This paper proposes a new fuzzy integral model which can treat interactions among arbitrary macro-attributes as an effective modeling method. Since a partition of the set of all attributes defines macro-attributes, this fuzzy integral is named partition type fuzzy integral. An attainment degree to each subset of a partition (i.e., macroattribute) is evaluated by a vector, so the partition type fuzzy integral is formulated by utilizing the multilinear fuzzy integral of vector valued functions. This method evaluates the interactions of the attributes each of which belongs to a distinct macro-attributes, which means that the evaluation process can be simply explained by fewer parameters. We verify these features by applying this method to a subjective evaluation problem.

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Fuzzy control rules are described with if-then expressions and the fuzzy controls can incorporate experts' control rules. It is, however, difficult to guarantee the stability of fuzzy control system. However, the distinguishing feature of fuzzy controls, i.e. easily understandable linguistic expressions, have not been utilized in these analyses.This paper presents a new method for stability analysis of fuzzy control systems using petri nets. By simplifying the fuzzy control system as a discrete system, the fuzzy control system can be expressed using the petri nets. This proposed method can describe the fuzzy control system using the next-state function, thereby enables to analyze the stability of the fuzzy control system. The analytic results using the petri nets have clear correspondence to the fired fuzzy rules. The dynamical behavior of the system are able to be understood easily. Simulations are done to verify the proposed stability analysis method.

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To emphasize that models for recognition are described with domain knowledge and that objects of different structures or feature measurements can then be identified if they have the same name in natural language, this paper use object understanding to distinguish from the usual object recognition. To avoid the bottleneck of obtaining a complete description to the objects of the same name, case-based reasoning (CBR) is employed where several known instances (called cases) of the named object are considered as domain knowledge and a building-block method is used for reasoning. The cases and unknown objects are represented by fuzzy attributed graphs (FAG's). Using an algorithm proposed in this paper for calculating similarity between two FAG's, an object can be recognized (understood) based on the cases through recognizing its functional parts. To identify the functional parts of an unknown object, genetic algorithms (GA) are adopted for searching the best matched structures in cases.Algorithms are verified by some examples of line drawings of chair and non-chair.

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In this paper, we focus on multiobjective structured 0-1 programming problem(block angular type) involving fuzzy parameters to consider the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process. To begin with, multiobjective block angular 0-1 programming problems with fuzzy parameters and the concept of their solutions are described. Then, the α-multiobjective 0-1 programming problems such as the value of each parameter included in the problem is set to the most desirable one for the decision maker whose membership value is greater than or equal to α and the corresponding α-Pareto optimality concept as a natural extention of Pareto optimality concept are defined. Next, in order to take advantage of the special structure of problems, an interactive method through a genetic algorithm with decomposition procedures is proposed and explained in detail. Finally, both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments.

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The paper proposes a causal network based on a multi-valued logic and inferencing on the network. The network is called Multi-valued Logic Network (MVL network), and is expressed as a directed acyclic graph as is probabilistic network. It describes a structure of causal relations among propositions or events; each node expresses a proposition with a logical variable that takes a truth value in [0,1], and each arc does an implication with a truth value. This paper deals with a problem to propagate truth intervals to all nodes, when those of some nodes called "determined nodes" are given. The truth interval expresses a constraint on truth of the corresponding node. When the nodes are considered to be events, the truth value could be interpreted as intensity of occurrence.First, this paper discusses and defines the propagation of truth interval using causal inference based on Lukasiewicz Infinite-valued logic. Then, it shows that the network can be devided into several subnetworks at determined nodes. The generated subnetworks are classified into two groups; one is singly connected networks and the other is multiply connected networks. The paper goes into details about propagation of truth interval for the two types of subnetworks. Finally, it shows the whole algorithm of propagation and a numerical example.

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A set of qualitative data obtained by rating a product usually has a large variance reflecting tastes and preferences of individuals. It is sensible to express such fluctuations by fuzzy numbers to treat vagueness and unvertainty of the feeling of individuals. This paper proposes a factor analysis technique for fuzzy data which are rating scores measured by words that are mainly adjective such as innovative, bright, elegant or cheerful. Fuzzy correlation coefficients are introduced and factor loadings are determined as fuzzy numbers through linear programming. Thus, words are identified as fuzzy objects in the factor space. After fuzzy distances between words in the factor space are defined, a covering problem is formulated as an integer programming problem to determine a set of representative words and an overlapped partition of words simultaneously. This provides a useful information to study the relation between words and design elements.

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Analytic Hierarchy Process(AHP), being used in decision making of various problems, is a method based on ratio scale. However, there are some problems in the use of the traditional AHP. We intend to solve those problems in this paper. We propose an AHP method based on ordinal scale which is appropriate to deal with subjective and qualitative criteria. We also consider methods of evaluation suitable for the ordinal-scale-based AHP. Fuzzy algebraic evaluation and fuzzy integral evaluation using the Sugeno integral are described. Finally, we show an example to illustrate the proposed methods.

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A fuzzy multiple objective decision making approach is propoed on the desirable features of compromise programming and the fuzzy set theory. The two-phase approach was proposed by Lee-Li guarantees both nondominated and balanced solutions for solving both the crisp and the fuzzy multiple objective decision making problems.We propose an interactive and improved Lee-Li approach for solving fuzzy multiple objective linear programming (f-MOLP)problem with the fuzzy goals and constraints. Some numerical experiments with comparisons are given for the illustration of effectiveness.

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In this paper, a new type of digital filter with fuzzy weighting function based on fuzzy rules is represented. This filter can be applied to the analysis of Acoustically Evoked Potentials(AEPs) and Evoked Otoacoustic Emissions(EOAEs). AEPs and EOAEs have been analyzed with conventional filtering and ensemble averaging techniques, but there are some problems remaining unsolved. The frequency characteristics of biological signal change depending on the stimulus conditions, and those of noise also change. It is difficult to determine the cutoff frequency of the filter before filtering operation. The proposed fuzzy filter presented in this paper is designed by using power spectrum of ensemble and alternative ensemble averaging data of biological measurement. An ambiguity of frequency characteristics of signal and noise can be treated effectively in this method.The signal to noise ratio of fuzzy-filtered data is improved significantly compared with unfiltered one. Result of the comparison between fuzzy filter and Wiener filter shows that the fuzzy filter is much more adequate for biological signal processing.

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The Kleene's fuzzy logic is repersented by Kleene algebra and its generalization is De Morgan algebra. In this paper, we present basic properties of Kleene algebra and De Morgan algebra, and various resalts on Kleene algebra, De Morgan algebra with centers. The necessary and sufficient condition for a distributive lattice to be a Kleene algebra (De Morgan algebra) is given. We also study the structure of the Kleene algebra (De Morgan algebra).

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Analytic Hierarchy Process (AHP) proposed by Saaty, T.L. in 1977 is a method of decision making. Natural human sense can be reflected in it. Fuzzy AHP which is expansion of it can show substitutive and complementary selection. Using AHP or Fuzzy AHP, we often cannot find the best alternative, because the weights of the alternatives are not much different from the others. Then it is very important to investigate which element of a comparison matrix has most large influence on the weight. It makes us know the key of interpretation and structure of the data.Two metods to evaluate them using sensitivity analysis have been proposed. However they have problems. The one changes the structure of the data, and the other is complex. And a method to evaluate for Fuzzy AHP has not been proposed. In this paper we propose a simple methods which does't change the data suructure in AHP and evaluation in Fuzzy AHP, and show an numerical experiment.

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