# Advanced Distributed Simulation Research Consortium

**SUBMITTED AND PUBLISHED PAPERS 1999-2000**

**SUBMITTED AND PUBLISHED PAPERS 1999-2000**

Considering The Cost Of Quality, When Adjusting Sample

Size To Meet Quality Goals

Andre de Korvin

Margaret F. Shipley

University of Houston-Downtown

Houston, Texas USA 77002

Determining the proper sample size such that quality is assured while costs are not unnecessarily incurred is critical to an effective quality program. The main purpose of the present work is to design a fuzzy controller to adjust sample sizes according to potential fuzzy loss penalties. A set of fuzzy rules is given where, depending on the antecedents, the sample size may be decreased, moderately modified, or increased. At any given moment the proportion of defects in the sample determines the firing strength of the rules suggesting an appropriate sample size. These rules are then modified to include an analysis of the decision maker's belief that in a particular situation an inappropriate rule is being considered such that an expected loss would be incurred.

Project Management: Using Fuzzy Logic and the Dempster-Shafer Theory of

Evidence to Select Team Members For the Project Duration

Margaret F. Shipley, Charlene A. Dykman, Andre de Korvin

University of Houston-Downtown

One Main Street

Houston, Texas 77001

Fuzzy logic and the Dempster-Shafer theory of evidence [IJ is applied to an IS multiattribute decision making problem whereby the project manager must select project team members from candidates, none of whom may exactly satisfy the ideal level of skills needed at arty point in time.

The decision mechanism is constrained by the uncertainty inherent in the determination of the relative importance of each skill acrd the classification of potential team members. This latter uncertainty of potential team membership is addressed through expert evaluation of the degree to which each potential team member possesses each skill. Then the Belief and Plausibility that a candidate will satisfy the decision maker's ideal skill levels are calculated and combined to rank order the available candidates. The changing skill requirements are addressed through an iterative process for each project phase.

Genetic Algebras - Their Fuzzy Analog

Elias Deeba and Andre de Korvin

Department of Computer and Mathematical Sciences

UH-D, 1 Main Street, Houston Texas 77002, USA

Generally speaking, a genetic algebra is a mathematical realization of genes interactions. Since such interactions may involve a good deal of uncertainty, it becomes natural to consider the fuzzy analog of these algebras. In this paper, we study and extend the ideas of genetic algebras to the fuzzy setting.

A Hierarchical Gird-Based Approach To Data Distribution In

The High-Level Architecture

A. Berrached, M. Beheshti, O. Sirisaengtaksin, A. de Korvin

Department of Computer and Mathematical Sciences

University of Houston-Downtown

Houston, Texas 77009

One of the key requirements for achieving large scale distributed simulations is to use the available communication bandwidth efficiently. In typical distributed simulations, a particular entity is interested in only a small subset of all other entities in the simulated "world". The objective of relevance filtering methods is to reduce the amount of irrelevant data exchanged among simulations by sending data only when and where it is needed. The High-Level Architecture (HLA), designated as the standard architecture for distributed interactive simulation, provides mechanisms to facilitate the implementation of various relevance filtering schemes. This paper gives an overview of the data distribution services provided by the HLA and analyzes, qualitatively and quantitatively, the performance of the traditional fixed-grid based approach used in current HLA implementations. A new hierarchical grid-based approach is described in detail and its performance compared against that of the basic fixed grid approach.

Determining the Larger of Two Continuous Fuzzy Sets with

Unbounded Support by the Cut-Off Method

A. de Korvin

University of Houston - Downtown

Houston Texas, 77002, USA

R. Kleyle

Department of Mathematical Sciences

Indiana University - Purdue University at Indianapolis

Indianapolis, IN 46202, USA

In a recent article, we extend Jain's Maximization Principle (Jain, 1976) to situations in which it is necessary to compare continuous fuzzy sets. This extension is more or less straight forward when the fuzzy sets being compared all have bounded support. When one or more of the supports are unbounded, the extension is rather more difficult and often analytically intractable. In this paper we establish an alternate method based on the use of cut-off points, which blends the extended Jain's Maximizing Principle and the traditional COA method for determining which of two continuous fuzzy sets having unbounded support is the "larger". The resulting method is far easier to apply than the extended Jain's Principle method, but is able to produce a definitive comparison in situations in which the COA method fails. The application of the both techniques are illustrated by an example.

Intelligent Access Control in Distributed Systems Using Fuzzy Relation Equations

A. Berrached M. Beheshti A. Dekorvin R. Alo

Department of Computer and Mathematical Sciences

University of Houston-Downtown

Houston, Texas 77002

Current computer security systems are based on the premise that once a user presents valid credentials to the authentication system (e.g. valid ID and password), they are granted access permission to all resources assigned to the user that they claim to be. However, numerous studies have shown that most security breaches are done by unauthorized users impersonating as authorized users or by circumventing the authentication system altogether.

Once the authentication system is broken, the system and the information kept in it become wide open to unauthorized access and malicious usage. Moreover, because of the interdependency among the various (computer and telecommunication) components of a distributed system, a security breach to one component can have repercussions throughout the system. The main objective of this paper is to present new security model that provides additional level of security checks based on heuristic information kept about various system components. The model allows a local host to evaluate and determine whether a remote request should be granted based on such information as the sensitivity level of the data being effected by the request, the type of request being made, and the probability of hostility of the user making the request. Typically, such information is very difficult to determine precisely since it depends on other attributes that are themselves imprecise or only partially known. The paper presents an algorithm for generating such fuzzy information based on their dependent attributes. The method is based on using basic rules of fuzzy set theory to establish a fuzzy relation between a set of dependent fuzzy quantities.

Assigning Tasks to Resource Pools: A Fuzzy Set Approach

A. de Korvin, S. Hashenu', G. Quirchmayrz, R. Kleyle

University of Houston - Downtown

Houston Texas, 77002, USA

Universitat Wien

Institut fur Informatik and Wirtschaftsinfomtatik

Liebiggasse 4, A-1010 Wien, Austria

Indiana University- Purdue University at Indianapolis

Indianapolis, IN 46202, USA

In this paper we address the problem of assigning tasks to resource pools. Each task has certain resource requirements, but with the capacity to provide these resources varying from pool to pool. We represent each task as a finite fuzzy set whose support consists of the resources and whose memberships reflect the degree of importance of each resource in performing this specific task. The resource pools are also represented by finite fuzzy sets having the same support, but now the memberships reflect the capability of a specific pool to provide each of these resources. We next define a measure of compatibility between each task and each resource pool. This compatibility is itself a fuzzy set which we defuzzify via the center of area (COA) method. We then develop an algorithm that describes how to recursively assign tasks to resource pools until some prespecified compatibility criterion has been violated. Finally, we add an assessment of cost to our algorithm, thereby enhancing its potential for practical application.

Evaluating Policies Based On Their Long Term Average Cost

A. de Korvin, S. Hashemi

University of Houston-Downtown

One Main Street, Houston, Texas 77002, USA

G. Quirchmayr

Universitat Wien, Institut f. Angewandte Informatik and Informationssysteme

Liebiggasse 4, A-1010 Wien, Austria

Many decision problems can be characterized by a set of possible states and a cost associated with each possible state transition. In this paper we discuss how to select a policy from a set of possible policies in the long term. If the cost matrix is not available the transition matrix can be used to compare expected return times to states. In our setting the transition matrix is defined by use of linguistic terms and as a consequence, the expected return times are fuzzy. In the case where the cost matrix is available, fuzzy average costs are computed. The resulting fuzzy quantities are compared by introducing the concept of minimizing sets. Finally, we look at the case where the transition takes place from a state to a state that is known to be an element of some subset of states, but we do not know which one. We use the Dempster-Shafer theory (Shafer 1976] together with techniques of Norton [Norton 1988] and Smetz [Smetz 1976] to approximate the transition probabilities.

On Firing Rules Of Fuzzy Sets Of Type II

Andre de Korvin, Chenyi Hu, Ongard Sirisaengtaksin

Dept. of Computer and Math. Sci.

University of Houston-Downtown

One Main Street

Houston, Texas 77002, USA

The objective of this work is to investigate a set of rules where antecedents are fuzzy sets of type II and input are fuzzy sets. First, a special case where all the fuzzy sets involved have interval valued memberships is determined. We develop an approach to defuzzify such sets and a range of possible actions. The strength of a rule is, in general, an interval and the firing is an interval. Additional information may determine how an action is to be picked from the firing interval. In the second part, we generalize these considerations to fuzzy sets of type II, using the a-cuts to carry off this generalization. An alternate approach defines the strength of a rule as a scalar instead of a fuzzy set.

Assignment Of Tasks To Competing Nodes When Task Duration Times Are Fuzzy

A. de Korvin, S. Hashemi

University of Houston -Downtown, Houston, TX, 77002, USA

R. Kleyle

Indiana University - Purdue University at Indianapolis, Indianapolis, IN 46202, USA

G, Quirchmayr

Universitat Wien, Institut fur Angewandte Informatik and Informationssysteme, Liebiggasse 4, A-1010

Wien, Austria

In this article, we introduce a formal scheduling algorithm that uses redirecting of tasks from a bottlenecked employee while minimizing the completion time for the scheduled jobs. The paper focuses on instances in which a number of employees are to perform several jobs that are divided into various tasks withfuzzy values for their estimated duration times.

Generally, efficient job scheduling requires that task and job duration be real values. This allows for precise calculation of time interval and time delay parameters when determining a job's completion time. When the precise values of either one of these parameters is unknown, not only can the job's completion time not be minimized, but the scheduling of tasks, without regard to the possible bottlenecks, will be haphazard.

Validation of Authentic Reasoning Expert Systems

Laurie Webster II, Jen-Gwo Chen , Simon S. Tan,

Carolyn Watson, Andre de Korvin

NASA Johnson Space Center, Life Sciences Research Laboratories, Mail Stop SD3,

Houston, TX 77058, USA

Department of Industrial Engineering, University of Houston, 4800 Calhoun Road,

Houston, TX 77004-4812, USA

Lockheed Engineering and Sciences Company, Houston, TX 77058, USA

Computer and Mathematical Sciences, University of Houston - Downtown,

Houston, TX 77001, USA

This paper outlines an approach for validating the expert system's performance by comparing the expert system to the consensus results of the experts (i.e., using several experts to solve the same problem that the authentic reasoning expert system solved).

We also discuss a mathematical process that includes the use of rough set theory as a means of capturing and quantifying the reasoning factors and reasoning processes of the experts. Additionally, a generalized entropy criterion for measuring consensus effectiveness based on Dempster-Shafer's theory of mathematical evidence is used in conjunction with rough set and fuzzy set theories. This is used for ascertaining whether or not the behavior of the expert system is evident in the behavior of the experts which is an essential task in validating authentic reasoning expert systems. Published by Elsevier Science Inc.

Analysis by Fuzzy Difference Equations of a Model of C02 Level in the Blood

E. Y. DEEBA AND A. DE KORVIN

Department of Computer and Mathematical Sciences

University of Houston-Downtown

One Main Street, Houston, TX 77002, U.S.A.

In this paper we shall consider a model to determine the carbon dioxide (CO2) level in the blood. The model consists of a set of nonlinear difference equations. However, the linearized model will be solved. Since many measurements and factors that determine the C02 level in the blood may be imprecise, we will consider the fuzzy analog of the linearized model as a method to compensate for these imprecise measurements. We will estimate, for a fixed threshold a, a solution to the fuzzy difference equation with belief at least a. We will show that the results reduce to the classical case when the fuzzy quantities are replaced by crisp ones.

Using Fuzzy Relation Equations for Adaptive Access Control in Distributed Systems

Richard A. Alo', Ali Berrached, Andre de Korvin and Mohsen Beheshi

University of Houston-Downtown

One Main Street, Suite 722-South

Houston, Texas 77002

Current computer security systems are based on the premise that once a user presents valid credentials to the authentication system (e.g. valid ID and password), they are granted access permission to all resources assigned to the user that they claim to be. However, numerous studies have shown that most security breaches are done by unauthorized users impersonating as authorized users (e.g. by cracking or stealing passwords) or by circumventing the authentication system altogether (by exploiting security "holes" in the system). Once the authentication system is broken, the system and the information kept in it become wide open to unauthorized access and malicious usage. Moreover, because of the interdependencies among the various (computer and telecommunication) components of a distributed system, a security breach to one component can have repercussions throughout the system. The main objective of this paper is to present new security model that provides additional level of security checks based on heuristic information kept about various system components. The model allows a local host to evaluate and determine whether a remote request should be granted based on such information as the sensitivity level of the data being effected by the request,. the type of request being made, and the probability of hostility of the user making the request. Typically, such information is very difficult to determine precisely since it depends on other attributes that are themselves imprecise or only partially known. The paper presents an algorithm for generating such fuzzy information based on their dependent attributes. The method is based on using basic rules of fuzzy set theory to establish a fuzzy relation between a set of dependent fuzzy quantities. The established relation can also be updated and adapted as the base information changes.

Fuzzy Analytical Hierarchial Processes

A. de Korvin

Department of Computer and Mathematical Sciences

University of Houston Downtown, Houston, TX 77002, USA

R. Kleyle

Department of Mathematical Sciences

Indiana University - Purdue University at Indianapolis

Indianapolis, IN 46202, USA

Many problems in decision making structure reality into constituent parts, that is, into hierarchial charts in which the goal is at the top, while the decisions are at the lowest level of the chart. At the intermediate levels of the chart are the various attributes and/or conditions which must be considered in order to arrive at a decision. A rather simplified hierarchial chart is given, in which the goal, all attributes and all possible decisions occupy boxes in the hierarchial structure. The main idea in the Analytical Hierarchial Process (AHP) approach is to construct a pairwise ranking of the boxes at any given level relative to the boxes at the next highest level to which they are connected. These pairwise rankings are used to construct priorities which are then combined to create an overall priority for each course of action under consideration. The course of action with the highest priority is then chosen. Uncertainty in the assigning of priorities and the use of semantic variables in their assignment lead naturally to the inclusion of fuzzy logic into the structure of the AHP paradigm. In this paper we propose a method for using fuzzy sets in the context of the Analytical Hierarchial approach to decision making. A rather comprehensive example illustrates this method.

An Access Control Model Based on Fuzzy Set Theory

A. Berrached, M. Beheshti, A. de Korvin, R. Alo

University of Houston-Downtown

One Main Street, Suite 722-South

Houston, Texas 77002

The main objective of this paper is to present an extension to a security access control model developed by the authors for distributed systems [1]. The model allows a local host (or its security guard) to evaluate and determine whether a remote user is permitted to access and perform particular operations on particular data sets. The access control mechanisms provide an additional level of security checks based on heuristic information such as the probability of hostility of the user, the sensitivity level of the data, and the type of service being requested. Such information is usually difficult to determine precisely since it depends on other attributes that are themselves imprecise or only partially known. This paper presents an algorithm for generating such fuzzy information based on their dependent attributes. The method is based on using basic rules of fuzzy set theory to establish a fuzzy relation between a set of dependent fuzzy quantities.

Techniques And Applications Of Fuzzy Set Theory To Difference And Functional Equation And Their Utilization In Modeling Diverse Systems.

Elias Deeba, Andre de Korvin, Shishen Xie

University of Houston-Downtown

One Main Street

Houston, Texas 77002

This paper deals with the study of difference and functional equations in the setting of fuzzy theory. This study has been initiated in [1], [2], [3], and [4]. In the analysis of many systems governed by such equations, one is faced with uncertainties due to imprecise measurements or lack of complete information. Indeed, the closer one looks at a real world problem, the apparent inherent uncertainties become. Parameters such as probability distributions, metabolic rates, genetic fitness, and other measurements that arise in the modeling of problems in economics, genetics, and population dynamics are rarely precisely known. Fuzzy set theory then becomes a natural setting for the definition of such quantities.

In section II we expand our motivation of this study. We present diverse systems and show why their study in the fuzzy setting renders a better understanding of their behavior. In Section III we introduce the elements of fuzzy theory that are needed for the development of this chapter. Section IV deals with a formulation of the method for casting a functional or a difference equation in the fuzzy setting. Indeed, we will introduce the steps needed to fuzzify a functional or a difference equation and the method for solving the resulting fuzzy equations. Section V deals with the Cauchy functional equations; Section VI deals with a linear system of difference equations and its fuzzy analog.

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