Crisp Data Research Articles

Applications of Soft Computing to Human-centered Information Systems

Applications of Soft Computing to Human-centered Information Systems

Multi-criteria analysis for dredger dispatching under uncertainty

Dredger dispatching is a complex decision making process in which multiple requirements and uncertain site conditions have to be taken into consideration simultaneously, for a specific dredging task. In evaluating the suitability of dredgers, besides quantitative assessments, qualitative assessments are often required to deal with uncertainty, subjectiveness and imprecision, which are best represented with fuzzy data. This paper formulates dredger dispatching as a fuzzy multi-criteria analysis model, and presents an effective algorithm for handling both crisp and fuzzy data in a straightforward manner. As a result, effective decisions can be made based on consistent evaluation results. An empirical study of a real case in China is conducted to demonstrate the applicability of the model. With its simplicity in both concept and computation, the model can be implemented as an effective decision aid in selecting dredgers for specific dredging tasks.

Robust interval regression analysis using neural networks

As a very important tool for dealing with both crisp data and fuzzy data, fuzzy regression analysis based on interval regression analysis has become an active area of research. Some neural network related methods for nonlinear interval regression analysis have been proposed on the assumption that given training data are totally “good” data. The performance of these methods will significantly worsen when the training data are spoiled by outliers. In this paper, we introduce the concepts of polarity and quality of the training data, on the basis of which we propose two robust learning algorithms for determining a robust nonlinear interval regression model, which makes a feature of a new cost function for reflecting not only the polarity of the training data but also the estimated knowledge about the quality of the training data. The two robust algorithms are derived in a manner similar to the back-propagation (BP) algorithm. Simulation results show that our robust algorithms outperform the existing methods remarkably in two aspects when outliers are present: (1) They are robust against outliers; (2) Their rates of convergence are improved to some extent.

Fuzzy loss less decompositions in databases

In this paper we deal with the problem of defining projection and join operators in the framework of a fuzzy relational database. We study the properties of such operators relating to the concept of fuzzy functional dependency. There are two main properties to achieve: On the one hand, if a relation r satisfies a dependency between two sets of attributes, X and Y, then we want to preserve this dependency in the fuzzy projection over XY of r. On the other hand, we want to test a fuzzy dependency just by looking at this projection. Therefore, such a projection operator must allow us to store the information conveyed in r into a separate relation with fewer tuples. In order to define the criterion for fuzzy dependency, we shall need to extend a resemblance relation defined for crisp data to the fuzzy case. Finally, we shall introduce a fuzzy join operator which will allow us to recover the information given in a relation, from its projections.

Fuzzy linear fractional goal programming applied to refinery operations planning

Chemical process plant operations planning in an oil refinery has been modelled as fuzzy linear fractional multiple goal programming problem. A variant of the fuzzy linear fractional goal programming model of Dutta et al. [Fuzzy Sets and Systems 52 (1992) 39–45] has been developed and used in the present study to solve the problem which has two fuzzy fractional goals and 22 crisp constraints. Linear membership functions have been assumed and min operator has been used as the aggregator. Linguistic variable has been taken as “ close” throughout the paper, following Dutta et al. (1992). A software has been developed in TURBO C to implement the model. The software takes the parameters defining the fuzziness and crisp data from the input field and solves the crisp equivalent to the fuzzy linear fractional goal programming problem. The parameters defining fuzziness are subjectively chosen by the user/decision maker. The software finally outputs satisfying decision variables, satisfying fuzzy fractional goal values, optimal values of the profit (numerator) and the capacities of the primary unit and cracker (denominators) which are involved in the fuzzy fractional goals. The results indicate that the present model yielded a more efficient solution compared to the crisp solution of Allen [British Chem. Eng. 16 (1971) 685–691] as far as the fractional objectives are concerned. This demonstrates the efficacy of the present model. However, a paltry decrement of 1.3% in the profit is noticed in the present study, in comparison to the crisp solution of Allen (1971).

Testing fuzzy hypotheses with crisp data

In this paper an approach is presented how statistical tests originally constructed to examine crisp hypotheses can also be applied to fuzzily formulated hypotheses. In particular, criterions α and β are proposed generalizing the probabilities of the errors of type I and type II, respectively. The general approach is applied to one- and two-sided Gauß tests. Here, diagrams are given to determine the critical values in the most popular cases of α = 0.01 and α = 0.05. If, in addition, the value of β is fixed in advance the sample size of a one- or two-sided Gauß test can be obtained using supplementary graphs.

COMPRESSION AND EXPANSION OF FUZZY RULE BASES BY USING CRISP-FUZZY NEURAL NETWORKS

A fuzzy neural network with knowledge discovery FNNKD is designed to perform adaptive compensatory fuzzy reasoning based on more useful and more heuristic primary fuzzy sets. In order to overcome the weakness of the conventional crisp neural network and the fuzzy operation oriented neural network, we have developed a general fuzzy reasoning oriented fuzzy neural network called a crisp-fuzzy neural network CFNN that is capable of extracting high-level knowledge such as fuzzy IF-THEN rules from either crisp data or fuzzy data. A CFNN can effectively compress a 5 5 fuzzy IF-THEN rule base of a cart-pole balancing system to a 3 3 one, then to a 2 2 one, and finally to a 1 1 one, and can expand on invalid sparse 3 3 fuzzy IF-THEN rule base of a cart-pole balancing system to a valid 5 5 one. In addition, a CFNN can control a more complex cart-pole balancing system with random fuzzy noise inputs and outputs i.e., nonconventional using crisp inputs and outputs without any noise . The simulations have indicated that a CFNN is an efficient neurofuzzy system with abilities to discover new fuzzy knowledge from either numerical data or fuzzy data, compress and expand fuzzy knowledge, and do fuzzy reasoning.

An approach to fuzzy hypothesis testing

In this paper an approach is presented how to test fuzzily formulated hypotheses with crisp data. The quantitiesα andβ, the probabilities of the errors of type I and of type II, are suitably generalized and the concept of a best test is introduced. Within the framework of a one-parameter exponential distribution family the search for a best test is considerably reduced. Furthermore, it is shown under very weak conditions thatα andβ can simultaneously be diminished by increasing the sample size even in the case of testingH0 against the omnibus alternativeH1: notH0, a result completely different from the case of crisp setsH0 andH1: notH0.

On a class of fuzzy c-numbers clustering procedures for fuzzy data

This paper describes a class of fuzzy clustering procedures for fuzzy data. Most fuzzy clustering techniques are designed for handling crisp data with their class memberships using the idea of fuzzy set theory. Here we derive new types of fuzzy clustering procedures in dealing with fuzzy data. These procedures are called fuzzy c-numbers ( FCN) clusterings. Specially, we construct these FCNs for LR-type, triangular, trapezoidal and normal fuzzy numbers.

Fuzzy optical metrology

When operating in the real world, the conventional fuzzy approach is to extract crisp data then fuzzify it. This paper explores the concept of measuring fuzzy set memberships directly and obtaining the underlying crisp values by defuzzification. Both speed and accuracy advantages of fuzzy over conventional, crisp metrology are noted.

759–4 Information Integration for Cardiology Decision Support

Electronic medical records pose a challenge because of the complex types of data which are included. Decision support systems must be able to deal effectively with these data types. In the expert system demonstrated here, a diversity of data types are included. These data are processed by three different methods. However, the different methods of processing are transparent to the user. An overall rule-based interface integrates the different methods into one comprehensive system. Data types include crisp data, fuzzy data, temporal data, and numerical representation of chaotic analysis. Some data items which appear to be crisp, for example, test results, are more accurately represented as fuzzy numbers which indicate the degree of precision of the test. Four types of temporal data are considered: change in value from previous value, change in value relative to a specified time interval, duration data, and sequence data. A measure developed by the authors which determines the degree of variability in time series data is also included. The knowledge-based portion of the system utilizes approximate reasoning techniques which allows weighting of antecedents and partial presence of symptoms. The rule base is used as the interface which invokes a neural network model or time series analysis if certain rules are substantiated. The neural network model is a three-level feed-forward model based on a non-statistical learning supervised learning algorithm developed by the authors. Input data can be of any ordered form, including binary, categoric, integer, or continuous. The network can categorize data into two or more classes, and also produces a degree of membership for each class. Time series data, such as electrocardiograms, are important measurements for many diagnoses. An ECG may have an overall interpretation which can be used in the rule-based component, or categorized to be used in the neural network component. However, other analyses may also prove useful. In the application shown, a measure of variability for 24-hour Holter tapes is used. The combination of these techniques is illustration in a decision support system for the diagnosis and treatment of heart disease, including the use of a rule base, a supplementary neural network model of exercise testing data (ETT), and a time series analysis for Holter data.

Evaluating aggregates in possibilistic relational databases

The need for extending information management systems to handle the imprecision iof information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature had dealt with queries involving a functional evaluation of a set of items, traditionally refered to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applciations, and thus this paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. The consistency of the proposed operations is shown. An extended operator is defined to be consistent if it defaults to its classical counterpart when evaluated on crisp data.

Fuzzy I/O controller

We describe a fuzzy controller which accepts and produces fuzzy data (linguistic variables) as well as crisp data (real numbers) for the control of man-machine systems.

Fuzzy linguistic data bases: An application

This paper discusses the empirical development and use of a fuzzy linguistic data base which is relational in character. Unlike conventional fuzzy searches for crisp data, we search a data base for fuzzy information. The data base supports another code which does fuzzy aggregation of data. It has been applied to support decision making connected with the construction of military budgets for command, control and communications (C3).

Simultaneous experimentation of self-learning classification, connectivity analysis and visualisation for data interpretation

Self-learning classification of data and connectivity analysis using probabilistic and fuzzy concepts are compared with subjective and visual rearrangement of data. Both methodologies are fully described and results are compared on two examples: crisp binary data and normalized real data.