Showing papers in "International Journal of General Systems in 1982"
TL;DR: The proposed measures of U-uncertainty and conditional U-UNcertainty provide a foundation for developing an alternative theory of information, one based on possibility theory rather than probability, as well as avoiding a current controversy in possibility theory.
Abstract: A measure of uncertainly and information for possibility theory is introduced in this paper The measure is called the U-uncertainty or, alternatively, the U-information. Due to its properties, the U-uncertainty/information can be viewed as a possibilistic counterpart or the Shannon entropy and, at the same time, a generalization or the Hartley uncertainty/information. A conditional U-uncertainty is also derived in this paper, it depends on the U-uncertainties or the joint and marginal possibility distributions in exactly the same way as the conditional Shannon entropy depends on the entropies or the joint and marginal probability distributions. The conditional U-uncertainty is derived without the use of the notion of conditional possibilities, thus avoiding a current controversy in possibility theory. The proposed measures of U-uncertainty and conditional U-uncertainty provide a foundation for developing an alternative theory of information, one based on possibility theory rather than probability...
317 citations
TL;DR: An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short) as discussed by the authors, which is actually set functions which are monotonic with respect to set inclusion.
Abstract: An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short). Fuzzy measures are actually set functions which are monotonic with respect to set inclusion. Triangular norms and conorms are semi-groups of the unit interval which have been thoroughly studied in the literature of functional equations. The proposed class encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures. Any set function of the class can be expressed in terms of a density, and constructively defined out of this density. This feature makes the proposed framework attractive from a practical point of view for the representation and manipulation of subjective evidence. The link between t-norm and t-conorm based set functions and Shafer's belief functions is invesligaled.
304 citations
TL;DR: In this article, it is argued that social systems are self-referential and can be best viewed as autopoietic systems, and various implications of this view are discussed.
Abstract: It is argued in the paper that social systems are self-referential. As such, they can be best viewed as autopoietic systems. Various implications of this view are discussed in the paper.
282 citations
TL;DR: Using some concepts from fuzzy set theory, a measure for the anxiety induced by a given decision function is suggested and some implications of this measure are investigated.
Abstract: The selection of one alternative from a set of alternatives as the one to implement is in general an anxiety provoking situation. Using some concepts from fuzzy set theory described in the paper, a measure for the anxiety induced by a given decision function is suggested. Some implications of this measure are investigated.
181 citations
TL;DR: An axiomatic framework for formalizing the most general class of fuzzy complements is introduced and it is shown that the various measures of fuzziness described previously in the literature are special cases of this general class.
Abstract: An axiomatic framework for formalizing the most general class of fuzzy complements is introduced in this paper. It is then used for investigating a general class of measures of fuzziness based on the view that the degree of fuzziness of a fuzzy set should characterize the lack of distinction between the set and its complement. It is shown that the various measures of fuzziness described previously in the literature are special cases of this general class. A class of so-called distance-based measures of fuzziness is also introduced. These measures are described in terms of the notion of an aggregation function of differences between the membership grades characterizing a fuzzy set and those of its complement. It is shown that the class of distance-based measures is equal to the class of general measures of fuzziness. It is also shown that, given a particular fuzzy complement, aggregation functions which differ only in a multiplication constant represent the same measure of fuzziness.
134 citations
TL;DR: In this paper, the definition of the and operation in multivalued logic and decision making is investigated, and a set of basic properties for selecting an appropriate operator are given, as well as a general class of connectives.
Abstract: We investigate the definition of the “and” operation in multivalued logic and decision making. A set of basic properties are suggested. Rules for selecting an appropriate operator are given. A general class of connectives is also suggested.
54 citations
TL;DR: In this article, the distribution law that specifies how many “coins” for each level must stay in circulation is deduced from empirically observed data from about ten different countries, and it is also possible to understand the processes of reorganization of monetary systems induced by inflation.
Abstract: Self-organizing systems are defined as able to change their structure, according to need, within specific equivalence classes. Once hierarchical levels and their value functions are assigned, requirements of invariance under transformations within an equivalence class can be used as a principle to determine the population of each level. This program is carried out in complete detail for the monetary system. It has been possible to deduce the distribution law that specifies how many “coins” for each level must stay in circulation; this law agrees well with empirically observed data from about ten different countries. It is also possible to understand the processes of reorganization of monetary systems induced by inflation, i.e. the disappearance of coins of low value and the simultaneous issue of coins or higher value.
36 citations
TL;DR: In this paper, a method for obtaining the equations for the reconstruction hypothesis in linearly independent form is presented, and the resultant matrix is in triangular form, which greatly reduces the size of the reconstructed hypothesis matrix.
Abstract: This paper is concerned with the determination of probabilistic reconstruction families. A method for obtaining the equations for the reconstruction hypothesis in linearly independent form is presented, and the resultant matrix is in triangular form. The procedure greatly reduces the size of the reconstruction hypothesis matrix, and the solution of the matrix equation is rendered trivial.
27 citations
TL;DR: Reconstructability analysis is defined as the process of investigating the possibilities of reconstructing properties of overall systems from the knowledge of the corresponding properties of collections of their various subsystems.
Abstract: Reconstructability analysis is defined as the process of investigating the possibilities of reconstructing properties of overall systems from the knowledge of the corresponding properties of collections of their various subsystems. In two recent papers, sets of procedures were presented which developed solutions of two problems associated with this process: that of generating a structure systems which could serve as appropriate collections of subsystems, and that of evaluating a structure system with respect to its adequacy for representing an overall system. Use of these tools on problems arising from an actual systems investigation, however, involves resolution of a number of inductive ambiguities. In the final analysis, it is necessary to recognize elements of arbitrariness in this resolution. The places where this arbitrariness creeps in all involve decisions by an investigator who is using the tools. Ultimately, interactive software can be developed to aid the investigator in making these de...
20 citations
TL;DR: The paper introduces the main concepts of singularity theory, catastrophe theory and q-analysis for the characterization of the global structure of social systems and develops an outline for a general mathematical theory of surprises.
Abstract: Methods based in algebra and geometry are introduced for the mathematical formulation of problems in the social and behavioral sciences. Specifically, the paper introduces the main concepts of singularity theory, catastrophe theory and q-analysis for the characterization of the global structure of social systems. Applications in urban land development, electric power generation and international conflict are given to illustrate the methodology. The paper concludes with an outline for a general mathematical theory of surprises, together with a program for investigating the systemic property of resilience.
18 citations
TL;DR: Several lines or evidence are presented in support of the hypothesis that systems on the stellar and atomic scales arc nontrivially self-similar as mentioned in this paper, however, none of these lines of evidence can be verified empirically.
Abstract: Several lines or evidence are presented in support of the hypothesis that systems on the stellar and atomic scales arc nontrivially self-similar.
TL;DR: Systems approach appears to be the only possible methodological tool for the analysis and synthesis of complex problems for solving complex phenomena in biology and biotechnology.
Abstract: The definition, strategy and goal of the systems approach (consisting of systems analysis and synthesis) and its application in solving complex phenomena in biology and biotechnology is presented. Next, the structural, functional, descriptive, control and dynamic organization (hierarchy) of biological systems is outlined. The decomposition of a biotechnological process into structural and functional hierarchy presents the fundamental way of analysis, giving rise to a set of elements or elementary biological and physico-chemical phenomena at each level of hierarchy. The process synthesis is based on a reduction of information on each level by means of purposeful selection of important systemic phenomena and on the definition of strong (between elements at each level) and weak (between levels) interactions. Based on systems approach, the scope for biological scale-up is outlined. Systems approach appears to be the only possible methodological tool for the analysis and synthesis of complex problems ...
TL;DR: It is proposed that a language specifically designed to help humans deal with complexity be developed and it is argued that Interpretive Structural Modeling already possesses some of these properties.
Abstract: Properties characterizing complexity are woven together with research on human information processing and behavioristic psychology to produce a theory of human limits. It is suggested I hat coupling the human and complexity, in problem solving situations, can be viewed at a design problem where an interface device is needed to link the human lo complexity, Interpretive Structural Modeling is discussed as an example of such an in I efface device. In addition, it is proposed that a language specifically designed to help humans deal with complexity be developed. The necessary properties of such 3 language arc presented, and it is argued that Interpretive Structural Modeling already possesses some of these properties.
TL;DR: In this article, the relation between a random vector and an equivalence relation on a reference space is defined as the reflexive and symmetric relation associated with A:B (A and B being random vectors) and a distance between random variables and a similarity relation having good independence properties is derived.
Abstract: Properties of the lattice or symmetric relations on a reference space Ω properties of the valued boolean lattices and an association between a random vector and an equivalence relation on tl are used to show how most or the formulae given by different authors concerning joint information of random vectors may easily be interpreted through introduction or a random object denoted A:B (A and B being random vectors). RA:Bis defined as the reflexive and symmetric relation associated with A:B. RA:B=RAwhere RA: equivalence relation associated with A RB: equivalence relation associated with B. A distance between random variables and a similarity relation having good independence properties are derived. These results are then extended to more complex structures of random objects.
TL;DR: In this article, the second principle of thermodynamics is used to study the thermal agitation of groups in hierarchically organized systems, where order is relative to a precise level of organization.
Abstract: In hierarchically organized systems, order is relative to a precise level of organization. Disordered movement of groups in a macroscopic level of observation appears as a collective ordered movement for the individuals belonging to the previous groups at a more microscopic level of observation. Ordered appearance of thermal agitation of groups can lead to structuration in the individual level. The inferences within the second principle of thermodynamics are then studied for hierarchical systems.
TL;DR: This paper explores the problem of finding behavioral models of finite state systems, given observed data of systems which are presumed to lie in this category, and several possible approaches to developing a solution to this general problem are discussed.
Abstract: This paper explores the problem of finding behavioral models of finite state systems, given observed data of systems which are presumed to lie in this category. Following an informal introduction, a formal definition of an identification problem is given along with the form that a solution to such a problem may be expected to lake. The most general type of such problem involving finite state systems is described and several possible approaches to developing a solution to this general problem are discussed. Several classes of more specialized classes of systems and their identification problems are developed. For these, a set of algorithms are described which may be used to solve them. The complexity of these algorithms is discussed.
TL;DR: Two major steps are identified as required to enable comparative policy analysis to take advantage of general systems methodology: adoption of various analytical tactics employing a cross-time/cross-jurisdictional (“pooled”) data matrix and methodological developments that transform the dominant form of analysis from concern with fixed independent and dependent variables to the analysis of time-relevant relationships.
Abstract: The authors have three purposes in this article:—To review and critique the field of comparative policy output research, as an example of applied systems analysis; —To identify gaps in knowledge and understanding which could be foreshortened by modest conceptual and methodological adjustments suggested by general systerrts analysis; and, —To propose specific conceptual and methodological techniques to that end. Two major steps are identified as required to enable comparative policy analysis to take advantage of general systems methodology:—Adoption of various analytical tactics employing a cross-time/cross-jurisdictional (“pooled”) data matrix; and, —Methodological developments that transform the dominant form of analysis from concern with fixed independent and dependent variables to the analysis of time-relevant relationships.
TL;DR: The pnncipic of self-similarity, which is a cornerstone of the Self-Similar Hierarchical Cosmology, is defined in this paper, and empirical and theoretical results that provide further indications of the validity of this principle are discussed.
Abstract: The pnncipic of self-similarity, which is a cornerstone of the Self-Similar Hierarchical Cosmology, is defined. New empirical and theoretical results that provide further indications of the validity of this principle are discussed.
TL;DR: In this article, a humanistic system is analyzed through psychophysical objects and aesthetic considerations, and psychophysical dynamics and valuation are portrated as requisite concepts for implementing the mathematical philosophy on which a recent pragmatic theory of fuzzy sets and systems is founded.
Abstract: Humanistic systems are analyzed through psychophysical objects and aesthetic considerations. An interpretation, a reference, an evaluation, and a comparison are shown to be the four important aspects of the general aesthetic system. Within the aesthetic system, psychophysical dynamics and psychophysical valuation are portrated as requisite concepts for implementing the mathematical philosophy on which a recent pragmatic theory of fuzzy sets and systems is founded.
TL;DR: The role of symbolic initiative in mathematics is reviewed and a sense in which computers compute mathematical functions is defined, which enables a clarification of the semantics of computer and communication data.
Abstract: We review the role of symbolic initiative in mathematics and then define a sense in which computers compute mathematical functions. This enables a clarification of the semantics of computer and communication data. Turing's view of machine intelligence is examined in terms of its use of symbolic initiative.
TL;DR: In this paper, the structure of composite digraphs, and subgraph interaction/decomposition are studied, and applications to computer systems, Markov chains, and to dynamic systems and control are presented.
Abstract: In Part I, certain fundamental structural properties of directed graphs (digraphs) are explored using a unified systemtheoretic approach. In the spirit of general systems theory, a digraph is modelled as a dynamic system with multiple inputs and outputs. The concept of controllability, observability, and the elegant theory of minimal realization, duality, and Kalman's decomposition in linear systems have all found their positions in digraphs. New computation algorithms are derived. In Part II (Vol, 8, No. 4 of this journal) of this paper, the structure of composite digraphs, and subgraph interaction/decomposition are studied. Applications to computer systems, Markov chains, and to dynamic systems and control are presented.