Bunpei Nakano

On conditions for a meeting not to reach a deadlock

A formal model for describing the interaction stage in a meeting, particularly, persuasion and compromise by the members in a meeting, is proposed. Using the model, a sufficient condition for a meeting not to reach a deadlock is provided. The condition implies that stable emotion of members of a meeting is essential for the meeting not to reach a deadlock.

A CHARACTERIZATION OF INTERACTIONS

A complex large-scale system is a central subject of systems engineering. However, there is no integrated theory for it partially because it has been treated on a specialized model built for a specific purpose. This paper, in order to lay a foundation for a theory of a complex large-scale system, introduces a general definition of a complex system in the framework of the general systems theory and characterizes an interaction which is one of the most basic concepts of a complex system. This paper shows that every interaction consists of two primitive interactions, process and system interactions and that they have some unique representations. Models of complex systems are classified according to their types of interactions and it is shown as an application of the above analysis that this classification is relative to realization of a system, that is, a model can be transformed from one type into another by restructuring its input-output pair.

Comparability of coalitions in committees with permission of voters by using desirability relation and hopefulness relation

In this paper, we treat committees with permission of voters, and examine comparability of the effectiveness and the efficiency of coalitions in a committee by using formal ways, that is, the desirability relation and the hopefulness relation. Consequently, we obtain a necessary and sufficient condition for desirability relation of the permission game of a committee with permission of voters to be complete, that is, the desirability relation is complete if and only if there is no pair of coalitions whose supporters are mutually different. Moreover, we give an example of committees in which there are coalitions whose effectiveness and efficiency cannot be compared.

ALGEBRAIC FORMULATION OF RELATIONSHIP BETWEEN A GOAL SEEKING SYSTEM AND ITS ENVIRONMENT

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 Ashbys 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...

A STRUCTURE OF RATIONAL DECISION PRINCIPLES

A problem of decision making under uncertainty or decision making with multiple objectives is not a simple optimization problem and so we have to assume some decision principles on making a decision. So far many decision principles have been proposed as rational ones. This paper tries to reveal an underlying structure of rational decision principles. We first formulate decision problems and principles from the viewpoint of the mathematical general systems theory and then, based on them, specify the class of decision problems as a category and a decision principle as a functor. As a conclusion, we claim that three conditions, i.e., the Pareto consistency, the similarity condition and the invariance condition, compose a fundamental structure of rational decision principles and are naturally represented in the category theoretic framework. In order to support the claim we demonstrated that the linear weighted sum decision principle can be characterized by using these conditions.

Causal ordering and the symmetry problem of basic linear systems

Abstract This paper treats causal ordering in the framework of mathematical general systems theory. Due to its importance causal ordering has been much discussed, however, it has not hitherto been formulated as a system theoretic property. This paper formulates causal ordering as one of the proper system theoretic properties that should be characterized only by the behaviour of a system. In particular, for a general system S given by a binary relation over system objects X ajnd Y. we say there exists a causal ordering from X to Y if X is non-trivially related to Y and if it is possible to decompose S into a class of functional subsystems where each functional subsystem expresses a determinism from events of X to events of Y such that an event of Y occurs after an event of X. Based on this formulation, Simons, symmetry problem of causal ordering, that is the mterehangeability problem of a cause and an effect, is considered. Characterizations of symmetry and asymmetry of causal. ordering are given for basi...

Complete stability and inside commonality of perceptions

To give a realistic structure of perceptions that satisfies inside commonality, the concepts of stability of perceptions and complete stability of perceptions are proposed. A framework for interperception of emotions by subjects is provided to deal with the concepts. The equivalence between stability and complete stability under inside commonality of perceptions is proven.

Meaning of state space representation and its relation to the.canonical form

State space is one of the key concepts of system theory. In general, a state space is introduced into a system description without examining its specific physical meaning. It is known, however, that if we select a suitable state space representation, it becomes easier for us to understand or to manipulate the property of a system. Thus, although it may not be meaningful to try to arrive at a physical meaning of the state space, it is important to find a way where a choice of a state space can be made in accordance with the system of interest, taking into account the theoretical meaning of that choice. In this paper, the choice of a state space is discussed in terms of the concepts that general systems theory have provided and the canonical forms of linear control theory are interpreted using the state space representation. Four realizations of a single-input and single-output discrete basic linear system are constructed, whose state spaces are derived from system properties. such as reachability, past-det...

A GENERAL SYSTEM THEORETIC CHARACTERIZATION OF RECONSTRUCTION FAMILY

This study gives some considerations to the reconstruction family. Usually, complex systems are represented by synthesizing several submodels which are recognized through various aspects. It is not always possible to construct a consistent global model from synthesization of submodels (subsystems) nor is it always construct the unique global model from those given subsystems. The reconstructed class of such global systems is called the reconstruction family. This paper gives several results on the characterization and structure of the reconstruction family.

Meaning of state-space representation and its relation to canonical form Part 2. Controllability and constructibility

State space is one of the key concepts of systems theory. In the previous paper (Nakano et al. 1987) a system-theoretic framework about the choice of a state space was developed and the canonical forms of linear control theory were interpreted. Four realizations of a single-input and single-output discrete basic linear system were constructed. The isomorphism between the realizations and the universal state space representation shows systemic meanings of the state space. In this paper, using the same approach, two other realizations—a controllability realization and a constructibility realization—are constructed. By the matrix representations of these realizations the meanings of the controllability and constructibility canonical forms are shown in relation to the universal state-space representation.