This study delves into the realm of healthcare data analysis within the framework of local differential privacy (LDP), aiming to assess the performance of various methodologies under this stringent privacy paradigm. Leveraging LDP, which ensures individual data privacy while allowing for analysis, we explore the landscape of healthcare data with a focus on meaningful performance evaluation. Through a systematic investigation, this research evaluates the performance and efficiency of different approaches, shedding light on their suitability for healthcare data applications. By synthesizing insights from diverse techniques and considering their implications within the context of LDP, this study contributes to the advancement of privacy-preserving healthcare analytics while maintaining the integrity and utility of the underlying data. Our findings indicate that Reduced and Castell approaches present the best performance while maintaining a low epsilon, ε < 1. The Castell approach, with its lower memory consumption than the Reduced approach, stands out as the best approach for large healthcare datasets.

In recent years, the handling of personal information in web advertisements have been regulated and updated frequently. The algorithms for targeted advertisements delivered based on users’ browsing history and search results is opaque, and hence there is a concern of invasion of privacy. Therefore, we have four research questions as a survey of targeted advertisements by cookie information. Which personas are most likely to be targeted? Which websites are most frequently targeted? How long are they displayed? Is automatic observation possible? To answer these questions, we developed a system that obtains automatically transitions websites and targeted advertisement URLs for each persona using Selenium, a portable framework. We report the development of the system and the results of our experiment.

Nowadays, our personal information is highly values with companies, hospitals, and internet services, among other industries, using it to create databases to extract user statistics or to improve their services. Local Differential Privacy (LDP) studies how these services can use the information while preserving users’ privacy through various techniques. LDP approaches have been proposed to preserve the privacy of databases and provide statistical approximation, but they are limited when dealing with k-dimensional distribution estimations. To address this drawback, we propose applying Bayesian ridge regression to the central server to recover the original distribution. The propose method has been tested on three open datasets with varying characteristics, including the number of users and the list of attributes, as well as their cardinality. Further, the proposed method outperformed the well-known LoPub and LoCop algorithms. With a privacy budget set at 0.16 per attribute and k-way set at 5, our work achieves a 57% decrease in the average variant distance compared to that of LoPub and a 50% decrease compared to LoCop. Our results suggest that a Bayesian ridge algorithm can be a useful tool for privacy preservation during data publication and it may have various applications where privacy is a concern.

For a better understanding of anonymization methods for location traces, we have designed and held a location trace anonymization contest that deals with a long trace (400 events per user) and fine-grained locations (1024 regions). In our contest, each team anonymizes her original traces, and then the other teams perform privacy attacks against the anonymized traces. In other words, both defense and attack compete together, which is close to what happens in real life. Prior to our contest, we show that re-identification alone is insufficient as a privacy risk and that trace inference should be added as an additional risk. Specifically, we show an example of anonymization that is perfectly secure against re-identification and is not secure against trace inference. Based on this, our contest evaluates both the re-identification risk and trace inference risk and analyzes their relationship. Through our contest, we show several findings in a situation where both defense and attack compete together. In particular, we show that an anonymization method secure against trace inference is also secure against re-identification under the presence of appropriate pseudonymization. We also report defense and attack algorithms that won first place, and analyze the utility of anonymized traces submitted by teams in various applications such as POI recommendation and geo-data analysis.

This work studies a vulnerability in face obfuscation techniques intended to preserve the privacy of individuals. There have been several attempts to prevent unauthorized face recognition from being performed, aiming to guarantee anonymity in video data. Most of these attempts have focused on facial areas that are thought as sensitive to contribute most to facial recognition. However, obfuscation of such facial areas is insufficient to preserve privacy because gait information such as arm movements and step characteristics can be used to identify individuals and other personal information such as gender. In this paper, we claim that individual tracking and gender estimation are possible just from the gait information extracted from a video without using face-related data. We propose a set of biometric features and an algorithm to estimate gender from skeleton data. Our experiments with more than 100 subjects demonstrate that gender is estimated with a significant accuracy of 99.86%. The proposed identification algorithm, which is based on pattern-matching techniques, is robust against changes in the manner of walking and successfully identifies subjects with only small error of 0.036.

Gait information can be used to identify and track persons. This work proposes a new gait identification method aggregating multiple features observed by a motion capture sensor and evaluates the robustness against obstacles in walking. The simplest gait identification is to use gait statistics, but these are not a significant feature with regard to identifying people accurately. Hence, in this work, we use the dynamic time warping (DTW) algorithm to calculate distances of gait sequences. DTW is a pattern-matching algorithm mainly used in speech recognition. It can compare two sets of time series data, even when they have different lengths. We also propose an optimal feature integration method for DTW distances. For evaluating the proposed method, we developed a prototype system and calculated the equal error rate (EER) using 31 subjects. As a result, we clarified that the EER of the proposed method is 0.036 for normal walking, and that it is robust to some obstacles in walking.

There is a great demand from the viewpoint of security insurance to calculate the value of damage due to leakage of personal information. The Japan Network Security Association(JNSA) proposed a model to calculate the damage compensation amount. However, the coefficient was determined by experts’ subjective evaluations for which there is no basis. We propose a new mathematical model by applying multiple regression using cyber incident records and information such as enterprise size as explanatory variables and the value of extraordinary losses to a company as a target variable. We apply the damage model to 15,000 cyber incidents, compare the two models’ loss amounts, and consider the relationship between them.

In recent years, quantitative analysis of sleep quality and stress estimation during sleep have been important social issues due to sleep deprivation. Conventionally, sleep quality is mainly subjectively evaluated by pittsburgh questionnaire, while stress is estimated by power spectral analysis of electrocardiogram. However, measurement is difficult during sleep since restrictions on respiration rate and body motion. Sleep depth transition presumable by heart rate variability is achieved, however, the correlation between heart rate and sleep quality during sleep is not clarified. In this paper, heart rate and sleep depth data are collected by wearable IoT devices. Then, stress index during sleep is estimated by autonomic balance evaluation index and correlation is analyzed using the collected biomedical data. Furthermore, homomorphic cryptography is applied to analysis for privacy preserving approach.

Anonymization is the process of modifying a data set to prevent the identification of individual people from the data. However, most studies consider only the anonymization of data from a single domain. No study has been made on the risk of re-identification from combined data sets involving more than one domain. This paper proposes an evaluation of the risk of re-identification from payment card histories in multiple domains. First, we model the correlation between two histories from different usage domains in terms of information entropy and use mutual information to quantify the risk of identification from the data. Second, we describe an experiment to evaluate the risk in payment card data. The results validated the proposed method for real payment card data from 31 subjects. Metrics for the privacy and utility of 47 anonymized data items were evaluated. Overall, we found that there was a correlation between the histories of transportation and item purchases stored in the payment card data and established that most (44 of 47) of the anonymized data enabled correct identification with more than 45% accuracy for any privacy metric. This indicates that the risk of re-identification from payment card data is very high.

In this study, we propose a new "onomatopoeia CAPTCHA" that applies onomatopoeia; i.e., words containing sounds similar to the noises they describe. Humans usually understand onomatopoeia unconsciously and use it in daily conversation; thus, it is clearly easy for humans to solve. However, it is difficult for computers because the mechanisms to recognize onomatopoeia are not very clear even now.

This paper studies the feasibility of privacypreserving data mining in epidemiological study. As for the datamining algorithm, we focus to a linear multiple regression that can be used to identify the most significant factors among many possible variables, such as the history of many diseases. We try to identify the linear model to estimate a length of hospital stay from distributed dataset related to the patient and the disease information. In this paper, we have done experiment using the real medical dataset related to stroke and attempt to apply multiple regression with six predictors of age, sex, the medical scales, e.g., Japan Coma Scale, and the modified Rankin Scale. Our contributions of this paper include (1) to propose a practical privacy-preserving protocols for linear multiple regression with vertically partitioned datasets, and (2) to show the feasibility of the proposed system using the real medical dataset distributed into two parties, the hospital who knows the technical details of diseases during the patients are in the hospital, and the local government who knows the residence even after the patients left hospital. (3) to show the accuracy and the performance of the PPDM system which allows us to estimate the expected processing time with arbitrary number of predictors.

Audio-CAPTCHA prevents malicious bots from attacking Web services and provides Web accessibility for visually-impaired persons. Most of the conventional methods employ statistical noise to distort sounds and let users remember and spell the words, which are difficult and laborious work for humans. In this paper, we utilize the difficulty on speaker-independent recognition for ASR machines instead of distortion with statistical noise. Our scheme synthesizes various voices by changing voice speed, pitch and native language of speakers. Moreover, we employ semantic identification problems between random phoneme sequences and meaningful words to release users from remembering and spelling words, so it improves the accuracy of humans and usability. We also evaluated our scheme in several experiments.

Data anonymization is required before a big-data business can run effectively without compromising the privacy of personal information it uses. It is not trivial to choose the best algorithm to anonymize some given data securely for a given purpose. In accurately assessing the risk of data being compromised, there needs to be a balance between utility and security. Therefore, using common pseudo microdata, we propose a competition for the best anonymization and re-identification algorithm. The paper addresses the aim of the competition, the target microdata, sample algorithms, utility and security metrics. The design of an evaluation platform is also considered.

Mobile devices such as smartphones and tables have permeated into our daily lives and are now often indispensable because of the constant Internet access they provide. Furthermore, with ever increasing concerns regarding privacy and security, it has become popular to utilize cryptographic operations when accessing Web application servers from such devices. However, since such operations cause high loading on the central processing units (CPUs) of personal computers (PCs) or servers, mobile device CPUs now often come equipped with hardware cryptographic modules. These cryptographic modules are frequently utilized by many mobile device applications via a process known as offloading. However, when all cryptographic operations can be offloaded to cryptographic modules, device CPUs may become idle, which is an ineffective use of total computing resources. In this paper, we propose the simultaneous balanced offloading of cryptographic operations to the cryptographic module of an AM3358 processor and CPU via load-balancing and then evaluate the performance of our implementation. We evaluated our proposed system and concluded that while it is capable of working effectively, in most cases files smaller than approximately 1000 bytes can be executed faster via the CPU alone, whereas when files are larger than 1000 bytes, the proposed system is faster. In the case of encrypting or decrypting a 7 Kbyte file, our proposed system is twice as fast as 'CPU only' operation.

In many hospitals, data related to patients are observed and collected to a central database for medical research. For instance, DPC dataset, which stands for Disease, Procedure and Combination, covers medical records for more than 7 million patients in more than 1000 hospitals. Using the distributed DPC data set, a number of epidemiological studied are feasible to reveal useful knowledge on medical treatments. Hence, cryptography helps to preserve the privacy of personal data. The study called as Privacy-Preserving Data Mining (PPDM) aims to perform a data mining algorithm with preserving confidentiality of datasets. This paper studies the scalability of privacy-preserving data mining in epidemiological study. As for the data-mining algorithm, we focus to a linear regression since it is used in many applications and simple to be evaluated. We try to identify the linear model to estimate a length of hospital stay from distributed dataset related to the patient and the disease information. Our contributions of this paper include (1) to propose privacy-preserving protocols for linear regression with horizontally or vertically partitioned datasets, and (2) to clarify the limitation of size of problem to be performed. These information are useful to determine the dominant element in PPDM and to figure out the direction of study for further improvement.

In this paper, we proposes a new mathematical model for evaluating a given anonymized dataset that needs to be reidentified. Many anonymization algorithms have been proposed in the area called privacy-preserving data publishing (PPDP), but, no anonymization algorithms are suitable for all scenarios because many factors are involved. In order to address the issues of anonymization, we propose a new mathematical model based on the Zipf distribution. Our model is simple, but it fits well with the real distribution of trajectory data. We demonstrate the primary property of our model and we extend it to a more complex environment. Using our model, we define the theoretical bound for reidentification, which yields the appropriate optimal level for anonymization.

This paper studies privacy issues related to epidemiological studies. Epidemiological studies need to preserve the privacy of subjects because they use personal information. Thus, privacy is preserved using a secure scalar product protocol based on a public-key cryptosystem and the secure function evaluation. However, the secure function evaluation has performance limitations in evaluating a product and a squared root. Therefore, this paper proposes a new computationally efficient scheme for privacy-preserving epidemiological analysis. The performance and the security of the proposed scheme are evaluated based on its trial implementation.

Many people with visual impairments complain about the poor accessibility of conventional CAPTCHA systems because the audio-style test is too difficult for humans. Even a U.S. governmental site, the “We the People” public website, was criticized for the same reason, and thus it implemented a more accessible quiz-based CAPTCHA system. However, this system is vulnerable to simple heuristics. In this study, we demonstrate the insecurity of this type of CAPTCHA system. We demonstrate that our solver program can beat the CAPTCHA with a success rate of over 99%. In addition, we propose a new verbal-style system to replace the quiz-based CAPTCHA. Our system synthesizes several sentences, which have different degrees of naturalness in terms of their contextual meaning, from a set of source documents using a flexible-order Markov chain. Only human users can perceive the difference in the semantics and select the most (or the least) meaningful option correctly. This test is implemented in a verbal style, which means that it is universally suitable for any type of perceptual channel. We implemented our proposed scheme and analyzed its security based on experiments.

Recommender systems typically use collaborative filtering to make sense of huge and growing volumes of data. An emerging trend in industry has been to use public clouds to deal with the computing and storage requirements of such systems. This, however, comes at a price -- data privacy. Simply ensuring communication privacy does not protect against insider threats or even attacks agagainst the cloud infrastructure itself. To deal with this, several privacy-preserving collaborative filtering algorithms have been developed in prior research. However, these have only been theoretically analyzed for the most part. In this paper, we analyze an existing privacy preserving collaborative filtering algorithm from an engineering perspective, and discuss our practical experiences with implementing and deploying privacy-preserving collaborative filtering on real world Software-as-a-Service enabling Platform-as-a-Service clouds.

This paper studies a privacy-preserving decision tree learning protocol (PPDT) for vertically partitioned datasets. In the vertically partitioned datasets, a single class (target) attribute are shared by both parities or carefully treated by either party in the existing studies. The proposed scheme allows both parties to have independent class attributes in secure way and to combine multiple class attributes in arbitrary boolean function, which gives parties a flexibility in data-mining. Our proposed PPDT protocol reduces the CPU intensive computation of logarithm by approximating with the piecewise linear function defined by light-weight fundamental operations of addition and constant-multiplication so that information gain for attribute can be evaluated in the secure function evaluation scheme. Using the UCI Machine Learning dataset and the synthesized dataset, the proposed protocol is evaluated in terms of the accuracy and the size of tree.

Automated Trust Negotiation aims to securely identify the consensus between two sets of policies consisting of certificates, with minimal disclosure of policies to each other. The paper proposes a new scheme that allows both parties to learn whether or not, both parties agree to transfer a given target certificate to the requesting party. No policy is revealed after performance of the protocol. No certificate is known to each other.

Rating-based collaborative filtering (CF) enables the prediction of the rating that a user will give to an item, based on the ratings of other items given by other users. However, doing this while preserving the privacy of rating data from individual users is a significant challenge. Several privacy preserving schemes have, so far been proposed in prior work. However, while these schemes are theoretically feasible, there are many practical implementation difficulties on real world public cloud computing platforms. In this paper, we approach the generalised problem of privacy preserving collaborative filtering from the cloud perspective and propose an efficient and secure approach that is built for the cloud. We present our implementation experiences and experimental results based on the Google App Engine for Java (GAE/J) cloud platform.

This paper studies the analysis on the Cyber Clean Center (CCC) Data Set 2009, consisting of raw packets captured more than 90 independent honeypots, in order for detecting behavior of downloads and the port-scans. The analyses show that some new features of the coordinated attacks performed by Botnet, e.g., some particular strings contained in packets in downloading malwares, and the common patterns in downloading malwares from distributed servers. Based on the analysis, the paper proposes the heuristic techniques for detection of malwares made by Botnet coordinated attack and reports the accuracy of the proposed heuristics. The detection process is automated in the proposed decision tree consisting of statistics, such as, a number of total inbound packets, and an average rate of downloading malwares.

A recommendation system enables us to take information from huge datasets about tastes effectively. Many cryptographical protocols for computing privacy-preserving recommendation without leaking the privacy of users are proposed. However, the current issue is the large computational overhead depending the number of users. Hence, the application of the protocol is limited within small communities. In this paper, we address the issue of scalability by replacing the similarity between users by that of between items. Since the similarities between items can be publicly available, the recommendation steps are processed without dealing with confidential information such as the similarities between users. We propose an efficient scheme by using item-item similarities for providing a prediction of arbitrary values of rating. We show the performance and the accuracy evaluation of our proposed scheme based on a numerical experiment.

More than 90 independent honeypots have observed malware traffic at the Japanese tier-1 backbone. Typical attacks were made by multiple servers, coordinating to send many kinds of malware. This paper aims to discover some frequent new sequential attack patterns of malware. It is not easy to identify particular patterns logs of one year because the volume of dataset is too large to investigate one by one. To overcome the problem, this paper proposes data mining algorithm, the PrefixSpan method. We implement the PrefixSpan algorithm to analyze the malware footprints and show the experimental result. The result of analysis shows that the attacks are performed by multiple sequential attack patterns within a short amount of time.

The privacy-preserving recommendation system enables us to evaluate the recommended value without leaking the private information of users to service providers. The large overhead in performing cryptographical operations in proportion to the number of users and the number of items is the current issue. In this article, we propose some efficient schemes reducing the preference matrix of the sets of items and users.

Several security protocols require a human to compare two hash values to ensure successful completion. When the hash values are represented as long sequences of numbers, humans may make a mistake or require significant time and patience to accurately compare the hash values. To improve usability during comparison, a number of researchers have proposed various hash representations that use words, sentences, or images rather than numbers. This is the first work to perform a comparative study of these hash comparison schemes to determine which scheme allows the fastest and most accurate comparison. To evaluate the schemes, we performed an online user study with more than 400 participants. Our findings indicate that only a small number of schemes allow quick and accurate comparison across a wide range of subjects from varying backgrounds.

We study an estimation of average duration of malicious port-scanning attempts, which would help for an analysis the statistical survey of malicious behaviors and an application to estimate activity of worms spread. This paper reports an average duration of worm activity estimated from random sampling of statistical data actually observed by the Internet Scan Data System, ISDAS.

Computer worms randomly perform port-scans to find vulnerable hosts to intrude over the Internet. Malicious software varies its port-scan strategy, e.g., some hosts intensively perform scans on a particular target and some hosts scan uniformly over IP address blocks. In this paper, we propose a new automated worm classification scheme from distributed observations. Our proposed scheme can detect some statistics of worm behavior with a simple decision tree consisting of some nodes to classify source addresses with optimal threshold values. The choice of thresholds is automated to minimize the entropy gain of classification. Once a tree is constructed, the classification can be done very quickly and accurately. In this paper, we analyze a set of source addresses observed by the distributed sensors in IS- DAS observed with 30 sensors in one year in order to clarify a primary statistics of worms. Based on the statistical characteristics, we present the proposed classification and show th e performance of the proposed scheme.

We propose a multiparty protocol for various computations using comparator networks such as sorting and searching. By repeating the execution of a comparator, the proposed protocol can efficiently detect outlier values, without revealing them. In our scenario, all input values to a comparator network and the intermediate output from each comparator are kept secret assuming the presence of an honest majority. Possible application areas for the proposed protocol include statistical analysis while preserving the privacy of respondents.

We propose a cryptographic protocol for biometrics authentication without revealing personal biometrical data against malicious verifier. Our protocol uses a neural network and zero-knowledge interactive proof. In this paper, we developed a sample implementation system of our proposed protocol and we evaluate the performance and the accuracy of the proposed protocol. Especially, we study several algorithms for feature extraction of minutiae of fingerprint which is appropriate to our protocol. We examine false acceptance rates and rejection rates

Juels et. al proposed a fuzzy vault scheme that extracts secret from inexact biometric information. However, typical feature extracted from fingerprint, called minutiae, is assumed to tolerate against re-ordering minutiae. In order to address the issue, we propose a new scheme of fuzzy vault for fingerprint that assigns identification number to all minutiae and chaff (fake minutia) and determines correct order in greedy short distance algorithm. We evaluate the accuracy and the performance of the proposed scheme in comparison to some of existing schemes.

This paper points out the privacy issue in the OCSP (Online Certificate Status Protocol), namely, the OCSP responder learns confidential information-who sends a message to whom. To preserve the privacy of the OCSP requester, this paper presents a cryptographic protocol for the authenticated dictionary, namely, an untrusted directory provides a verifiable answer to a membership query for a given element. In the protocol, a user is able to retrieve whether or not a target element belongs to a database that the directory has without revealing which element he/she wishes to know against the untrusted directory. The protocol requires linear exponentiations to the number of elements in the database, but achieves a constant size communication complexity between a user and a directory. The privacy of query is assured under the /spl Phi/-hiding assumption introduced by Cachin.

A new algorithm for efficient key management for secure group communication in wireless ad hoc network with mobile nodes is presented. In order to address the dynamic receiver update operations such as leave or join, the subset difference (SD) method proposed by Naor et al. is introduced. The SD method allows senders to reduce drastically the size of ciphertext to be sent to 2r-1 using a pseudo random number generator, where r is the number of revoked users (who leave the group). In the SD method, the subsets of authorized users are represented by some differences of two subsets such that i covers valid users and j excludes the revoked users in i. To have all subsets (i,j) necessary to cover all valid users in a tree, a sender has to test all possible combinations of revoked users. A naive exhaustive search for the purpose takes O(r/sup 3/) time. This is a drawback of the SD method. Hence, to address the issue for finding the cover, we propose a new efficient algorithm to reduce the cost up to O(rlog r logn) by introducing the technique for indexing nodes to be dealt with in the necessary subsets. In addition, we implement the proposed algorithm and demonstrate the performance in terms of processing time in this paper.

This paper proposes a secure protocol for Web-based questionnaire that preserves the privacy of responders and ensures the robustness. The proposed protocol is based on secure electronic voting protocol proposed by Cramer et al. confidentiality and efficiency, which are common requirements for both applications. This paper points out an issue particular in the secure questionnaire, that is, a requirement to deal with a multiple-choice question, and shows that the communication overhead grows exponentially with the number of choices n. To address the issue, the proposed protocol reduces the cost from /spl Theta/(2/sup n/) to /spl Theta/(n). The performance based on the experimental implementation is also shown.

A directory service for Webpages is widely used over the Internet. Webpages, however, are not always disjointly partitioned into subcategories, i.e., there are some pages to be belonging to multiple groups. To classify pages, conventional clustering algorithms are not adequately applied. This paper proposes a new algorithm of fuzzy clustering specialized for Webpage directory.

We study a security enhancement of instant messaging service. After the requirements and the assumptions are addressed, a modified Diffie-Hellman protocol suitable to instant messaging is presented. The main feature of the proposed protocol is to prevent malicious administrator from intercepting plain message and applying data mining techniques to obtain privacy of end users. From the viewpoint of communication and computational costs, the proposed protocol are evaluated and the comparison of some existing protocols is given. In addition, a trial implementation of secure instant messaging system is demonstrated.

Modlnt is a compact Java class designed for the arbitrary-precision modular arithmetic operations used in secure cryptographical applications, including auctions and electronic voting. The library is small enough to port to a Java-enabled cellular phone. In this paper, we present a new electronic voting system using the Modlnt library, in which voters have their ballots encrypted with the public key of a trusted agent and cast them to an untrusted server, which tallies them without decrypting the ballot and updates a linear-feedback shift register (LFSR) consisting of log n ciphertexts. The privacy of voters is therefore assured assuming that the security of the public-key crypto system is maintained, and the trusted party keeps their private key secure. This feature reduces the costs of management of the counting server, which is now free from the risks of being compromised.

In the context of circuit design, 1 the concept is called "disjoint decomposition.

We studied non-convex or sub-normal linguistic truth values that has not been considered so far. The logical operations based on the extension principle are closed into V/sub N/, V/sub C/ and V/sub R/ and arbitrary intersection of any of these is also closed. There are infinite number of subsets outside of the convex truth value, that are classified by the ranks. We show that a set of linguistic truth values of a common rank is not closed.

Many types of fuzzy truth values have been proposed, for example, numerical truth values, interval truth values, triangular truth values and trapezoid truth values and so on. This paper will discuss on algebraic structures on a new type of fuzzy truth values called multi-interval truth values. A multi-interval truth value is defined by the union of some of interval truth values. The operations on multi-interval truth values will be defined by applying the extension principle to the operations AND, OR, and NOT on numerical truth values. Then, the paper will show that an algebraic structure of multi-interval truth values with the operations defined is a de Morgan bisemilattice, which is a bisemilattice with the unit and zero, and with a unary operation that satisfies the involution and de Morgan's laws.

This paper focuses on incompletely specified multiple-valued Kleenean functions (1991). It is easy to verify that they do not have functional completeness in the class of all functions on the unit interval. Therefore, not all incompletely specified functions on the unit interval are incompletely specified multiple-valued Kleenean functions. In this paper, we will clarify a necessary and sufficient condition for an incompletely specified function to be an incompletely specified multiple-valued Kleenean function. Further, we show an algorithm which derives one of the logic formulas representing the incompletely specified multiple-valued Kleenean function. In considering the application of multiple-valued Kleenean functions, we will show an example which suggests the possibility that input-output data can be described abstractly in terms of multiple-valued Kleenean functions.

Genetic Algorithms (GA) are a useful and convenient tool to find the solution in combinatorial optimal problems, and widely used in the various engineering fields. Here we apply GA to identify both of the composite operations and fuzzy relations under that operation at the same time from the given input-output system data. There exist many composite operations and associated fuzzy relations, which satisfy the same input-output system data. Then, it is supposed that many composite operations and fuzzy relations, which satisfy the original data, are generated when we apply GA to this problems. Tne authors propose a method to identify the fuzzy system from these composite operations and fuzzy relations, generated by GA, by an unweighted pair-group method using arithmetic average (UPGMA) which was developed to make a taxonomic tree of the expression in molecular biology.