This paper describes Kleenean coefficients that are a subset of Kleenean functions for use in representing multiple-valued logic functions. A conventional multiple-valued sum-of-products expression uses product terms that are the MIN of literals and constants. In this paper, a new sum-of-products expression is allowed to sum product terms that also include variables and complements of variables. Since the conventional sum-of-products expression is complete, so also is the augmented one. A minimization method of the new expression is described besed on the binary Quine-McCluskey algorithm. The result of computer simulation shows that a saving of the number of implicants used in minimal expressions by approximately 9% on the average can be obtained for some random functions. A result for some arithmetic functions shows that the minimal solutions of MOD radix SUM, MAX and MIN functions require much fewer implicants than those of the standard sum-of-products expressions. Thus, this paper clarifies that the new expression has an advantage to reduce the number of implicants in minimal sum-of-products expressions.

In this letter we propose an interpolation technique for low-quality fingerprint images for highly reliable feature extraction. To improve the feature extraction rate, we extract fingerprint features by referring to both the interpolated image obtained by using a directional Laplacian filter and the high-contrast image obtained by using histogram equalization. Experimental results show the applicability of our method.

This paper presents a feature extraction model MAGNET' to find the deepest point of branched sulcus. Our model demonstrates magnetic principle and consists of four types of ideal magnetic poles: an N-pole and three S-poles. According to attractive or repulsive Coulomb forces between their poles, one of the S-poles is pushed to the deepest point of the sulcus. First, we explain our model on the simple sulcus model. Second, we apply it to the sulcus with implicit branches. Our model can detect the target points in every branch. Then an example to realize the model on a synthetic image is introduced. We apply our model to human brain MR images and human foot CT images. Experimental results on human brain MR images show that our method enable us to successfully detect the points.

In this paper, we propose a method to design ternary cellular arrays by using Ternary Decision Diagrams (TDD's). Our cellular array has a rectangular structure composed of ternary switch cells. The ternary functions represented by TDD's are realized by mapping the TDD's to the arrays directly. That is, both the nodes and the edges in the TDD are realized by some sets of the cells. Since TDD's can represent easily multiple-output functions without large memory requirements, our arrays are wuitable for the realization of multiple-output functions. To evaluate our method, we apply our method to some benchmark circuits, and compare our arrays with the ternary PLA's. The experimental results show that our arrays have the advantage for their sizes, especially in the realization of symmetric functions. The results also clarify that the size of our arrays depends on the size of TDD's.

This paper presents a rough sets-based method for clustering nominal and numerical data. This clustering result is independent of a sequence of handling object because this method lies its basis on a concept of classification of objects. This method defines knowledge as sets that contain similar or dissimilar objects to every object. A number of knowledge are defined for a data set. Combining similar knowledge yields a new set of knowledge as a clustering result. Cluster validity selects the best result from various sets of combined knowledge. In experiments, this method was applied to nominal databases and numerical databases. The results showed that this method could produce good clustering results for both types of data. Moreover, ambiguity of a boundary of clusters is defined using roughness of the clustering result.

This letter shows that an m-valued majority function is realized by m-1 two-valued threshold functions with common weight vector. A necessary and sufficient condition for an m-valued logical function to be a majority function is provided by using the concept of asummability.

A method is proposed for realizing any k-valued n-variable function with a celluler 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 kn-1 one-variable functions and remaining (n1)-variable function. The parts of one-variable functions are realized by the input arrays, remaintng the (n1)-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 (kn2)kn-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.

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 proposes an automated 3D visualization method of embedded tubes applicable to the scanned result of pulse-radar Non-Destructive Testing (NDT). The proposed method consists of three stages. First, our method defines the processing region which includes a pattern generated by a tube. This region is determined by referring to the composition of a received wave. Second, after expert knowledge of a tube is translated into fuzzy inference rules, the positions of embedded tubes are identified by inferring them. Third, 3D links of the identified positions are formed to visualize the continuous shape of the tubes. Consequently, the tubes are extracted, and their 3D shapes are visualized. The experimental result on the specimens shows that our method was able to find all tubes that exist in the radiograph and the schematic. Our method could thus provide the internal information of concrete with sufficient accuracy required in the practical construction work.

This paper presents a method for implementing the testing and realization of three-valued majority functions by using properties of 02-complete monotonicity which is an extended concept of complete monotonicity in binary logic. It is shown that reduced functions of three-valued majority functions are 02-completely monotonic, and all 7 or less variable three-valued logical functions satisfying the M(1) majority condition are three-valued majority functions if two-valued input three-valued output functions obtained by taking out only output values for 02-input vectors are 02-completely monotonic. For the realization of majority functions, m-variable inequalities are defined from 02-complete monotonicity. The weight vector is determined by solving weight inequalities derived from m-variable inequalities, and then thresholds are obtained. The overall algorithm of the method is given along with an example.

We describe a new automated method for detecting embedded objects in the ultrasonic non-destructive testing (NDT) system. A-scan waves collected by our developed system are converted into a B-scan image. The sensor system has the noise signals independent from targets to be detected. In the ultrasonic NDT system, the signals are due to disturbing of echoes produced by the transducers and multiple reflections. These signals are called inherent wave. This paper first proposes the estimation method of the inherent wave from the B-scan image. After this method subtracts the inherent wave, the resultant image (suppression image) is considered as the image consisting of only echoes from the embedded objects. Second, analysis of the intensity histogram of the suppression image leads the candidate points of embedded objects. Finally, fuzzy if-then rules can represent information on distribution of the intensity histogram and the homogeneous intensity levels of the objects. Evaluated degrees from the inference results can demonstrate the embedded objects. The method was applied to concrete members with reinforcing bars, resin tubes and steel pipes. The experimental results showed that this method was able to automatically detect the embedded objects with high accuracy and to display the location of embedded objects.

This paper analyzes the relationship between the changes of Body Mass Index (BMI) and those of the other health checkup data in one year. We divide all data of the subjects into 13 groups by their BMI changes. We calculate these variations in each group and classify the variations into gender, age, and BMI. As the result by gender, men were more influenced by the changes of BMI than women at Hb-A1c, AC, GPT, GTP, and TG. As the result of classification by age, they were influenced by the changes of BMI at Hb-A1c, GPT, and DTP by age. As the result of classification by BMI, inspection values such as GOT, GPT, and GTP decreased according to the decrement of BMI. Next we show the result on gender-age, gender-BMI, and age-BMI clusters. Our results showed that subjects should reduce BMI values in order to improve lifestyle-related diseases. Several inspection values would be improved according to decrement of BMI. Conversely, it may be difficult for subjects with under 18 of BMI to manage them by BMI. We show a possibility that we could prevent the lifestyle disease by controlling BMI.

Finding intracranial aneurysms plays a key role in preventing serious cerebral diseases such as subarachnoid hemorrhage. For detection of aneurysms, magnetic resonance angiography (MRA) can provide detailed images of arteries non-invasively. However, because over 100 MRA images per subject are required to cover the entire cerebrum, image diagnosis using MRA is very time-consuming and labor-intensive. This article presents a computer-aided diagnosis (CAD) system for finding aneurysms with MRA images. The principal components are identification of aneurysm candidates (= ROIs; regions of interest) from MRA images and estimation of a fuzzy degree for each aneurysm candidate based on a case-based reasoning (CBR). The fuzzy degree indicates whether a candidate is true aneurysm. Our system presents users with a limited number of ROIs that have been sorted in order of fuzzy degree. Thus, this system can decrease the time and the labor required for detecting aneurysms. Experimental results using phantoms indicate that the system can detect all aneurysms at branches of arteries and all saccular aneurysms produced by dilation of a straight artery in 1 direction perpendicular to the principal axis. In a clinical evaluation, performance in finding aneurysms and estimating the fuzzy degree was examined by applying the system to 16 subjects with a total of 19 aneurysms. The experimental results indicate that this CAD system detected all aneurysms except a fusiform aneurysm, and gave high fuzzy degrees and high priorities for the detected aneurysms.

This paper describes an ultrasonic system that estimates the cell quantity of an artificial culture bone, which is effective for appropriate treat with a composite of this material and Bone Marrow Stromal Cells. For this system, we examine two approaches for analyzing the ultrasound waves transmitted through the cultured bone, including stem cells to estimate cell quantity: multiple regression and fuzzy inference. We employ two characteristics from the obtained wave for applying each method. These features are the amplitude and the frequency; the amplitude is measured from the obtained wave, and the frequency is calculated by the cross-spectrum method. The results confirmed that the fuzzy inference method yields the accurate estimates of cell quantity in artificial culture bone. Using this ultrasonic estimation system, the orthopaedic surgeons can choose the composites that contain favorable number of cells before the implantation.

This paper proposes a sensing system for a behavior detection system using an ultrasonic oscillosensor and an air pressure sensor. The ultrasonic oscillosensor sensor has a cylindrical tank filled with water. It detects the vibration of the target object from the signal reflected from the water surface. This sensor can detect a biological vibration by setting to the bottom bed frame. The air pressure sensor consists of a polypropylene sheet and an air pressure sensor, and detects the pressure information by setting under the bed's mattress. An increase (decrease) in the load placed on the bed is detected by the increase (decrease) in the pressure of the air held in the tube attached to the sheet. We propose a behavior detection system using both sensors, complementally. The system recognizes three states (nobody in bed, keeping quiet in bed, moving in bed) using both sensors, and we detect the behavior before getting out of bed by recognized these states. Fuzzy logic plays a primary role in the system. As the fundamental experiment, we applied the system to five healthy volunteers, the system successfully recognized three states, and detected the behavior before getting out of bed. As the clinical experiment, we applied the system to four elderly patients with dementia, the system exactly detected the behavior before getting out of the bed with enough time for medical care support.

This paper proposes a thresholding based segmentation method aided by Kleene Algebra. For a given image including some regions of interest (ROIs for short) with the coherent intensity level, assume that we can segment each ROI on applying thresholding technique. Three segmented states are then derived for every ROI: Shortage denoted by logic value 0, Correct denoted by 1 and Excess denoted by 2. The segmented states for every ROI in the image can be then expressed on a ternary logic system. Our goal is then set to find "Correct (1)" state for every ROI. First, unate function, which is a model of Kleene Algebra, based procedure is proposed. However, this method is not complete for some cases, that is, correctly segmented ratio is about 70% for three and four ROI segmentation. For the failed cases, Brzozowski operations, which are defined on De Morgan algebra, can accommodate to completely find all "Correct" states. Finally, we apply these procedures to segmentation problems of a human brain MR image and a foot CT image. As the result, we can find all "1" states for the ROIs, i. e. , we can correctly segment the ROIs.

In this paper, we discuss problems in design and fault masking of multiple-valued cellular arrays where basic cells having simple switch functions are arranged iteratively. The stuck-at faults of switch cells are assumed to be fault models. First, we introduce a universal single-level array and derive the ratio of the number of single faults whose influence can be masked to the total number of single faults. Next, we propose a universal two-level array that outputs correct values even if single faults occur in it and derive the ratio of the number of double faults whose influence can be masked compared to the total number of double faults. By evaluating the universal single-level array and the universal two-level array from the viewpoints of design and fault masking, we show that the latter is superior to the former. Finally, we compare our universal two-level array with formerly presented arrays in order to demonstrate the advantages of our universal two-level array.

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 (xy, p1) and DPRODUCT (x, y)max (xy(p1), 0) is newly defined as the product that is derived by applying De Morgan's laws to TSUM. We call the functions T-functios. 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-functios 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.

This paper proposes a repairable and diagnosable k-valued cellular array. We assume a single fault, i.e., either stuck-at-O fault or stuck-at-(k1) fault of switches occurs in the array. By building in a duplicate column iteratively, when a stuck-at-(k1) fault occurs in the array, the fault never influences the output of the array. That is, we can construct a fault-tolerant array for the stuck-at-(k1) fault. While, for the stuck-at-O fault, the diagnosing method is simple and easy because we don't have to diagnose the stuck-at-(k1) fault. Moreover, our array can be repaired easily for the fault. The comparison with other rectangular arrays shows that our array has advantages for the number of cells and the cost of the fault diagnosis.