Kokichi Tanaka

Some properties of fuzzy sets of type 2

The concept of fuzzy sets of type 2 has been defined by L. A. Zadeh as an extension of ordinary fuzzy sets. The fuzzy set of type 2 can be characterized by a fuzzy membership function the grade (or fuzzy grade) of which is a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1]. This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊔, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzy grades form a distributive lattice under ⊔ and ⊓. Moreover, the algebraic properties of fuzzy grades under the operations and which are slightly different from ⊔ and ⊓, respectively, are briefly discussed.

Pattern Classification Based on Fuzzy Relations

A method of classifying patterns using fuzzy relations is described. To start with, we give a suitable value of the measure of subjective similarity to each pair of patterns that is taken from the population of patterns to be classified. Then a similitude between any two patterns is calculated by using the composition of a fuzzy relation. The similitude induces an equivalence relation. Consequently, we can classify the present population of the patterns into some classes by the equivalence relation. An experiment of the classification of portraits has been performed to test the method proposed here.

Fuzzy sets and type 2 under algebraic product and algebraic sum

Abstract The concept of fuzzy sets of type 2 has been proposed by L.A. Zadeh as an extension of ordinary fuzzy sets. A fuzzy set of type 2 can be defined by a fuzzy membership function, the grade (or fuzzy grade) of which is taken to be a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1]. This paper investigates the algebraic properties of fuzzy grades (that is, fuzzy sets of type 2) under the operations of algebraic product and algebraic sum which can be defined by using the concept of the extension principle and shows that fuzzy grades under these operations do not form such algebraic structures as a lattice and a semiring. Moreover, the properties of fuzzy grades are also discussed in the case where algebraic product and algebraic sum are combined with the well-known operations of join and meet for fuzzy grades and it is shown that normal convex fuzzy grades form a lattice ordered semigroup under join, meet and algebraic product.

Some considerations on fuzzy conditional inference

Abstract In much of human reasoning, the form of reasoning is approximate rather than exact as in ‘A red apple is ripe and this apple is more or less red. Then this apple is more or less ripe.’ L.A. Zadeh and E.H. Mamdani suggested methods for such a fuzzy reasoning as an application of fuzzy set theory. The method involves an inference rule and a conditional proposition which contains fuzzy concepts. In this paper we point out that the consequence inferred by their methods does not always fit our intuitions and we suggest the improved methods which fit our intuitions under several criteria.

Direct-drive inertial confinement fusion: A review

The direct-drive, laser-based approach to inertial confinement fusion (ICF) is reviewed from its inception following the demonstration of the first laser to its implementation on the present generation of high-power lasers. The review focuses on the evolution of scientific understanding gained from target-physics experiments in many areas, identifying problems that were demonstrated and the solutions implemented. The review starts with the basic understanding of laser–plasma interactions that was obtained before the declassification of laser-induced compression in the early 1970s and continues with the compression experiments using infrared lasers in the late 1970s that produced thermonuclear neutrons. The problem of suprathermal electrons and the target preheat that they caused, associated with the infrared laser wavelength, led to lasers being built after 1980 to operate at shorter wavelengths, especially 0.35 μm—the third harmonic of the Nd:glass laser—and 0.248 μm (the KrF gas laser). The main physics areas relevant to direct drive are reviewed. The primary absorption mechanism at short wavelengths is classical inverse bremsstrahlung. Nonuniformities imprinted on the target by laser irradiation have been addressed by the development of a number of beam-smoothing techniques and imprint-mitigation strategies. The effects of hydrodynamic instabilities are mitigated by a combination of imprint reduction and target designs that minimize the instability growth rates. Several coronal plasma physics processes are reviewed. The two-plasmon–decay instability, stimulated Brillouin scattering (together with cross-beam energy transfer), and (possibly) stimulated Raman scattering are identified as potential concerns, placing constraints on the laser intensities used in target designs, while other processes (self-focusing and filamentation, the parametric decay instability, and magnetic fields), once considered important, are now of lesser concern for mainline direct-drive target concepts. Filamentation is largely suppressed by beam smoothing. Thermal transport modeling, important to the interpretation of experiments and to target design, has been found to be nonlocal in nature. Advances in shock timing and equation-of-state measurements relevant to direct-drive ICF are reported. Room-temperature implosions have provided an increased understanding of the importance of stability and uniformity. The evolution of cryogenic implosion capabilities, leading to an extensive series carried out on the 60-beam OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)], is reviewed together with major advances in cryogenic target formation. A polar-drive concept has been developed that will enable direct-drive–ignition experiments to be performed on the National Ignition Facility [Haynam et al., Appl. Opt. 46(16), 3276 (2007)]. The advantages offered by the alternative approaches of fast ignition and shock ignition and the issues associated with these concepts are described. The lessons learned from target-physics and implosion experiments are taken into account in ignition and high-gain target designs for laser wavelengths of 1/3 μm and 1/4 μm. Substantial advances in direct-drive inertial fusion reactor concepts are reviewed. Overall, the progress in scientific understanding over the past five decades has been enormous, to the point that inertial fusion energy using direct drive shows significant promise as a future environmentally attractive energy source.

Three-dimensional echocardiograms and two-dimensional echocardiographic images at desired planes by a computerized system

Abstract We applied our newly developed computerized image processing system for three-dimensional (3-D) echocardiographic display with binocular parallax shift and for constructing two-dimensional (2-D) echocardiographic images in desired planes from sequential recordings of 2-D echocardiograms recorded with antero-posterior emission of ultrasound beams. This system mainly consisted of a flying spot scanner, a minicomputer and a display cathode ray tube. This study was done in a healthy subject and a case with atrial septal defect. In the stereogram of the healthy subject the left ventricle, atrium and the aorta were visualized in depth with a stereoviewer. In the stereogram of atrial septal defect, the defect and the remaining atrial septum were clearly observed also in depth. We could accomplish the reconstruction of 2-D echocardiograms of these materials in desired planes. The frontal plane 2-D echocardiograms provided useful data.

fstds System: A fuzzy-set manipulation system

This paper describes an implementation of a system for fuzzy sets manipulation which is based on fstds (Fuzzy-Set-Theoretic Data Structure), an extended version of Childss stds (Set-Theoretic Data Structure). The fstds language is considered as a fuzzy-set-theoretically oriented language which can deal, for example, with ordinary sets, ordinary relations, fuzzy sets, fuzzy relations, L-fuzzy sets, level-m fuzzy sets and type-n fuzzy sets. The system consists of an interpreter, a collection of fuzzy-set operations and the data structure, fstds, for representing fuzzy sets. fstds is made up of eight areas, namely, the fuzzy-set area, fuzzy-set representation area, grade area, grade-tuple area, element area, element-tuple area, fuzzy-set name area and fuzzy-set operator name area. The fstds system, in which 52 fuzzy-set operations are available, is implemented in fortran, and is currently running on a FACOM 230-45S computer.

Soft x-ray emission from ω0, 2ω0, and 4ω0 laser-produced plasmas

The soft x‐ray spectra from Au plasmas in 0.1–1.6 keV range and x‐ray conversion efficiencies of Au (high Z) and Al (low Z) targets with three laser wavelengths of 0.26, 0.53, and 1.05 μm are measured. In addition, the intensity dependence of the x‐ray conversion efficiency at 0.26 μm is obtained for Au targets. For 0.26‐μm laser light, the conversion efficiency of Au targets can be as high as 80% at an intensity of 2.4×1013 W/cm2.

FUZZY ROBOT CONTROLS

Abstract A fuzzy program is defined as an ordered sequence of fuzzy instructions. In the execution of a fuzzy program, fuzzy instructions are translated into machine instructions by the use of MAX-METHOD and backtracking. To show how a fuzzy program is executed, a simulation system is exploited which controls a simple inchworm robot. A few examples of computer simulations are presented which deal with the behavior of a stranger (or a robot) searching for his destination in a modeled town under simple fuzzy instructions.

Initial cone-in-shell fast-ignition experiments on OMEGAa)

Fast ignition is a two-step inertial confinement fusion concept where megaelectron volt electrons ignite the compressed core of an imploded fuel capsule driven by a relatively low-implosion velocity. Initial surrogate cone-in-shell, fast-ignitor experiments using a highly shaped driver pulse to assemble a dense core in front of the cone tip were performed on the OMEGA/OMEGA EP Laser [T. R. Boehly et al., Opt. Commun. 133, 495 (1997); L. J. Waxer et al., Opt. Photonics News 16, 30 (2005)]. With optimal timing, the OMEGA EP pulse produced up to ∼1.4 × 107 additional neutrons which is a factor of ∼4 more neutrons than without short-pulse heating. Shock-breakout measurements performed with the same targets and drive conditions demonstrate an intact cone tip at the time when the additional neutrons are produced. Velocity interferometer system for any reflector measurements show that x-rays from the shell’s coronal plasma preheat the inner cone wall of thin-walled Au cones, while the thick-walled cones that are...