畑 豊

In this paper we propose controllability and observability measures to guide the D-algorithm for multiple-valued logic circuits. The former is determined in one forward transversal of the circuit, and used in determining the line where the consistency operation should proceed The latter is determined in one backward traversal, and used in executing the D-drive at the fanout point. Our measures are computed by simple recursive formulas, and the time required for computing them is relatively short. The experimental results show that our measures are helpful in reducing the number of times for backtracking.

This paper presents a fuzzy rule-based region growing method for segmenting two-dimensional (2-D) and three-dimensional (3-D) magnetic resonance (MR) images. The method is an extension of the conventional region growing method. The proposed method evaluates the growing criteria by using fuzzy inference techniques. The use of the fuzzy if then rules is appropriate for describing the knowledge of the legions on the MR images. To evaluate the performance of the proposed method, it was applied to artificially generated images. In comparison with the conventional method, the proposed method shows high robustness for noisy images. The method then applied for segmenting the dynamic MR images of the liver. The dynamic MR imaging has been used for diagnosis of hepatocellular carcinoma (HCC), portal hypertension, and so on. Segmenting the liver, portal vein (PV), and inferior vena cava (IVC) can give useful description for the diagnosis, and is a basis work of a pre-surgery planning system and a virtual endoscope. To apply the proposed method, fuzzy if-then rules are derived from the time-density curve of ROIs. In the experimental results, the 2-D reconstructed and 3-D rendered images of the segmented liver, PV, and IVC are shown. The evaluation by a physician shows that the generated images are comparable to the hepatic anatomy, and they would be useful to understanding, diagnosis, and pre-surgery planning.

Non-destructive testing (NDT) using ultrasonic wave rapidly advances with the development of hardware. The NDT of the concrete using ultrasonic wave is the most promising approach to find crack depth and internal flaw of the concrete. It is required in NDT research to find buried pipes such as steel pipes, resin tubes. However, there is no work on finding by ultrasonic system. The variety of the formation from concrete to concrete prevents to find them. In this paper, we propose a novel method to extract the buried pipes aided by fuzzy logic. First, we show a method to remove direct wave from the raw data. It can find the signals of the pipes. Second, buried pipes can be extracted by the fuzzy inference based on signal value and voxel number.

To diagnose the cerebral diseases, visual perception for the cerebrovascular is essential. We propose a method for segmenting the cerebrovascular region from the computed tomography angiography (CTA) images. By segmenting it, we can generate the surface shade display, which is appropriate for evaluating the morphology. The proposed method first derives a rough image by combining a law image and the difference image. The difference image is obtained by applying Laplacian filter. For the rough image, the venae and artery are segmented by fuzzy inference; The method then extracts Willis Ring contacted the blood vessels based on region growing techniques. The experimental result shows that our method can extract the blood vessel in CTA image with high accuracy.

We propose a learning algorithm to enhance the fault tolerance of feedforward neural networks (NNs for short) by manipulating the gradient of sigmoid activation function of the neuron. For the output layer, we employ the function with the relatively gentle gradient. For the hidden layer, we steepen the gradient of function after convergence. The experimental results show that our NNs are superior to NNs trained with other algorithms employing fault injection and the calculation of relevance of each weight to the output error in fault tolerance, learning cycles and time. Besides our gradient manipulation never spoils the generalization ability.

This paper shows the best operators for sum-of-products expressions. We first describe conditions of functions for product and sum operations. We examine all two-variable functions and select those that meet the conditions and then evaluate the number of product terms needed in the minimum sum-of-products expressions when each combination of selected product and sum functions is used. As a result of this, we obtain three product functions and nine sum functions on three-valued logic. We show that each of three product functions can express the same functions and MODSUM function is the most suitable for reduction of product terms. Moreover, we show that similar results are obtained on four-valued logic.

This paper shows the effectiveness of an output permutation for the implementation of current-mode CMOS circuits. A combination of a simple function and an output permutation can realize a difficult function and cost for the combination will be lower than the cost for a difficult function. The output permutation can be realized by a universal literal and we can calculate the cost. We first examine the all combinations of universal literals and output permutations and show that some combinations can realize one-variable functions with lower costs. Next, we minimize two-variable functions and compare the costs with the costs obtained by some output permutations. As the result, we show that about 70% functions can reduce the costs and their reduction ratio is about 12% on average.

Clustering is primarily used to uncover the true underlying structure of a given data set. Most algorithms for fuzzy clustering often depend on initial guesses of the cluster centers and assumptions made as to the number of subgroups presents in the data. In this paper, we propose a method for fuzzy clustering without initial guesses on cluster number in the data set. Our method assumes that clusters will have the normal distribution. Our method can automatically estimates the cluster number and achieve the clustering according to the number, and it uses structured Genetic Algorithm (sGA) with graph structured chromosome.

This paper evaluates the number of product terms needed in the minimal sum-of-products expressions for extended product and sum operators based oil Shannon expansion. We show definitions of a product-type and a sum-type function. According to the definitions, we list all product-type and sum-type functions by investigation all three-valued two-variable functions. Using the functions, we examine the numbers of product terms needed in the minimal, slim-of-product expressions for any three-valued two-variable functions and show that the MODSUM-of-MINs expressions require the fewest product terms of the all. On investigating all four-valued sum-of-products expressions, it is shown that MODSUM-of-MINs expressions require the fewest product terms. Furthermore, on investigating the expressions with the weak conditions for the product-type function. we find some expressions requiring fewer product terms that the MODSUM-of-MINs expressions.

In this paper, we discuss a reconfigurable tree-connected multiprocessor system and its arraylike layout. Each level in our tree consists of several blocks with PEs. The reconfiguration is executed for each block by shifting PEs to the right. it is valid if the number of faulty PEs in each block is less than or equal to that of spare ones in it. We introduce a 7x7 square module with a five-level tree to simplify the array like layout. The system with sir or more levels is constructed easily by arranging several modules regularly. The comparison with other trees layoutable in the planar arrays shows that our tree is superior to others irt maximum interconnection length.

This paper describes useful fuzzy logic techniques for medical image segmentation. Specific methods to be reviewed include fuzzy information granulation, fuzzy inference and fuzzy cluster identification. Fuzzy information granulation is introduced as a powerful scheme to find the thresholds to obtain the whole brain region in MR data. Fuzzy inference technique succeeds to segment the brain region into the left cerebral hemisphere, right cerebral hemisphere, cerebellum and brain stem. The fuzzy inference aided segmentation procedure is also useful to human foot CT image. Fuzzy cluster identification is adapted to determine the obtained clusters into blood vessel or other tissues in MRA image.

In this paper, we propose concurrent tests of fuzzy controllers. We assume multiple stuck-at faults in membership functions. For tests of antecedent membership functions, we observe the sum of degrees by matching a current measured input with each function and that of degrees at several easily calculated co-ordinates, For tests of consequent ones, we absente the sum of their maximum degrees, that of degrees of applicability and that of degrees at several co-ordinates an the union of output fuzzy sets. We can find all the multiple faults except redundant ones. Our tests are superior to other tests in the number of additional membership functions and multiple fault detection.

This paper describes an approach to minimize multiple-valued logic expressions by genetic algorithms. We encode a multiple-valued logic expression as a ''chromosome'' whose length allows to change and corresponds to the number of implicants of the expression. Our fitness function evaluates the following three items. 1. How may outputs does the logic expression represent correctly? 2. How many implicants does the logic expression require? 3. How many connections does the logic expression require? Our method employs the fitness function and minimizes sum-of-products expressions, where sum refers to TSUM or MAX and product refers to MIN of set literals or window literals. The simulation results show that our method derives good results for some arithmetic functions and intends to avoid the local minimal solution, compared to neural-computing-based method.

A universal literal is a single-variable function and has an ability to manipulate more information than a set literal. The array size therefore could be eliminated by using universal literal generators (ULGs for short) in programmable logic arrays (PLAs), compared to PLAs with set literals. This paper discusses what operator is the most suitable in the term of eliminating the array size. We find four solutions as the good operator structures to eliminate the array size. A speculation of the upper bound of the array sizes is shown. Experiments are also done for randomly generated functions and some arithmetic functions. The experimental results show that the MAX-of-TPRODUCT form PLAs require the smallest array size.

Truncated sum (TSUM for short) can be useful for MV-PLAs realization. This paper introduces multiple-valued product-of-sums expressions where sum refers to TSUM and product does MIN. We investigate the multiple-valued product-of-sums expressions and show the minimization method and the simulation results. We describe the minimization method based on binary Quine-McCluskey algorithm. It is proved that in the minimal product-of-sums expressions, the implicate number of the expressions with TSUM is equivalent to the number of those with MAX. Next, we propose multiple-valued product-of-sums expressions with variables. The expressions involve the TSUM of variables and nonzero constants as the coefficients of the implicates. The minimization method is also proposed. Finally, we show the simulation results for some multiple-valued arithmetic functions. In them, an efficiency of the product-of-sums expressions with variables is shown and some comparisons are made.

This paper presents a novel model to detect the deepest point of a ditch as cerebral sulcus. Our model demonstrates magnetic behavior and consists of four ideal magnetic pales: an N-pole and three S-pales. Due to their Coulomb forces as the inverse square of the distance, one of S-poles automatically reaches the deepest point of the ditch, This model can also detect the point in case of ditch with implicit branches. Our experimental results an sliced human brain MR images show that our method can detect the paints at 90% correct detection ratio.

The purpose of this paper establishes a method to decompose the brain region into the inherent portions. In it fuzzy inference is used to evaluate what portion each voxel belongs to. We develop a decomposition method based on standard region growing algorithm, which requires the inference results. The comparison of the volumes of our extracted portions with manually measured volumes by a medical doctor shows that on the average, the error rate is 2% for some MRI data.

In the field of medical science, the extraction of the brain regions from MR images is valuable to diagnose: an Alzheimer's disease. We propose here a novel approach to extract the brain region using the fuzzy matching technique. We describe a modeling of the intensity histogram by fuzzy logic and evaluate fuzzy matching techniques for the extraction of the brain region. We develop the extraction algorithm based on a standard region growing technique. An experimental result on 36 MRI data shows that the error rate is 2.4%, on the average, against manually extracted volumes by a medical doctor.

In this paper, we discuss easily testable cellular arrays that are constructed from Multiple-valued Decision Diagrams (MDD's). The cellular arrays consist of cells having simple switch functions. Since control inputs that specify switches of cells are determined easily by tracing paths activated in MDD's, our method for constructing cellular arrays is simple. We propose faults tests for multiple stuck-at faults of switch cells. We can locate any row having at least one faulty cell. We apply our array to the realizations of numerous binary and multiple-valued logic functions and compare our array with other cellular arrays.

Fuzzy PLAs can realize fuzzy logic functions that are composed of fuzzy AND, OR, NOT, and variables. In this article, first, four meaningful special classes of the fuzzy logic functions are introduced, and two types of fuzzy PLAs are demonstrated, one is an AND-OR fuzzy PLA and the other is an AND-OR/OR-AND fuzzy PLA. Next, we introduce a Fuzzy Decision Diagram and a Fuzzy Decision Diagram with Binary Terminals to design their fuzzy PLAs. We compare the column number on realizing their functions and clarify that an AND-OR/OR-AND fuzzy PLA has an advantage of hardware cost in the viewpoint of the requiring plane area. © 1995 Taylor &amp Francis Group, LLC.

This paper proposes a method to design ternary cellular arrays with high testability. In it, stuck-at faults of switch cells are assumed. Testing of the array composed of switch cells can be executed easily because of the regular structure of the array. Moreover, if a faulty cell is identified, we can isolate the faulty cell from the remaining cells. The ternary functions represented by Ternary Decision Diagrams (TDD's) are realized by mapping the TDD's to the cellular arrays directly. Proposed arrays are more advantageous than ternary PLA's for their sizes in realizations of symmetric functions and are also useful for the realizations of multiple-output functions.

Truncated sum (TSUM for short) is useful for MV-PLA's realization. This paper introduces a new class of multiple-valued logic functions that are expressed by truncated sum, differential product (DPRODUCT for short), NOT and variables, where TSUM(x, y)=min(x + y, p - 1) and DPRODUCT (x, y) = max (x + y - (p - 1), 0) is newly defined as the product that is derived by applying De Morgan's laws to TSUM. We call the functions T-functions. First, this paper clarifies that a set of T-functions is not a lattice. It clarifies that Lukasiewicz implication can be expressed by TSUM and NOT. It guarantees that a set of p-valued T-functions is not complete but complete with constants. Next, the speculations of the number of T-functions for less than ten radixes are derived. For eleven or more radix p, a speculation of the number of p-valued T-functions is shown. Moreover, it compares the T-functions with B-functions. The B-functions have been defined as the functions expressed by MAX, MIN, NOT and variables. As a result, it shows that a set of T-functions includes a set of B-functions. Finally, an inclusion relation among these functional sets and normality condition is shown.

われわれの周りに存在する情報のほとんどは, 曖昧, 不確か, 漠然等で表される不完全な情報であり, 人の思考や推論においてもしばしばこのような情報が取り扱われる.本論文ではこのような情報を取り扱う類推システムの1つとして, MYCINで見られる確信度を用いた推論法と類推法を提案する.真理値の集合としては[0,1]を用い, 真理値は可能性を表すものとする.我々は含意A→Bの仮定Aと結論Bには密接な関係が存在すると考え, 含意A→Bに確信度cfを与え, AとA→Bの推論結果を前提の真理値T(A)とその確信度cfの積として導く.次に「類似した原因は類似した結論を導く」という基本仮定に従った変換類推モデルについて述べる.この類推は, 我々が目標としている事実と同じ対象内にある既知の知識を変換することにより新事実を発見するものであり, 前提と規則の仮定部の事実間の類似性を表す対応付けを用いることにより可能となった.最後に異なる経路から導き出された同一の結論を結合する方法について述べる.これは各々独立した原因から得られた結論を統合した場合, その結合後の確信度は上下幅を持つという考えに基づくものである.この結合規則は可能性の程度を結合するのに適する規則である.

An efficient fault diagnostic method should be developed to reduce the turnaround time and the cost for developing binary LSI's. For the multiple‐valued logic system that has been expected in the post‐binary electronics, research on the fault diagnosis for the logic circuit will be essential. This paper discusses the design and the fault diagnosis in multiple‐valued cellular arrays. First, the single‐level array, two‐level array, three‐level array, and n‐level array realizing k‐valued n‐variable logic functions are introduced. It is clarified that the two‐level array is the most suitable structure solving both problems of the number of cells and the fault location. Next, further investigation is made for the fault diagnosis. The stuck‐at faults, the open fault, and the AND bridging fault are treated under the assumption that the single fault occurs in the array. In the authors' fault diagnostic method, the test inputs can easily be generated from the control inputs that specify the switches of cells. Moreover, the comparison with other testing methods for cellular arrays shows that our method reduces the order of steps for generating all test inputs. Copyright © 1994 Wiley Periodicals, Inc., A Wiley Company

2値LSIの開発においては,設計期間の短縮やコストの低減のために,効率の良い試作段階での故障診断法の開発が必要になっている.ポストバイナリエレクトロニクスの有力候補である多値論理システムにおいても,論理回路の故障診断は重要な研究分野になると考えられる.本論文では多値セルラアレーの設計とその故障診断について考察する.まず.k値n変数関数を実現する回路構造として1段アレー回路,2段アレー回路網,3段アレー回路網,n段アレー回路網を考える.次に,これらの中で2段アレー回路網がセル数と故障セルの位置指摘の両方において最も有効な回路構造であることを明らかにする.そしてこの回路構造の故障診断方法について考察する.本論文では単一故障の仮定のもとでセルのスイッチの縮退故障,オープン故障,ANDブリッジ故障を取り扱う.このとき,この回路構造の検査入力は,セルのスイッチ動作を決定する制御入力から容易に生成できること,また他の文献のセルラアレーに対する検査法との比較により,本方法はすべての検査入力の生成に必要な計算ステップ数に関して利点をもつことが示された.

An idea of optimal output permutation of multiple-valued sum-of-products expressions is presented. The sum-of-products involve the TSUM operator on the MIN of window literal functions. Some bounds on the maximum number of implicants needed to cover an output permuted function are clarified. One-variable output permuted functions require at most p - 1 implicants in their minimal sum-of-products expressions, where p is the radix. Two-variable functions with radix between three and six are analyzed. Some speculations of maximum number of the implicants could be established for functions with higher radix and more than 2-variables. The result of computer simulation shows that we can have a saving of approximately 15% on the average using permuting output values. Moreover, we demonstrate the output permutation based on the output density as a simpler method. For the permutation, some speculation is shown and the computer simulation shows a saving of approximately 10% on the average.

A method is proposed for realizing any k-valued n-variable function with a cellular array, which consists of linear arrays (called input arrays) and a rectangular array (called control array). In this method, a k-valued n-variable function is divided into k(n-1) one-variable functions and remaining (n-1)-variable function. The parts of one-variable functions are realized by the input arrays, remaining the (n-1)-variable function is realized by the control array. The array realizing the function is composed by connecting the input arrays with the control array. Then, this array requires (k+n-2)k(n-1) cells and the number is smaller than the other rectangular arrays. Next, a ternary cell circuit and a literal circuit are actually constructed with CMOS transistors and NMOS pass transistors. The experiment shows that these circuits perform the expected operations.

本論文では, ファジィコンピュータの基礎研究としてプログラマブル・ロジック・アレイ(PLA)に注目し, ファジィ論理関数を実現するファジィ PLA の提案を行う.ファジィ論理関数は, ファジィ AND, OR, NOT, 変数によって構成されるファジィ論理式で表現可能な関数であり, 現在, その簡単化法や代数的性質の解明等種々の研究がなされている.本論文では P 形論理関数, C形論理関数に代表される, 工学上重要な意味を持つ特別なクラスのファジィ論理関数を考え, これらをファジィ PLA で実現するための回路設計法について述べる.まず, 2値の PLA として標準的な AND-OR 型の PLA をファジィ論理に適用した AND-OR ファジィ PLA を提案する.そして任意の多出力 n 変数ファジィ論理関数が3^n+n-1の列数で実現できることを示す.次に, PLA の列数は回路コストへ直接影響するため, この最大列数を最小化することを考える.そこで, AND-OR 型のファジィ PLA と OR-AND 型のファジィ PLA を相互接続し, 更に出力デコーダを付加した AND-OR/OR-AND ファジィ PLA の提案を行う.そして, この PLA は2^<n+1>の列数で任意の多出力ファジィ論理関数が実現できることを示す.このように AND-OR/OR-AND ファジィ PLA は AND-OR 型のファジィ PLA に対して列数の上限が小さくなること, また, 変数の数が増すほど有効となることを明らかにする.

The set of multiple‐valued Kleenean functions define a model of a Kleene algebra (a fuzzy algebra) suitable for treating ambiguity. This paper enumerates the Kleenean functions exactly, using the relation that the mapping from p‐valued Kleenean functions to monotonic ternary input p‐valued output functions is a bijection. Thus, the number pn of input vectors that should be searched is 3n for p‐valued n‐variable Kleenean functions. In this paper, we show how to obtain this number for 4‐ to 8‐valued Kleenean functions with 3 or fewer variables. We show that the number increases stepwise as the radix becomes larger and that the number of even (2m)‐valued Kleenean functions is uniquely determined by the number of odd (2m ‐ 1)‐valued Kleenean functions. These results show that the essence of Kleenean algebra is principally revealed by its odd‐valued functions. Moreover, the number of input variables increases exponentially as the variable becomes larger, and increases logarithmically as the radix becomes larger. Thus, increasing the number of variables has more of an effect on increasing this number than does incrementing the radix. Copyright © 1993 Wiley Periodicals, Inc., A Wiley Company

Multiple-valued Kleenean functions discussed in this paper are a model of a Kleene algebra and are logic functions expressed by logic formulas composed of variables, constants, and logic operations AND, OR, and NOT. The set of Kleenean functions is a model with the largest number of logic functions among existing models of a Kleene algebra, such as fuzzy logic functions, regular ternary logic functions, and B-ternary logic functions. Mainly, this paper shows the following facts: any p-valued Kleenean function is derived from a monotonic ternary input function, and any p-valued unate function is derived from an unate binary input function. We clarify the mapping relations between them, and the method to determine the logic formula of the Kleenean function and unate function from that of the monotonic ternary input function and unate binary input function, respectively. Moreover, by using the preceding facts, we enumerate 7-or-less-valued Kleenean functions and unate functions of 3-or-less variables. We know that the number of p-valued Kleenean functions increases stepwise and that of unate functions increases smoothly as p becomes larger. © 1993 IEEE

光学的な指紋検出方法として光路分離法と全反射法などが一般に用いられているが, その光学的な特性は明かでない.光学的に検出した指紋面像の品質が指紋表面の湿り具合いや光源の明るさ, 指紋入力面の汚れにより, どの程度影響を受けるか調べた.まず, 光学的な指紋検出方法を紹介し, 基本的な指紋検出方法である全反射法と光路分離法を用いて行った社験について述べる.実験結果より, 指の表面が乾燥していた場合, 全反射法による検出画像は著しく画質が劣化するため照合に必要な指紋情報を充分抽出できない.一方, 光路分離法でも指表面の乾燥により, 検出画像の品質は多小劣化するが比較的安定して指紋情報が抽出できるため高精度の照合が行えることを確認した.また, 検出画像の品質は光源の照度により変化する.最適な光源照度は指の表面状態により異なる.指紋入力面の汚れの影響は高照度側で顕著に現れることがわかった.