Fuzzy Information Processing Research Articles

A uniform framework for deductive processing of fuzzy information

Fuzzy Logic proposed by Zadeh is a mathematical model expressing the degree of uncertainty in terms of possibility distribution. In this paper we introduce Fuzzy Implicit Predicate (F_IP) for reconstructing the fuzzy relational database in the logical point of view. We demonstrate that this new logic paradigm (1) provides a unified framework integrating various techniques related to fuzzy relational database and (2) provides a way exploiting powerful inference mechanisms to fuzzy data manipulation. Deductive database and fuzzy prolog can be examples of the inference mechanisms.

A hierarchical neural model of matching

The issue of matching two fuzzy sets emerges as an essential design aspect in many algorithms of processing fuzzy information including fuzzy controllers, pattern classifiers, knowledge-based systems, etc. This paper introduces a new model of matching. The primordial features of the proposed model involve: 1. (i) matching being carried out with respect to the grades of membership of the discussed fuzzy sets as well as some of their functionals (like energy, entropy, transom); 2. (ii) the concepts of hierarchies of matching in the model leading directly to a straightforward distinction between “local” and “global” levels of matching; and 3. (iii) a distributed character of the model that is realized as a logic-based neural network with enhanced learning capabilities.

Fuzzy JK flip-flops as computational structures: design and implementation

Current research on fuzzy set applications has yielded a better understanding of complex design problems involving nondeterministic human factors. This has in turn resulted in a significant number of efficient software case-study oriented realizations. Concurrently, efficient hardware implementations involving integration of a large number of discrete components have become feasible in light of existing technological achievements. Hirota and Ozawa (1989) introduced the notion of the fuzzy JK flip-flop, considering it an essential and basic component for effective processing of fuzzy information. Continuing with this line of reasoning, a discussion is presented of VLSI implementation issues with emphasis on design platforms to be used with the new structures. Next some comparisons are performed pertaining to the usefulness and realization of several logical connectives, followed by an examination of fuzzy sequential system design. The combinational part of the circuit is embodied in a single layer neural network in which weights are adjusted on the basis of training situations. Numerical considerations highlight the performance of the design process.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Current-mode fuzzy memory element

Recent research in fuzzy logic indicates a growing interest in practical and commercial applications. An improved fuzzy processor would embody both fuzzy (multilevel) and classical (binary) information processing in the same machine. One of the basic building blocks for the fuzzy processor is the fuzzy memory element. Such a circuit is proposed in the Letter.

DETERMINATION OF FUZZY RELATIONSHIP BY FUZZY REGRESSION

Abstract This paper presents a new approach and procedure for performing fuzzy regression based on JHE method, a method for processing fuzzy information based on the Monte Carlo simulation technique. The new procedure is tested by applying it to determining fuzzy relationships between fuzzy variables. Methods for interpreting results of fuzzy regression are presented and discussed. Examples are presented to demonstrate this new procedure. Potential applications of this fuzzy regression procedure are discussed.

AGGREGATING EXPERT OPINIONS BY FUZZY ENTROPY METHOD

Abstract This paper is a sequel to an earlier paper by the authors in which a model was developed for determining weights of criteria using a single expert's opinion. This paper further addresses the issue of aggregating individual expert opinions. A new technique, called fuzzy entropy method, is presented for aggregating expert opinions. In this study, the relative importance of expert opinions is scaled by fuzzy entropy, an entropy measure of the fuzzy information. The fuzzy entropy method is a combination of the conventional entropy method and the JHE method, a fuzzy information processing technique. One emphasis of the paper is placed on computational aspect of this new method. Examples are presented to demonstrate this method. Results of this study indicate that the fuzzy entropy method is a promising tool for aggregating expert opinions.

The Fuzzy Neural Network: The Emerging Paradigms

In recent years, an increasing number of researchers have become involved in the subject of fuzzy neural networks in the hope of combining the reasoning strength of fuzzy logic and the learning and adaptation power of neural networks. This provides a more powerful tool for fuzzy information processing and for exploring the functioning of human brains. In this paper, an attempt has been made to establish some basic models for fuzzy neurons. First, several possible fuzzy neuron models are proposed. Second, synaptic and somatic learning and adaptation mechanisms arc proposed. Finally, the possibility of applying non-fuzzy neural networks approaches to fuzzy systems is also described.

Fuzzy information processing by the Monte Carlo simulation technique

Abstract This paper presents a new method utilizing the Monte Carlo simulation technique for processing fuzzy information. The method was primarily developed for determining the weighted average of a group of ratings that are represented by fuzzy subsets. By generating a uniform random number, normalizing it with respect to the maximum functional value of the cumulative membership function, and then equating the normalized uniform random number to the cumulative function F(x), a value x can be back-calculated for each fuzzy subset. The resulting value x is a random number representing that fuzzy subset. The weighted average was then calculated with these random numbers. The first through fourth moment parameters were obtained and used to fit the random values of the weighted average with a beta distribution. By normalizing the curve-fitted beta distribution function with respect to its maximum functional value, the membership function of the final fuzzy subset was obtained. Comparison is made between the new method and the vertex method which provides an exact but discrete solution. The results show that the new method always yields a very good approximation in a significantly shorter computation time-as much as two orders of magnitude in some of the cases presented.

Processing in relational structures: Fuzzy relational equations

The paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations. The origin and the central role of relational calculus in general, and fuzzy sets in particular, is explained with special emphasis paid to its role and representation capabilities. It is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets. Many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid, well developed formalisms, techniques, and clarity of exposition. We will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty. Moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality (such as for instance type-2 sets, interval-valued sets) can be algorithmically determined. Finally, we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory.

Fuzzy information representation and processing in conventional GIS software: database design and application

Currently used methods for representing geographical information are inadequate because they do not tolerate imprecision. This leads to information loss and inaccuracy in analysis. Such expressive inadequacy is largely due to the underlying membership concept of classical set theory. To improve information processing in GIS research and application, an alternative membership concept is required. In this paper, we explore the inadequacy imposed upon geographical information representation by classical set theory and address the problems of information loss. A fuzzy relational data model is defined which is more representative for geographical information. A GIS database for agricultural land resource management is created by using the data model and a new technique for assessing land suitability is developed. The fuzzy representation largely facilitates data analysis in this GIS. The methods are tested with data from North Java, Indonesia using a vector-based GIS software package, Arc Info, and the analysis results are presented.

FILIP: A fuzzy intelligent information system with learning capabilities

FILIP (fuzzy intelligent learning information processing) system is designed with the goal to model human information processing. The issues addressed are uncertain knowledge representation and approximate reasoning based on fuzzy set theory, and knowledge acquisition by “being told” or by “learning from examples”. Concepts that can be “learned” by the system can be imprecise (fuzzy), or the knowledge can be incomplete. In the latter case, FILIP uses the concept of similarity to extrapolate the knowledge to cases that were not covered by examples provided by the user. Concepts are stored in the Knowledge Base and employed in intelligent query processing, based on flexible inference that supports approximate matches between the data in the database and the query. The architecture of FILIP is discussed, the learning algorithm is described, and examples of the system's performance in the knowledge acquisition and querying modes, together with its explanatory capabilities are shown.

Convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing

This paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form λ·( x ( k) Δ 2)+ − λ· ( x ( k) · R) = y ( k) ( k = 1,2,…, K), where x k and y k denote fuzzy sets, R and 2 fuzzy relations, · the sup · min compositional operator, Δ the inf · max one, and λ a fuzzy convex combinator whose complement is −λ. Furthermore, we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations, focusing our attention on the modeling of fuzzy input-output systems, normality of fuzzy sets characterizing fuzzy input, fuzzy logical aspects of systems, and association between fuzzy information. Finally, it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems.

A programmable fuzzifier integrated circuit—synthesis, design, and fabrication

A membership function circuit which fuzzifies a nonfuzzy input signal to a fuzzy grade is needed for fuzzy information processing hardware systems. This paper describes the algebraic method for designing programmable membership function (PMF) circuits in current mode. In this method, the elementary functions r 1(ƒ, x) , r 2(ƒ,x) , and δ( x) are proposed. These functions are suitable for implementing a current mode circuit. The test chip of PMF designed by this method is fabricated in p-MOS integrated circuit technology. The characteristics of PMF are verified by this test chip and the spice ii simulation. The PMF has the following features: 1. (1) various shapes of membership functions can be produced by assigning six parameters; 2. (2) it exhibits low sensitivity to supply voltage (1%F.S./V for 8–14 V) and to temperature (0.07%F.S./°C for −55 to 60°C); 3. (3) it is suitable for real-time processing systems. (The speed of response is as high as 30 ns.) The PMF described here is indispensable for fuzzy information processing hardware systems.

Fuzzy information processing in seismic hazard analysis and decision making

This paper describes a methodology to incorporate vague information, based upon heuristic knowledge and expertise, into the conventional probabilistic approach for the seismic hazard analysis. The interval analysis method is introduced to process interval information with interpretation from Dempster and Shafer's evidence theory. The Vertex Method is discussed to handle fuzzy information which is a generalization of interval information. These methods, along with the current approach of seismic hazard analysis, are used to assess the seismic hazard for the San Francisco Bay Area in California and to provide information for deciding strengthening policy of existing buildings.

Chinese Conference on Fuzzy Information Processing

Chinese Conference on Fuzzy Information Processing

The Current Mode Fuzzy Logic Integrated Circuits Fabricated by the Standard CMOS Process

Nine basic fuzzy logic circuits employing p-ch and n-ch current mirrors are presented, and the fuzzy information processing hardware system design at a low cost with only one kind of master slice (semicustom fuzzy logic IC) is described. The fuzzy logic circuits presented here will be indispensable for a "fuzzy computer" in the near future.

Basic fuzzy logic circuit formed by using p‐MOS current mirror circuits

AbstractModern digital computers have great numerical calculation ability, but processing of fuzzy information is poor in terms of effectiveness and cost. Consequently, hardware systems peculiar to fuzzy information processing are anxiously awaited. This paper proposes a basic fuzzy logic circuit formed by using p‐MOS current mirror circuits, discusses the zero‐error condition and verifies their operations by the semicostom fuzzy logic IC designed in a standard Al‐gate p‐MOS technologyThe distinctive features of the proposed fuzzy logic circuits are: any fuzzy logic functions can be implemented with one kind of master slice (Bounded‐Difference array); variations of process parameters affect the electrical characteristics of the logic circuits very little; the basic logic cell is accurate; the current mode design facilitates the algebraic sum only by Al‐wiring; and these fuzzy logic circuits can be useful in binary logic and multiple‐valued logic The basic fuzzy logic cell described here will be a candidate for a logic circuit of Fuzzy Computer in the near future.

Call for papers: International symposium on fuzzy information processing in artificial intelligence and operational research : September 4–6, 1984, Churchill College, Cambridge, U.K.

Call for papers: International symposium on fuzzy information processing in artificial intelligence and operational research : September 4–6, 1984, Churchill College, Cambridge, U.K.

Symposium: Fuzzy Information Processing and Its Application

Symposium: Fuzzy Information Processing and Its Application

Precise past—fuzzy future

This paper examines the motivation and foundations of fuzzy sets theory, now some 20 years old, particularly possible misconceptions about possible operators and relations to probability theory. It presents a Standard uncertainty logic (SUL) that subsumes Standard propositional, fuzzy and probability logies, and shows how many key results may be derived within SUL without further constraints. These include resolutions of Standard paradoxes such as those of the bald man and of the barber, decision rules used in pattern recognition and control, the derivation of numeric truth values from the axiomatic form of the SUL, and the derivation of operators such as the arithmetic mean. The addition of the constraint of truth-functionality to a SUL is shown to give fuzzy, or Lukasiewicz infinitely-valued, logic. The addition of the constraint of the law of the excluded middle to a SUL is shown to give probability, or modal S5, logic. An example is given of the use of the two logies in combination to give a possibility vector when modelling sequential behaviour with uncertain observations. This paper is based on the banquet address with the same title given at NAFIP-1, the First North American Fuzzy Information Processing Group Workshop, held at Utah State University, May 1982.