Tsutomu Da-te

Some properties of minimal solutions for a fuzzy relation equation

Abstract Some properties of the solution set and minimal solutions of a fuzzy relation equation are considered. In this paper, we show the necessary and sufficient condition for existence of a minimal solution of a finite fuzzy relation equation defined on infinite index sets.

A calculation method for solving fuzzy arithmetic equations with triangular norms

The authors apply a previously developed calculation method using a digital representation to obtain an approximate solution to a fuzzy arithmetic equation. A t-norm and a phi -operator which is defined in connection with a given t-norm are summarized. Nonstandard operations based on the inf- phi convolution are discussed as a solution for the fuzzy arithmetic equation. Formulas involving the solution of the equations as well as the classifications of t-norms and phi -operators that are necessary for applying the formulas are presented. Some numerical examples are included.<<ETX>>

A necessary condition for solvability of fuzzy arithmetic equations with triangular norms

This paper treats a fuzzy arithmetic equation based on sup-(t-norm) convolution. The authors have investigated the properties of the procedure to solve the equation (i.e. inf- /spl phi/ convolution) and discussed its solvability. A necessary condition for solving the equations involving addition and multiplication has been derived as the main result of this work.<<ETX>>

Parameter formulae for fundamental operations of weakly non-interactive fuzzy numbers

D. Dubois and H. Prade (1981) introduced the concept of weakly noninteractive fuzzy numbers whose operations are based on the extension principle corresponding to each t-norm in place of the minimum operator. Some properties of weakly noninteractive fuzzy numbers and their practical method of calculation are investigated. Three parameters indicating the mean value and the left/right spreads of the fuzzy number are considered. Various parameter formulas for arithmetic operations and power function operation of certain kinds of weakly noninteractive fuzzy numbers involving no-interactive fuzzy numbers are presented. The formulas are applicable to both cases of the L-R fuzzy number of Dubois and Prade (1978) and an improved version of the calculation method using the digital representation. An attempt is made to classify general t-norms into the three classes from the viewpoint of the parameter formulas. The results of numerical experiments are shown for the formulas and the calculation method using the digital representation.<<ETX>>

Some algebraic properties of weakly non-interactive fuzzy numbers

Abstract This study focuses on the concept of sup-(t-norm) convulution, a generalized version of Zadehs extension principle. The authors treat the algebraic structure of fuzzy arithmetic based on the sup-(t-norm) convolution, and especially show some new properties comparing them with those of the conventional fuzzy arithmetic based on sup-min convolution.

An ultrasonic 3-D object identification system using pulse neural network

In this paper a new 3-D object identification system is proposed. It is constructed by combining an ultrasonic phase measuring method with an artificial pulse neural network following the physiological knowledge of the auditory processing. Our experimental results show that 3 ultrasonic sensors are sufficient for the identification of objects in the proposed system.

A TREATMENT OF USEFULNESS OF KEYWORDS IN FUZZY REQUESTS FOR AN INFORMATION RETRIEVAL SYSTEM WITH BAYESIAN NETWORKS

We improve a document retrieval method based on the so-called maximum entropy principle proposed by Cooper, and show how to implement this system on a Bayesian network. A Bayesian network is a probabilistic model for expressing probabilistic relations among random variables. We show advantages of a document retrieval system on a Bayesian network in comparison with Coopers system. The original document retrieval system based on the maximum entropy principle has a drawback: a result of retrieval can not be obtained in some cases. In this paper, we resolve this drawback by fuzzification of user retrieval requests.

The correspondence of belief changes in logical settings and the possibilistic framework

Belief change operations in logical settings and the possibilistic framework are reviewed. In logical settings, the Alchourron-Gardenfors-Makinson (AGM) paradigm (1985) and the Katsuno-Mendelzon framework (1992) are reviewed and interdefinability between update and erasure in the AGM paradigm is explained precisely. Moreover, a new identity that captures a relationship from contraction to erasure in the AGM paradigm is introduced and clear relationships among revision, contraction, update and erasure in the AGM paradigm are established. In the possibilistic framework, expansion and above four types of belief change are also formulated, and it is shown that two identities that capture the relationships between update and erasure in the AGM paradigm still remain valid between updating rule and the refined erasing rule.

Capacity of the associative memory using the Boltzmann machine learning

In the present paper, the capacity of an associative memory using the Boltzmann machine learning is evaluated by numerical experiments in the case where the size of the network is small. The authors consider the capacity as the upper bound of the ratio of the number of the nominal patterns to the number of the units, where the network can recall any of such patterns correctly as well as every nominal pattern has the basin of attraction of some proper size. It is shown that this capacity is around 0.6 in both cases where the recalling algorithm is asynchronous and synchronous. It exceeds the well-known capacity by the simple correlation learning, 0.15. The authors also examine what combination of the nominal patterns generates spurious memories. It is shown that there are some particular combinations of the patterns generating spurious memories by any of the different learning methods.

Modeling and Analysis of Genetic Algorithms Using Neural Networks

Vose’s genetic algorithm model assuming an infinite population is useful for a theoretical analysis. However, it is generally difficult to know transitions of infinite populations. In this paper, we propose a method for modeling genetic algorithms for infinite populations by using neural networks. We use a neural network for estimating deterministic transitions of infinite populations from stochastic data obtained through observing a process of a genetic algorithm for finite populations. Then the trained network approximates a mapping (or a vector field) which characterizes the genetic algorithm. Our method introduces a framework for analyzing genetic algorithms from the viewpoint of neural networks. In this paper, we use a mixture‐of‐experts architecture for modeling and show that an optimization problem, which the genetic algorithm solves, is represented as a combination of some other optimization problems corresponding to expert networks.