stellar objects that may account for the enigmatic "dark matter", which is known to be the dominant constituent of galaxies but which has yet to be identified.
TL;DR: The problem of discovering those properties of systems that remain invariant under a given type of connection is considered and a solution of this problem is proposed for the parallel and serial connections of automata, due to an application of some appropriately formulated rules of the structural inference.
Abstract: The paper deals with one of the main issues of systems theory, i.e. the relationship between the part and the whole. This issue is discussed within the framework of the structural inference. The problem of discovering those properties of systems that remain invariant under a given type of connection is considered. A solution of this problem is proposed for the parallel and serial connections of automata, due to an application of some appropriately formulated rules of the structural inference.
TL;DR: A data-voice integrated network with N clusters of users, N interface message processors-concentrators, one central processor and one intermediate processor-Concentrator is described and a polynomial time-complexity algorithm for overall design is provided.
Abstract: This paper describes a data-voice integrated network with N clusters of users, N interface message processors-concentrators, one central processor and one intermediate processor-concentrator. The network is described and a polynomial time-complexity algorithm for overall design is provided.
TL;DR: In this paper, a categorical treatment of general time systems using the categorization method presented in our previous paper is presented, in particular, a conceptual equivalence between the causality and the state space representability is proved in the categorical terms.
Abstract: In this paper we show a categorical treatment of general time systems using the categorization method presented in our previous paper Various concepts about general time systems are categorized in the unified framework Some category theoretical tools for the investigation of such time systems are presented Using those tools some basic properties of time systems are explored in our framework In particular, a conceptual equivalence between the causality and the state space representability is proved in the categorical terms These results show that our method can be a universal tool for a categorization and a categorical treatment of mathematically defined general systems
TL;DR: In this article, the authors provide rigorous methods for identifying the functional components of systems in such a way as to facilitate making relationships between the components and the overall system, based on the definitions of function commonly used.
Abstract: This article provides certain fairly rigorous, although still heuristic, methods for identifying the functional components of systems in such a way as to facilitate making relationships between the components and the overall system. Based on the definitions of function commonly used, making such a relationship is not always as easy as it could be made. Specific matters discussed herein include the following: functions and objectives-oriented thinking; logical versus physical thinking; functional outputs versus functional objectives; functional objectives versus system mission; directness of relationship to an objective; relationships between multiple functional objectives; distinguishing specific objectives within more general ones; the need to develop a consistent set of terms; etc.
TL;DR: A model of understanding texts of a natural language is presented, which consists of three levels and the system uses only information in the given text and employs additional information from a knowledge base.
Abstract: A model of understanding texts of a natural language is presented, which consists of three levels. On the first level, the system uses only information in the given text. On the second level, it employs additional information from a knowledge base. On the third level, understanding is connected with some activity of the system stimulated by the available information.
TL;DR: In this article, the existence of transversals in certain types of general structures that frequently arise in reconstructabihty studies is investigated, and it is verified that Hall's condition is satisfied by two types of structures, known as beta and loopless structures.
Abstract: Some combinatorial problems originating in reconslructability theory are studied. The investigation concerns the incidence properties of finite sets of reconslructability structures. The results deal with the existence of transversals in certain types of general structures that frequently arise in reconstructabihty studies. It is verified that Hall's condition is satisfied by two types of structures, known as beta and loopless structures. This assures the existence of transversals in such structures. It is also shown that loopless struclures can be considered a special case of beta structures provided that the assumption of maximality is relaxed in the definition of the latter.