Showing papers on "Fuzzy number published in 1997"
TL;DR: A related topic of the paper is to introduce an alternative representation of fuzzy measures, called the interaction representation, which sets and extends in a common framework the Shapley value and the interaction index proposed by Murofushi and Soneda.
891 citations
TL;DR: The basic concepts of the so-called “intuitionistic fuzzy topological spaces” are constructed, the definitions of fuzzy continuity, fuzzy compactness, fuzzy connectedness and fuzzy Hausdorff space are introduced, and several preservation properties and some characterizations concerning fuzzy compactity and fuzzyconnectedness are obtained.
691 citations
Book•
27 Apr 1997
TL;DR: Information, uncertainty and complexity classical logic basic concepts and notation fuzzy sets - basic concepts of fuzzy sets and further properties classical relations fuzzy relations fuzzy logic applications - a survey an historical overview established applications prospective applications illustrative examples.
Abstract: Information, uncertainty and complexity classical logic basic concepts and notation fuzzy sets - basic concepts and properties fuzzy sets - further properties classical relations fuzzy relations fuzzy logic applications - a survey an historical overview established applications prospective applications illustrative examples
519 citations
TL;DR: This paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance, cost and frequency, on which scientific traditions exist.
485 citations
TL;DR: For solving multiple criteria's decision making in a fuzzy environment, a new algorithm for evaluating naval tactical missile systems by the fuzzy Analytical Hierarchy Process based on grade value of membership function is proposed.
466 citations
TL;DR: This paper proposes a new approach to fuzzy modeling that can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985) because it has the same structure as that of Takagi & Sugeno (1985), because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model.
Abstract: This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm.
461 citations
TL;DR: Fuzzy systems, including fuzzy set theory and fuzzy logic, provide a rich and meaningful improvement, or extension of conventional logic, in soil science, and may be seen as a generalisation of classic set theory.
382 citations
TL;DR: The main contribution of this paper is the development of a decomposition principle that is, the design of a fuzzy discrete-time control system can be decomposed into a set of discrete- time subsystems.
377 citations
TL;DR: A learning method for fuzzy classification rules is discussed, based on NEFCLASS, a neuro-fuzzy model for pattern classification that is able to derive fuzzy rules from a set of training data very quickly, and tunes them by modifying parameters of membership functions.
374 citations
TL;DR: It will be shown that all (reasonable) fuzzy functions can be approximated to any degree of accuracy in this way and an interpretation of fuzzy initial value problems is proposed.
Abstract: Coping with uncertainty in dynamical systems has recently received some attention in artificial intelligence (AI), particularly in the fields of qualitative and model-based reasoning. In this paper, we propose an approach to modelling and simulation of uncertain dynamics which is based on the following ideas: We consider (linguistic) descriptions of uncertain functional relationships characterizing the behavior of some dynamical system. Based on a certain interpretation of such rule-based models, we derive a fuzzy function $\tilde{F}$. It will be shown that all (reasonable) fuzzy functions can be approximated to any degree of accuracy in this way. The function $\tilde{F}$ is then used as the "fuzzy" right hand side of a set of differential equations, which leads us to consider fuzzy initial value problems. We are going to propose an interpretation of such problems. Moreover, several aspects of simulation methods for characterizing the set of all system behaviors compatible with this interpretation will be...
344 citations
TL;DR: The proposed linguistic approximation method consists of two linguistic rule tables, which can realize exactly the same nonlinear mapping as an original system based on fuzzy if-then rules with consequent real numbers.
TL;DR: This paper is the first of two dealing with the analysis and design of a class of complex control systems using a combination of fuzzy logic and modern control theory, which can be represented by a fuzzy aggregation of a set of local linear models.
Book•
31 Aug 1997
TL;DR: This chapter introduces the author's fuzzy logic system, which combines the Additive and the Multiplicative AHP with Stochastic and Fuzzy PERT to achieve multi-Objective Optimization.
Abstract: 1. Introduction. 2. Basic Concepts of Fuzzy Logic. 3. Stochastic and Fuzzy PERT. 4. Fuzzy SMART. 5. The Additive and the Multiplicative AHP. 6. The ELECTRE Systems. 7. Fuzzy Multi-Objective Optimization. 8. Colour Perception. Subject Index. About the Author.
TL;DR: A new concept of the optimization problem under uncertainty is proposed and illustrated with a simple numerical example that converts the introduced intuitionistic fuzzy optimization (IFO) problem into the crisp (non-fuzzy) one.
TL;DR: It is shown that this compensating controller guarantees global stability of the closed-loop fuzzy system and the issues of a state observer for the fuzzy system are addressed.
TL;DR: In this paper, an online structure/parameter learning algorithm, FALCON-ART, is proposed for constructing a fuzzy adaptive learning control network (FALCON), which combines backpropagation for parameter learning and fuzzy ART for structure learning.
Abstract: This paper addresses the structure and an associated online learning algorithm of a feedforward multilayer neural net for realizing the basic elements and functions of a fuzzy controller. The proposed fuzzy adaptive learning control network (FALCON) can be contrasted with traditional fuzzy control systems in network structure and learning ability. An online structure/parameter learning algorithm, FALCON-ART, is proposed for constructing FALCON dynamically. It combines backpropagation for parameter learning and fuzzy ART for structure learning. FALCON-ART partitions the input state space and output control space using irregular fuzzy hyperboxes according to the data distribution. In many existing fuzzy or neural fuzzy control systems, the input and output spaces are always partitioned into "grids". As the number of variables increases, the number of partitioned grids grows combinatorially. To avoid this problem in some complex systems, FALCON-ART partitions the I/O spaces flexibly based on data distribution. It can create and train FALCON in a highly autonomous way. In its initial form, there is no membership function, fuzzy partition, and fuzzy logic rule. They are created and begin to grow as the first training pattern arrives. Thus, the users need not give it any a priori knowledge or initial information. FALCON-ART can online partition the I/O spaces, tune membership functions, find proper fuzzy logic rules, and annihilate redundant rules dynamically upon receiving online data.
TL;DR: A robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement: removing impulse noise, smoothing out nonimpulse noise, and enhancing (or preserving) edges and certain other salient structures is proposed.
Abstract: In this paper, we propose a robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement: (i) removing impulse noise, (ii) smoothing out nonimpulse noise, and (iii) enhancing (or preserving) edges and certain other salient structures. We derive three different filters for each of the above three tasks using the weighted (or fuzzy) least squares (LS) method, and define the criteria for selecting each of the three filters. The criteria are based on the local context, and they constitute the antecedent clauses of the fuzzy rules. The overall result of the fuzzy rule-based system is the combination of the results of the individual filters, where each result contributes to the degree that the corresponding antecedent clause is satisfied. This approach gives us a powerful and flexible image enhancement paradigm. Results of the proposed method on several types of images are compared with those of other standard techniques.
01 Feb 1997
TL;DR: The application of "alpha-cut" and "fuzzy arithmetic operations" are considered to make the fuzzy weighted average (FWA) method easier to program and the data easier to manipulate, which results in a more practical method for fuzzy decisions.
Abstract: When ranking a large quantity of fuzzy numbers, the efficiency, accuracy, and effectiveness of the ranking process is critical. The paper considers the application of "/spl alpha/-cut" and "fuzzy arithmetic operations" to the fuzzy weighted average (FWA) method which can be used to rank aggregated fuzzy utilities (or generalized fuzzy numbers). The purpose of this application is to make the method easier to program and the data easier to manipulate, which results in a more practical method for fuzzy decisions.
TL;DR: This work provides the methods for performing fuzzy arithmetic and shows that the PFN representation is closed under the arithmetic operations, and proposes six parameters which define parameterized fuzzy numbers (PFN), of which TFNs are a special case.
TL;DR: The determination of a unique optimal solution of the problem is discussed, a meta-heuristic is cast (simulated annealing-SA) to this particular framework for optimization and the obtained schedule remains feasible for all realizations of the operations durations.
Abstract: Jobshop scheduling problems are NP-hard problems. The durations in the reality of manufacturing are often imprecise and the imprecision in data is very critical for the scheduling procedures. Therefore, the fuzzy approach, in the framework of the Dempster-Shafer theory, commands attention. The fuzzy numbers are considered as sets of possible probabilistic distributions. After a review of some issues concerning fuzzy numbers, we discuss the determination of a unique optimal solution of the problem and then we cast a meta-heuristic (simulated annealing-SA) to this particular framework for optimization. It should be stressed that the obtained schedule remains feasible for all realizations of the operations durations.
TL;DR: Some types of representation of fuzzy numbers are described and the notions of the distance and orders between fuzzy numbers based on these representations are studied.
TL;DR: Six methods are described that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data.
Abstract: This paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool. Within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms. These approaches attempt to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data. Because the main objective is to obtain an approximation, the methods we propose must be as simple as possible, but also, they must have a great approximative capacity and in that way we work directly with fuzzy sets induced in the variables input space. The methods are applied to four examples and the errors obtained are specified in the different cases.
TL;DR: A new entropy of a fuzzy set is defined based on the membership functions of the intersection and union of the set and its complement set and the concept of fuzzy cross-entropy is introduced.
TL;DR: A study of the different roles played by the fuzzy operators in fuzzy control is developed, and a comparison of the accuracy of many fuzzy logic controllers designed by means of these operators is carried out.
[...]
TL;DR: This paper proposes an adaptation of Watkins' Q-learning for fuzzy inference systems where both the actions and the Q-functions are inferred from fuzzy rules, showing its effectiveness.
Abstract: This paper proposes an adaptation of Watkins' Q-learning (1989, 1992) for fuzzy inference systems where both the actions and the Q-functions are inferred from fuzzy rules. This approach is compared with genetic algorithm on the cart-centering problem, showing its effectiveness.
TL;DR: It is shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition.
Abstract: Derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c-means and fuzzy learning vector quantization. These algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning. Derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent. A close relationship between the resulting algorithms and fuzzy c-means is revealed by investigating the functionals involved. It is also shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition.
TL;DR: This paper discusses how fuzzy clustering techniques can be applied to construct a fuzzy controller from data and introduces special clustering algorithms that are tailored for this problem.
TL;DR: It is proved that an NSFLS can uniformly approximate any given continuous function on a compact set and does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system (FLS).
Abstract: In this paper, we present a formal derivation of general nonsingleton fuzzy logic systems (NSFLSs) and show how they can be efficiently computed. We give examples for special cases of membership functions and inference and we show how an NSFLS can be expressed as a "nonsingleton fuzzy basis function" expansion and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations. We prove that an NSFLS can uniformly approximate any given continuous function on a compact set and show that our NSFLS does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system (FLS).
TL;DR: This paper proposes an efficient algorithm to compute fuzzy weighted average, which turned out to be superior to the previous works by reducing the number of comparisons and arithmetic operations to O(n log n).
TL;DR: F fuzzy logic concepts are used to introduce a tool useful for robot perception as well as for planning collision-free motions, and proper instances of the A* algorithm are devised.
Abstract: An essential component of an autonomous mobile robot is the exteroceptive sensory system. Sensing capabilities should be integrated with a method for extracting a representation of the environment from uncertain sensor data and with an appropriate planning algorithm. In this article, fuzzy logic concepts are used to introduce a tool useful for robot perception as well as for planning collision-free motions. In particular, a map of the environment is defined as the fuzzy set of unsafe points, whose membership function quantifies the possibility for each point to belong to an obstacle. The computation of this set is based on a specific sensor model and makes use of intermediate sets generated from range measures and aggregated by means of fuzzy set operators. This general approach is applied to a robot with ultrasonic rangefinders. The resulting map building algorithm performs well, as confirmed by a comparison with stochastic methods. The planning problem on fuzzy maps can be solved by defining various path cost functions, corresponding to different strategies, and by searching the map for optimal paths. To this end, proper instances of the A* algorithm are devised. Experimental results for a Nomad 200™ robot moving in a real-world environment are presented. © 1997 John Wiley & Sons, Inc.