Namdar Mogharreban

Comparison of Defuzzification Techniques for Analysis of Non-interval Data

Defuzzification plays an important role in the implementation of a fuzzy system since the crisp value generated best represents the possibility distribution of all possible fuzzy control outputs. The focus of this paper is on comparison of several defuzzification strategies in two fuzzy inference systems designed to analyze questionnaires. Two different questionnaires were analyzed, one having two fuzzy rules and one having three fuzzy rules for the inference component. The output of centroid, bisector, mean of maximum (MOM), and largest of maximum (LOM) defuzzification methods were compared with the output of a conventional statistical analysis. Significant correlation was found between the statistical outputs and the fuzzy inference outputs. It appears that with non-interval data, typical of the kind of data collected in social science studies, the choice of defuzzification method has no influence on the output. As is suggested in the literature, this may be due to the match between the properties of the various defuzzification methods and the application

Adaptation of a Cluster Discovery Technique to a Decision Support System

Introduction In every day decision making there are very few decisions made without a number of competing alternatives. A decision maker must choose an alternative by evaluating a number of criteria. As the number of alternatives and criteria increases, the task of selecting the best alternative becomes increasingly difficult. A typical multi-criteria multi-alternative decision making model can be represented by a matrix, such as shown in Table 1, with M number of alternatives and N criterion such that i = 1,2,3, ..., m and j = 1,2,3, ..., n [14]. Each element of the matrix [a.sub.ij] indicates the users response to alternative Ai when it is evaluated in terms of criterion [C.sub.j]. To accommodate the importance of different goals or criteria a weight value, sometimes referred to as decision weight, is associated with each criterion that signifies the importance of the criterion. A numeric value is then assigned to each cell in the matrix by the decision maker that represents the level of significance a criterion may have within a particular alternative. The populated matrix is then manipulated and a rank ordering of the alternatives is obtained. The best alternative considering the inputs by the decision maker can then be selected. Depending on the number of criteria and the units upon which each is evaluated determining the best alternative becomes a complex task. In this paper, we are proposing a modification of a clustering technique that indicates the degree of closeness of a vector to a vector representing an alternative. The alternative choices employed are different disorders of the eye and the criteria are different symptoms of the eye disorders. An alternative is determined by the cluster discovery technique ART1, an unsupervised cluster discovering technique using the set of values for 10 different symptoms. ART1 is then modified and the closeness of the new set of values representing the users symptoms to different clusters is determined. The closest matching alternative to the given symptoms is returned by the system. This allows for determination of the best matching disorder to the set of symptoms. This paper is organized as follow. First, some typical multi-criteria decision methods (MCDM) that are utilized to validate our design are discussed. We then present the clustering technique used and the modifications of its algorithm. The results of comparisons between the typical MCDM models and our design are then presented. Finally, the implementation of and the development of future related work we are currently engaged in are discussed. MCDM Methods Different MCDM methods have been proposed for the numeric manipulation of a decision matrix to arrive at the best alternative (Chen, & Hwang, 1991; Hwang, & Yoon, 1981; Zimmerman, 1996). The first stage of processing the matrix is manipulation of the criteria to obtain a value that can best represent each alternative. However, depending on the type of values being considered, the operation may not be a straightforward process. For example, a manager is trying to decide between three different venders. The criteria on which the alternatives are compared include price, delivery cost, and restocking cost for the surplus. Each criterion is evaluated based on its dollar value and the lower the values the more attractive the alternative. The criteria are said to be homogeneous and along the same dimension. They are both costs, measured in dollar terms, and the lower the cost the better the alternative. However, if the choices are between foreign and domestic vendors one of the criterion might be the delivery time. The criteria, cost value verses time, are along different dimensions. That is, of course, to assume that time can not be measured in dollar terms. Thus it is not clear the type of operations that would result in the most accurate representation for the criteria (Hamalainen & Salo, 1997). …

Approximate Degrees of Similarity between a User's Knowledge and the Tutorial Systems' Knowledge Base

A typical tutorial system functions by means of interaction between four components: the expert knowledge base component, the inference engine component, the learners knowledge component and the user interface component. In typical tutorial systems the interaction and the sequence of presentation as well as the mode of evaluation are predetermined and follow a somewhat linear sequence. This model was implemented in many of the early computer based trainings, computer assisted instruction systems and tutorial drill programs. However, by introducing artificial intelligence in the inference engine or by enhancing the expert system component (by means of including feedback), by improving the evaluation of the learners responses and facilitating interaction between these components one may provide a learning environment that more closely resembles a real teacher and student interaction. This approach is known as Intelligent Tutoring Systems (ITS). Various tutorial systems were developed based on this paradigm that proved useful in knowledge domain areas that are highly structured and relatively small (e.g. solving math problems or balancing chemical equations). The difficulty resides in the complexity involved in making the various components encompassing and complete in a knowledge area. For instance, understanding why learners commit a particular error and then assisting them is highly challenging since the cause of an error might be different for every learner. Variations on this ITS model have been employed with success in developing tutoring systems in less structured knowledge domains and more generic environments. Another element that improves ITS functionality is the ability to deliver the correct and necessary granule of material for effective coverage and completion of the knowledge area. The question of where to start a learner in the tutorial system and how to choose the next step is difficult to delineate. In this paper we propose an approach based on the fuzzy set theory to determine the entry knowledge level possessed by a learner in a specific area of learning. Two relations between the knowledge area and the skill levels of a user are established. The first relation is created between the given behavior or knowledge and the mastery of the foundation skills required for it. The second relation is between the given behavior or knowledge and the required exposure to the knowledge domain. The matrices are manipulated

PORSEL: an expert system for assisting in investment analysis and valuation

During the last few years, we have developed an expert system, called PORSEL (PORtfolio SELection system), which uses a small set of rules to select stocks. PORSEL consists of three components: the Information Center, the Fuzzy Stock Selector, and the Portfolio Constructor. The purpose of the information center is to provide representation of several technical indicators such as candlestick charts, moving average of closing prices, and price trends. The fuzzy stock selector evaluates the listed stocks and then assigns a composite score for each stock. The portfolio constructor generates the optimal portfolios for the selected stocks. The PORSEL also includes a user-friendly interface for adding and deleting rules during the run time. The results of simulation shows that PORSEL outperformed the market almost every year during the testing period.

Regaining the 'Object' of Learning Objects

Learning objects were to bring a seismic shift to the field of computer-based instruction by introducing transportability and reusability. Supposedly outfitted with the concepts taken from object-oriented (OO) design, learning objects have long promised dramatic savings of time and money in course and curricula development. However, they have failed to deliver the return on investment that seems a natural extension of their existence, in large part because the conceptual mechanisms adopted by OO design for transportability and reusability are lacking in learning objects. Object-oriented software development, first discovered in the 1960s, had ushered in a new era of programmatic coding and design by the 1990s. Instead of thinking in terms of “verbs,” or the processes that act upon information, developers could directly conceive of “nouns,” or the objects that define the world around us, and provide these objects with real-world attributes. These transportable and reusable objects would then possess a library of ready-to-use actions that provide both a rich feature set as well as isolation for the user from implementation complexity. Software languages designed with support for such concepts as classes, methods, instantiation, overloading, overriding, inheritance, polymorphism, and encapsulation, achieved this tectonic shift in computer engineering and resulted in dramatic improvements in reliability, reusability, and cost. In response to this shortcoming, we have proposed a new entity - the learning pod (Mogharreban & Guggenheim, 2008). The learning pod is our conception of the Learning Object. Engineered with the original concepts behind object-oriented development, the proposed conception uses OO technology to create an experientially seamless interconnection between disparate learning variables and delivers on the promise of sharing and reuse. The proposed learning object is construed as a class in OOP. A class may be considered as a blueprint, a schematic for replicating an object. Using a class begins with instantiating a new object based on that blueprint. Instantiation is the process by which a new copy of an object is created for use by invoking a constructor. This “instance” of a class referred to as an object has all the properties of the original, and is immediately available for application.

Reusability and Learning Objects: Problems and a Proposed Solution

Learning objects have long promised dramatic savings of time and money in course and curricula development, but they have failed to deliver the return on investment that seems a natural extension of their existence reusability. Because a single hour of online instruction can take up to 300 hours to develop (Kapp 2003), reusability is the core value message offered by learning object promoters, from the earliest days to the present. Yet, after 12 years of successive evolution, learning objects are still primarily a collection of stand-alone modules that rarely interconnect outside of strictly controlled regimes, such as those imposed by corporate and military training guidelines. Among the contributing factors to this impediment are definition of learning object, size of a learning object and aesthetics of a learning object. In response to this shortcoming, we propose to introduce a new entity the learning pod. Engineered for reusability, the learning pod incorporates several modules that bring current technology to create an experientially seamless interconnection between disparate learning objects. These modules communicate with one another to build a consistent unit of instruction that uses several learning objects depending on the requirements. Several technologies including semantic web, XSL/XML and CSS are utilized to achieve presentation cohesiveness.