Increasing attention is being recently devoted to various problems inherent to the topological design of networks systems. The topological structure of these networks can be based on service centers, terminals(users), and connection cable. Lately, these network systems are well designed with fiber optic cable, because the requirements from users become increased. But considering the high cost of the fiber optic cable, it is more desirable that the network architecture is composed of a spanning tree. Network topology design problems consist of finding a topology that optimizes the design criteria such as connection cost, message delay, network reliability, and so on. Recently, genetic algorithms(GAs)have got a great advancement in related research fields, such as network optimization problem, combinatorial optimization, multi-objective optimization, and so on. Also, GA has received a great deal of attention about its ability as optimization techniques for many real-world problems. In this paper, A GA for solving bicriteria network topology design problems of wide-band communication networks connected with fiber optic cable, is presented, considering the network reliability related to the probability of failures. We also employ the Prufer number and cluster string in order to represent chromosomes. Finally, we get some experiments in order to certify the quality of the networks designs obtained by using proposed GA.

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This paper deals with adaptation, evolution, and learning in collision avoidance problems in a fuzzy-based intelligent robotic system. But the intelligence of a robot depends on the structure of hardware and software for processing information. So we have proposed a robotic system with structured intelligence. We focus on a mobile robotic system with fuzzy controller, and have proposed a sensory network as perception ability for the mobile robot. Therefore if environment is state, it is possible to evolve a robot system. However, if environment changed, it is hard to evolve a robot system promptly. So as maintain of variety, we propose Perception-GA to select crossover's partners according the environment information without increasing fuzzy rule, and as evaluations over internal evaluations, which law changing parameter of function of evaluations and learning rate. We discuss the effectiveness of the proposed method through computer simulation results of Perception-Based Robot.

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Fuzzy integrals can be considered as averaging operators. They can cover a wide variety of averaging operators. Smoothing filters have been treated in the field of digital filtering and the essence of filtering is averaging. Moving averaging and median filtering are typical examples of linear filter and non-linear filter. Some extensions of median filter were studied by many authors. There is another approach of non-linear filter from the field of mathematical morphology. These two fields, namely fuzzy integral and smoothing filter, have been developed independently, but there are many similarities between the two fields. In this paper, we investigate the relationship between the two fields. More precisely, we treat the relationship between fuzzy integral filters which are defined by using Choquet integral, Sugeno integral and opposite Sugeno integral and smoothing filters which are linear filter, order filter, stack filter and mathematical morphology filter. Finally, we propose new idempotent filters by using a cascade connection of two fuzzy integral filters i.e. Sugeno integral filter and opposite Sugeno integral filter.

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Fuzzy control is very popular at present, but the application field of fuzzy system will be wider if design not only automatic system but also man-machine system. We have studied fuzzy control systems which kept stable a triple inverted pendulum. However, the identification of control rules is so difficult and also their membership functions are so sensitive that their design is not easy. We suggest, in this paper, a man-machine cooperating system where a beginner operator can manipulate easily a triple inverted pendulum assisted by a simple fuzzy controller. We adopt a method to tune the membership function of the fuzzy controller by using genetic algorithm. This tuning create good membership function. As the result, this man-machine cooperation system is that ever a beginner operator can keep stable the triple inverted pendulum. And also, this system improves control performance for the triple inverted pendulum with skilled operator and fuzzy controller.

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Conditional Causal Probability(CCPR)and Conditional Causal Possibility(CCPO)have been proposed to express exact degrees of uncertainty in causalities, and some reasoning methods have been studied to obtain probablities or possibilities of unknown events under the condition that some events are known. CCPR is defined as a conditional probability of a Causation event conditioned by the Cause event. Causation event is an "event that a cause actually causes an effect." CCPO is a conditional possibility of a Causation event conditioned by the Cause event. The paper proposes to classify causal models using Causation events into two types-symmetrically valued and asymmetrically valued causal models-depending on the properties of variables, which take an event as their value. It also shows that the relations between conventional conditional possibilities and CCPOs are different between these models. Then, it discusses solutions and their properties of a Causality Consistency Problem using a hierarchical causal network, which is a problem to obtain the possibilities of combinations of values of arbitrarily chosen unknown variables, when values of some other variables are known. The discussion of the two different models can be conducted in the same way, because it is possible using conditional possibilities derived from CCPOs except proofs of some propositions. The proposed Causality Consistency Problem is a general one including Inverse Causality Problem and Causality Analysis Problem studied in the previous research.

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In this paper, we first define "advanced partitions type fuzzy integral(Definition 4)"by extending the range of partitions. Since this functional utilizes partitions only for the choice of interaction terms, it expresses more intermediate multilinear fuzzy integrals. Moreover, we develop a new modeling algorithm such that the choice of interaction terms is not dependent on statistical criteria, such as Akaike's Information criterion(AIC)and tests, aiming at making the expression of interactions by partitions applicable to the general statistical model(e.g.orthogonal polynomials). Through a concrete evaluation problem, we compare interaction terms by AIC with those by the tests based on the analysis of variance and analyze the cause of difference between them. As a result, we add the necessary procedure to the modeling algorithm(Fig.2)based on AIC.

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This paper proposes a fuzzy modeling technique taking into account selection of premise variables and the number of fuzzy rules. This technique is effective for a large-scale data set and of a large number of variables. In fuzzy modeling, a fuzzy clustering method is also proposed in order to determine a data partition and consequence parameters simultaneously under the assumed consequence variables. The proposed criterion of the fuzzy clustering has two purposes to detect the linearity in the space of consequence variables and the continuity in the space of premisse variables.

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The main difficulty in applying a fuzzy modeling method based on fuzzy if-then rules to a nonlinear system with many input variables is the exponential increase in the number of fuzzy if-then rules with the number of the input variables. For avoiding the exponential increase without losing a clear linguistic interpretation of each fuzzy if-then rule, we need to utilize general fuzzy if-then rules with only a few antecedent conditions. Such a general fuzzy if-then rule, which has many "don't care" conditions in the antecedent part, covers a large area of the multi-dimensional input space of the nonlinear system. Thus the entire input space can be covered by a small number of general fuzzy if-then rules. Since there may exist some complicated parts of the nolinear system that can not be captured by the general fuzzy if-then rules, specific fuzzy if-then rules with many linguistic conditions may be required in the fuzzy modeling of the nonlinear system. As a result, our fuzzy model is a mixture of general and special fuzzy if-then rules. Some fuzzy if-then rules have many antecedent conditions and others have only a few conditions. In this paper, we first discuss the fuzzy reasoning for fuzzy if-then rules with different specificity levels. Next we propose a fuzzy reasoning method for realizing implicit hierarchies of fuzzy if-then rules where specific rules have priority over general rules in the fuzzy reasoning. Then we demonstrate that fuzzy reasoning results by the proposed method coincide with our intuitive understanding of fuzzy if-then rules. Finally we demonstrate that a small number of fuzzy if-then rules can be found from numerical data by genetic algorithms and the proposed fuzzy reasoning method.

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A fuzzy linear regression method is proposed for the data in which plural different output data exist for the same input. Examples of such a situation include some evaluators make their judgment of articles of trade, environment, or students. This paper proposes a technique to map the relations between locations of evaluators in the data set, preserving them in the model parameter space as much as possible. This approach is based on Tanaka's identification method and provides a quite easy way without using the linear programming, and gives a good perspective of the data.

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An analysis of the project network in which each activity duration time is represented by fuzzy number is discussed. The main methods used in previous approaches are classified into some groups with respect to the calculation of maximum of fuzzy numbers, i.e.the composite method and the comparison method and so on. Each method has some advantages while it has serious disadvantages. In this paper, introducing the concept of α-level set of fuzzy numbers and the fuzzy maximum operator, we propose an efficient method for determining the fuzzy project completion time and the degree of criticality for each activity in the project network. We point out the computational difficulty and the contradiction involved in the conventional definition of the degree of criticality, and improve the definition from the practical point of view. Furthermore, providing labels which consist of the set of preceding node and the fuzzy earliest node time, critical activities and paths can be identified without the backward pass. We can overcome the some drawbacks of the previous approaches. The Proposed method consists of two procedures called Algorithm 1 and 2. In Algorithm 1, we determine the project completion time represented as an interval and identify entire activities which degree of criticality are greater than a given threshold α. In Algorithm 2, we determine the degree of criticality for each activity by repeating Algorithm 1 with the threshold α increased gradually. Non-critical activities are eliminated in the network after each iterative procedure in Algorithm 2. Therefore the computing time is progressively shortened. Finally, a numerical illustration is shown.

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Recently, it has been proposed that there exists a variety of fuzzy logic systems which can incorporate numerical input-output pairs and linguistic information in a natural and systematic way. Those systems using nearest neighborhood clustering can be used to group the samples so that a group can be represented by only one rule, and have a function of same learning as neural network. A fuzzy logic systems using nearest neigborhood clustering were learned by optimal gains of PID control searched experimentally, and the three gains of PID control are changed by this learning processing. After there, when robot vehicle makes a straight drive with and without an angle of a road surface inclination, control methods that can continue to travel at constant speed in control subject are proposed in this paper. I saw that the advantages of those fuzzy logic systems have a small number of learning times, perform a one-pass operation on the training data, have a generalization ability and are computationally simple by comparing with and examining the results of speed control using neural network.

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We introduce a new fuzzy integral named opposite Sugeno integral. It can be considered to be an averaging operator because it has three essential properties of an averaging operator such as monotonicity, continuity and value between min and max. Usually an averaging operator shrinks variance. It is, however, proved that if fuzzy measure is assumed to be additive and the probability distribution of input vector is assumed to be uniform, the probability distribution after opposite Sugeno integral is operated is also uniform.

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D, T, and SR fuzzy flip-flops are proposed. Their characteristics are shown when their t-norm and s-norm are restricted to four-max-min, algebraic, bounded, drastic-logical operation system. Their electrical circuits are designed using VHDL and are synthesized to make FPGAs as target devices. The conventional JK fuzzy flip-flops are also designed in the same manner and the performances are compared with those of proposed flip-flops on a circuit simulator. The results of the simulation experiment show that the combinatorial circuit areas(without areas of latches)of D, T, SR fuzzy flip-flops are nearly 0, 1/2, 2/3 of the JK's, respectively and the delay times of D, T, SR fuzzy flip-flops are nearly 0, 2/3, 2/3 of the JK's, respectively. The areas and delay times of the proposed flip-flops increase in the first or second order with the number of their quantization bits of [0, 1], the range of fuzzy logical value. Although the functions of the proposed fuzzy flip-flops are restricted compared with those of the JK fuzzy flip-flops and are not suitable for general purpose use, they will provide the foundation for the relization of fuzzy temporary memory modules-e.g.with a multi-steps fuzzy reasoning system.

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In this paper, we deal with a linear programming problem whose objective function coefficient vector is not known exactly but contained in a convex polytope. While the independence among uncertain coefficients has been implicitly assumed in interval linear programming problms, a certain kind of interaction(dependency)among uncertain coefficients can be treated in our problem. To such a problem, two kinds of optimal solutions are defined : possibly and necessarily optimal solutions. A necessarily optimal solution is the most reasonable solution. However, it does not exist in many problems. On the other hand, a possibly optimal solution is the least reasonable solution and always exists. Any possibly optimal solution can be represented as a convex combination of possibly optimal extreme points. Therefore, enumeration of possibly optimal extreme points is discussed in this paper. It is shown that the possibly optimal solution set coincides with the weakly efficient solution set to a certain multiobjective linear programming problem. This result implies that all possibly optimal extreme points can be enumerated by tracing adjacent basic solutions from a possibly optimal basic solution. In order to apply this approach, a possible optimality test of an adjacent basic solution is necessary. We show that the possible optimality test problem is reduced to a linear programming problem. Based on this possible optimality test, an enumeration algorithm of possibly optimal extreme points is proposed. On the other hand, in many applications, it is sufficient to obtain a superset of the possibly optimal extreme point set. From this point of view, an alternative method is conceivable, i.e., using an outer box-set approximation of the given convex polytope, such a superset can be obtained by Steuer's enumeration method previously proposed for the interval coefficient case. By numerical experiments, the proposed enumeration method is compared with the above alternative method. The results show that the proposed method is more efficient.

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A new image segmentation method by artificial life approach using autonomous agents is proposed in this paper. Each agent moves on the image according to some rules as follows:Each agent has the features such as color. It moves onto a pixel which has the most similar features. It also puts virtual Pheromone on the pixels. The pheromone is the idea based on the chamical substance which has the property to keep agents away. Each agent serches for the pixel which has smaller amount of pheromone and the most similar features. The locus of each agent becomes a segmented region. The proposed method has the following features:(1)it costs less amount of calculation;(2)it can be applied to a wide variety of images.

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In this paper, taking into account experts' imprecise or fuzzy understanding of the nature of parameters in a problem-formulation process, we consider two-level linear programming problems with fuzzy parameters. Assuming some behavior of the decision maker at the lower level, we analyze rational decisions of the decision maker at the upper level from the prescriptive point of view. We examine two situations:one is a situation that, judging that the degree of all the membership functions of the fuzzy numbers involved in the problem should be greater than or equal to some value, the decision maker at the upper level makes a rational decision in a certain sense;the other is a situation that fuzzy goals for the objective functions and fuzzy constraints are introduced and each decision maker makes a decision by employing the fuzzy decision.

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In this paper, we deal with some solution concepts in cooperative fuzzy games, games with fuzzy coalitions, which admit the representation of rates of players' participation in each coalition. In our previous research, we have introduced a natural class of fuzzy games and a definition of Shapley function. Furthermore, we have given an explicit form of the Shapley function on the class. In this paper we introduce a core function and a dominance core function as functions which derive the core and the dominance core from a given pair of a fuzzy game and a fuzzy coalition. It is shown that they coincide if v is superadditive and monotone nondecreasing with respect to rates of players' participation. Balancedness is also defined. We show that the core of a fuzzy game is nonempty if and only if the game is balanced, as in a crisp game. Furthermore, we show that the center of gravity of the core is the Shapley value for a convex game in our proposed class. Finally, an illustrative example is given.

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