Feature subset selection Filter–Wrapper based on low quality data

Today, feature selection is an active research in machine learning. The main idea of feature selection is to choose a subset of available features, by eliminating features with little or no predictive information, as well as redundant features that are strongly correlated. There are a lot of approaches for feature selection, but most of them can only work with crisp data. Until now there have not been many different approaches which can directly work with both crisp and low quality (imprecise and uncertain) data. That is why, we propose a new method of feature selection which can handle both crisp and low quality data. The proposed approach is based on a Fuzzy Random Forest and it integrates filter and wrapper methods into a sequential search procedure with improved classification accuracy of the features selected. This approach consists of the following main steps: (1) scaling and discretization process of the feature set; and feature pre-selection using the discretization process (filter); (2) ranking process of the feature pre-selection using the Fuzzy Decision Trees of a Fuzzy Random Forest ensemble; and (3) wrapper feature selection using a Fuzzy Random Forest ensemble based on cross-validation. The efficiency and effectiveness of this approach is proved through several experiments using both high dimensional and low quality datasets. The approach shows a good performance (not only classification accuracy, but also with respect to the number of features selected) and good behavior both with high dimensional datasets (microarray datasets) and with low quality datasets.     

A geometric approach to cluster validity for normal mixtures

 We study indices for choosing the correct number of components in a mixture of normal distributions. Previous studies have been confined to indices based wholly on probabilistic models. Viewing mixture decomposition as probabilistic clustering (where the emphasis is on partitioning for geometric substructure) as opposed to parametric estimation enables us to introduce both fuzzy and crisp measures of cluster validity for this problem. We presume the underlying samples to be unlabeled, and use the expectation-maximization (EM) algorithm to find clusters in the data. We test 16 probabilistic, 3 fuzzy and 4 crisp indices on 12 data sets that are samples from bivariate normal mixtures having either 3 or 6 components. Over three run averages based on different initializations of EM, 10 of the 23 indices tested for choosing the right number of mixture components were correct in at least 9 of the 12 trials. Among these were the fuzzy index of Xie-Beni, the crisp Davies-Bouldin index, and two crisp indices that are recent generalizations of Dunn’s index. Received: 29 July 1997/Accepted: 1 September 1997     

Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices. Crisp judgments cannot be given for real-life situations, as most of these include some level of fuzziness and complexity. In these situations, judgments are represented by the set of fuzzy numbers. Most of the fuzzy optimization models derive crisp priorities for judgments represented with Triangular Fuzzy Numbers (TFNs) only. They do not work for other types of Triangular Shaped Fuzzy Numbers (TSFNs) and Trapezoidal Fuzzy Numbers (TrFNs). To overcome this problem, a sum of squared error (SSE) based optimization model is proposed. Unlike some other methods, the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments. A fuzzy number is simulated using the Monte Carlo method. A threshold-based constraint is also applied to minimize the deviation from the initial judgments. Genetic Algorithm (GA) is used to solve the optimization model. We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods. Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments. Thus, the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29% compared to the existing studies.     

Logical operators of some statistical computing packages and missing values

When using statistical computer packages in general, we rely on the results they produce. We are aware that numerical approximations are made and trust that the best algorithms are chosen to do them. Most manuals give us instructions about precision of calculations and some report how missing values are administered. What we are unaware of is that some packages can invent results when creating atomic formulas and compounding complex formulas out of atomic ones, what inflates sample sizes, and possibly leads us to incorrect statistical decisions. Two simple indicator variables, with missing values positioned so the results are always missing values, were tested as numerical, as logical and as character variables, by compounding them through connective ‘and’ (&) and ‘or’ (|) to form new indicator variables. The results show that one of the three very known packages does not, statistically, correctly handle missing values, and the three make atomic formulas out of character variables assigning the value false (0) for missing value, what can be said an statistical error. The conclusion is that statisticians and users of statistics must be aware of the capabilities of logically operating missing values of the statistical packages they use, otherwise wrong statistical decisions can be made. And that programmers of statistical packages should correct their algorithms in order to not permit their packages invent non-existing values.     

Management of uncertainty in LIFE FEShell fuzzy frame system

LIFE FEShell is a fuzzy expert system shell that handles several kinds of uncertainty. LIFE FEShell is based on fuzzy logic, possibility theory, fuzzy measures and the fuzzy integral and is constructed in four parts: Fuzzy Production System (FPS), Fuzzy Frame System (FFS), FPS Object Editor (FPOE), and Fuzzy Frame Editor (FFE). We are now developing a few expert systems on LIFE FEShell to study and solve problems that are likely to arise during the implementation of these systems.

In this paper, we present an analysis of uncertainty in the frame system and show details of the LIFE FEShell Fuzzy Frame System and its handling of uncertainty. LIFE FEShell FFS allows linguistic representations in data and evaluation functions and handles its hierarchical definitions to accommodate their linguistic polysemy. Data may be set not only with crisp values, but also using possibility distributions as slot values, data grades, and link grades.     

Incorporating fuzzy membership functions into the perceptron algorithm

The perceptron algorithm, one of the class of gradient descent techniques, has been widely used in pattern recognition to determine linear decision boundaries. While this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable, it exhibits erratic behavior if the data are not linearly separable. Fuzzy set theory is introduced into the perceptron algorithm to produce a ``fuzzy algorithm' which ameliorates the convergence problem in the nonseparable case. It is shown that the fuzzy perceptron, like its crisp counterpart, converges in the separable case. A method of generating membership functions is developed, and experimental results comparing the crisp to the fuzzy perceptron are presented.     

On Two‐Player Interval‐Valued Fuzzy Bayesian Games

Game theory is an important basis to simulate several situations where multiple agents interact strategically for decision making and support. In many applications, such as auctions, frequently used for resource management involving two or more agents competing for the resources, the interacting agents only know their own characteristics and must make decisions while having to estimate the characteristics of the others. When probabilities are assigned for the different types of the interacting agents, this kind of strategic interaction constitutes a Bayesian game. In cases in which it is very difficult to characterize the private information of each agent, the payoffs can be given by approximate (not probabilistic) values, but the concept of Bayesian Nash equilibrium cannot be applied in this context. Fuzzy set theory is an excellent basis for studying this type of game, where the payoffs are represented by fuzzy numbers. When it is the case that there is also uncertainty about such fuzzy numbers, the use of interval fuzzy numbers appears as a good modeling alternative. This paper introduces an approach for interval‐based fuzzy Bayesian games, based on interval‐valued fuzzy probabilities for modeling the types of agents involved in the interaction. We present two different case studies, namely the (Interval) Fuzzy Bayesian Hiring Game and (Interval) Fuzzy Bayesian Prisoner's Dilemma with Moral Standards, comparing the results obtained with the crisp, fuzzy and interval fuzzy approaches, highlighting a particular case in which the interval fuzzy approach presents a solution although the two other do not.     

A semantics for Fuzzy Logic

 We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Received: 25 February 1997 / Accepted: 12 March 1997     

A Philosophy of Information Technology and Systems (IT & S) as Tools: Tool Development Context, Associated Skills and the Global Technology Transfer (GTT) Process

It is the intent of this paper to discuss a philosophy of Information Technology and Systems (IT & S) as tools and the impact of this philosophy on the Global Technical Transfer (GTT) process of IT & S.It is argued that IT & S by definition, are artefacts, tools that have been made, used, inherited and studied within a cultural context which encompasses economic, historical, technical and social values and assumptions which are focussed in particular skill sets. It is assumed that these skill sets are mostly in evidence in any culture that receives the IT & S tool for use in a technical transfer process. It is argued, therefore, if we understand the cultural context in which a tool is made then we will understand the skills to transfer and use such tools in an effective manner. The issue we must face as makers, users, inheritors and scholars of IT & S tools, however, is that the tool context and inherent in-built values and skill sets, may not be in evidence across all cultures. This would make the effective use of IT & S, in a global sense, a difficult and complex (if not impossible) undertaking.From this position it is argued that IT & S tools reflect the IT & S discipline, as it is these tools which embody the assumptions of the discipline and hence, its paradigm. The Bunker and Dean (Bunker DJ, Dean RG. Philosophical Traditions in Information Systems: Challenger of an Interdisciplinary View, Faculty of Commerce Workshop, University of Wollongong, July 10--11, 1997) disciplinary model is highlighted as a means of understanding how tools are made within a cultural context and how they reflect the discipline in which they are created. This paper then goes on to explain the ramifications of IT & S as a discipline on the GTT process and proposes a skill-focussed approach, within a culture, to determining what IT & S may be appropriate for that particular cultural context.     

两种模糊决策树算法的对比研究

模糊决策树归纳是从具有模糊表示的示例中学习规则的一种重要方法,从符号值属性类分明的数据中提取规则可视为模糊决策树归纳的一种特殊情况。由于构建最优的模糊决策树是NP-hard,因此,针对启发式算法的研究是非常必要的。该文主要对两种启发式算法即FuzzyID3和Min-Ambiguity算法应用于符号值属性并且类分明情况所作的分析比较。通过实验与理论分析,发现FuzzyID3算法应用于符号值属性类分明的数据库时从训练准确度、测试准确度和树的规模等方面都要优于Min-Ambiguity算法。     

Approximate reasoning applied to unsupervised database mining

A computational approach is shown for unsupervised, reactive, database mining. This approach is dependent on soft computing techniques. Database mining seeks to discover noteworthy, unrecognized associations between database items. A novel approach is suggested for unsupervised search controlled by dissonance reduction. Both crisp and noncrisp data are subject to discovery. Another aspect of uncertainty is the metric that controls discovery. Issues involve: coherence measures, granularization, user intelligible results, unsupervised recognition of interesting results, and concept equivalent formation. © 1997 John Wiley & Sons, Inc.     

An experience-based system supporting inventory planning: A fuzzy approach

The study aims to extend the Uncapacitated Fuzzy Single Item Lot Sizing Problem (known as F-USILSP) model and extend it for inventory planning. The F-USILSP model is a good choice when there is no statistical data collection, but where there is verbal or qualitative information from experts with experience. Previously, the mixed integer linear programming (MILP) relied on the crisp assumption which hinders the use of the F-USILSP. In this paper, a Possibility Approach is adapted to convert the F-USILSP to a mathematically solvable equivalent crisp USILSP (EC-USILSP). The EC-USILSP model is tested with a case. The organization under study is a petrochemical company power plant with trapezoidal fuzzy demand and triangular fuzzy unit price. The overall results show that the EC-USILSP is more practical and exhibits more flexibility when there is a need to add more realistic situations.     

Indistinguishability operators in measurement theory,Part I: Conversions of indistinguishability operators with respect to scales

For two given ordinal scales in a measurement process, the present paper investigates how an indistinguishability operator evaluated according to one of these ordinal scales can be converted to another indistinguishability operator w.r.t. the other ordinal scale, and establishes the mathematical base of these conversions under the framework of measurement theory [Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A. (1971) Foundations of Measurement, Vol. 1 (Academic Press, San Diego)]. Additionally, this work exposes the rudimentary facts behind the studies in [“Fuzzy Numbers and Equality Relations”, Proc. FUZZ'IEEE 93 (1993) 1298–1301; “Fuzzy Sets and Vague Environments”, Fuzzy Sets and Systems 66 (1994) 207–221; “Fuzzy Control on the Basis of Equality Relations-with an Example from Idle Speed Control”, IEEE Transactions on Fuzzy Systems 3 (1995) 336–350; and “T-partitions of the Real Line Generated by Idempotent Shapes”, Fuzzy Sets and Systems 91 (1997) 177–184], and points out the measurement theoretic derivations of the results in these studies.     

Compromise Fuzzy Multi-Objective Linear Programming (CFMOLP) heuristic for product-mix determination

This paper models a crisp Linear Programming (LP) as a Compromise Fuzzy Multi-Objective LP (CFMOLP). The application of CFMOLP has been focused on an industrial engineering problem that seeks profit maximisation by optimising product-mix. Imprecision of the large volume of industrial data and the conglomerated decision from all levels of management lead fuzzication of the identified constraints and the objective functions as well. The crisp model described is in the form of crisp-Multi-Objective Linear Programming (MOLP) with objective functions, functional constraints and non-negativity constraints. This model is formulated as a fuzzy-MOLP and subsequently converted into an equivalent compromise-MOLP model. The paper describes the development process for the CFMOLP model and its application along with appropriate interpretation.     

Multi-objective solid transportation problems with budget constraint in uncertain environment

This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.     

SLIGA Based underwater weapon safety and arming system

 The Naval Surface Warfare Center, Indian Head Division (NSWCIHD) is applying microelectromechanical system (MEMS) technology to underwater weapon Safety and Arming (S&A) system development. MEMS technology provides an opportunity to develop a miniaturized S&A system that is more sophisticated with improved safety and reliability at a lower cost compared to current systems. An S&A system prevents premature initiation of the weapon while reliably ensuring initiation at the appropriate time. An S&A system uses multiple sensors and devices. In comparison with other weapon S&A systems, a critical aspect of underwater weapon S&A systems is the mechanical interlock system utilizing actuators and mechanical sensors. This paper describes the design, development and fabrication of S&A SLIGA device prototypes and of a SLIGA based S&A system. NSWCIHD worked with members of the HI-MEMS Alliance during design, development and fabrication. Advancements achieved by the HI-MEMS Alliance and SLIGA S&A design issues are discussed. Received: 25 August 1997/Accepted: 10 September 1997     

Ranking of fuzzy numbers by a new metric

In this paper, a new approach for comparison among fuzzy numbers based on new metric distance (D _TM) is proposed. All reasonable properties of ranking function are proved. At first, the distance on the interval numbers based on convex hall of endpoints is proposed. The existing distance measures for interval numbers, (Bardossy and Duckstein in Fuzzy rule-based modeling with applications to geophysical, biological and engineering systems. CRC press, Boca Raton, 1995; Diamond in Info Sci 46:141–157, 1988; Diamond and Korner in Comput Math Appl 33:15–32, 1997; Tran and Duckstein in Fuzzy Set Syst 130:331–341, 2002; Diamond and Tanaka Fuzzy regression analysis. In: Slowinski R (ed) Fuzzy sets in decision analysis, operations research and statistics. Kluwer, Boston, pp 349–387, 1998) do not satisfy the properties of a metric distance, while the proposed distance does. It is extended to fuzzy numbers and its properties are proved in detail. Finally, we compare the proposed definition with some of the known ones.     

Distributed fuzzy case based reasoning

This paper presents a framework for a distributed knowledge based system by integrating case based reasoning (CBR) and Fuzzy Logic. Fuzzy Logic gives CBR the power to deal with impreciseness and uncertainty. The framework for handling distributed case bases enables our system to construct solution based on collective experience distributed by discipline, time, and geography. In the proposed system the cases can be expressed in terms of attributes that can be crisp as well as fuzzy and appropriately similarity scores are computed. The cases can have attributes from a vocabulary, which can be defined with the constraint of global commitments so that the attributes can be shared and interpreted in a distributed setting. We have implemented a knowledge sharing protocol with common ontology as the repository of exchange vocabulary for knowledge sources with different Universe of Discourses (UOD). We have developed a shell for tailored application development in different domains. We have used RDBMS as the back end repository for cases, DAML + OIL for Ontology design, SAX and DOM for ontology access and RMI for remote procedure call. We have illustrated effectiveness of our approach by developing a travel planning and a help desk application.     

An algebraic environment to process fuzzy images

We develop a system, called the Fuzzy Image Algebra, to handle the processing of fuzzy images algebraically extending the work of G.X. Ritter who considered the algebraic manipulation of crisp pictures. Our system is able to process both fuzzy and crisp pictures. There are certain operations on fuzzy images which result in crisper pictures whereas certain other operations may turn a fuzzy image to a more blurred picture.