DOCSLIB.ORG

Patterns of Fuzzy Rule-Based Inference Valerie Cross Systems Analysis Department, Miami University, Oxford, Ohio

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Patterns of Fuzzy Rule-Based Inference Valerie Cross Systems Analysis Department, Miami University, Oxford, Ohio Patterns of Fuzzy Rule-Based Inference Valerie Cross Systems Analysis Department, Miami University, Oxford, Ohio Thomas Sudkamp Department of Computer Science, Wright State University, Dayton, Ohio ABSTRACT Processing information in fuzzy rule-based systems generally employs one of two patterns of inference: composition or compatibility modification. Composition origi- nated as a generalization of binary logical deduction to fuzzy logic, while compatibility modification was developed to facilitate the evaluation of rules by separating the evaluation of the input from the generation of the output. The first step in compatibility modification inference is to assess the degree to which the input matches the antecedent of a rule. The result of this assessment is then combined with the consequent of the rule to produce the output. This paper examines the relationships between these two patterns of inference and establishes conditions under which they produce equivalent results. The separation of the evaluation of input from the generation of output permits a flexibility in the methods used to compare the input with the antecedent of a rule with multiple clauses. In this case, the degree to which the input and the rule antecedent match is determined by the application of a compatibility measure and an aggregation operator. The order in which these operations are applied may affect the assessment of the degree of matching, which in turn may cause the production of different results. Separability properties are introduced to define conditions under which compatibility modification inference is independent of the input evaluation strategy. KEYWORDS: fuz~ inference, compatibility measures, approximate analogi- cal reasoning, fuzzy if-then rules 1. INTRODUCTION Fuzzy set theory provides a formal system suitable for the representation of the vague, imprecise, and ambiguous information that pervades many Address correspondence to Valerie Cross, Systems Analysis Department, Miami University, Oxford, Ohio 45056. E-maiL" vcross@sasrisc, aps .muohio. edu. Received June 1993; accepted April 1994. International Journal of Approximate Reasoning 1994; 11:235-255 © 1994 Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010 0888-613X/94/$7.00 235 236 Valerie Cross and Thomas Sudkamp common problem domains. Approximate reasoning using fuzzy techniques has successfully been employed in decision theory, database retrieval, expert systems, and automatic control. The fundamental representation used in many of these applications is that of a fuzzy rule. This paper examines the foundations of the two standard patterns of fuzzy rule-based inference: composition and compatibility modification. Composition origi- nated as a generalization of binary logical deduction to fuzzy logic. Compatibility modification (CM), which was specifically developed for inference in fuzzy rule-based systems, separates the evaluation of the antecedent of a rule from the generation of the output. Compositional inference integrates the analysis of the input and the creation of the output into a single inference step. In CM inference, a compatibility measure is used to determine the degree to which the input matches the antecedent of a rule. After the analysis of the input, the output is constructed from the consequent of the rule and the degree of satisfaction of the antecedent. This paper examines the functions of these two distinct patterns of inference, analyzes their efficiency, and establishes relation- ships between them. The examination of fuzzy inference begins with a brief review of the semantics and notation of fuzzy set theory. This is followed by a presenta- tion of the principles of compositional and compatibility modification inference. These inference techniques are then compared, and conditions are established under which they produce the same results. An analysis of the generation of support in CM inference produces the notion of aggrega- tion separability. A compatibility measure and an aggregation operator are said to aggregation separable if the same result is obtained regardless of the manner in which the compatibility is evaluated. It is shown that several common families of CM inference techniques satisfy the separability condition. 2. BACKGROUND A fuzzy set A over domain U is a function /z4 : U ~ [0, 1]. The function /zA is called the membershipfunction of the fuzzy set. As a generalization of binary logic, a fuzzy set A may be considered to be a predicate. Under this interpretation, tZA(U)represents the degree to which A is satisfied by u. An alternative semantics views a fuzzy set as defining a concept. In this case, the membership function expresses the degree to which u matches the criteria that define the concept. Thus, tZA(U)indicates the similarity or the compatibility of u with the concept defined by A. The value ~A(u) = 1 indicates that u is completely compatible with the concept defined by A, while IZA(U)= 0 indicates u is incompatible with A. Patterns of Fuzzy Rule-Based Inference 237 Following the interpretation of fuzzy set theory as an extension of binary logic, the basic fuzzy set operations correspond to the propositional con- nectives. T-norms provide the fuzzy generalization of conjunction. For- mally, a T-norm is a nondecreasing, commutative, and associative function T :[0, 1] × [0, 1] ~ [0, 1] that satisfies T(0, x) = 0 and T(1, x) = x. Several common T-norms that will be used in the sequel are given in Table 1. Every T-norm T assumes values bounded by T O and T 3. That is, To(x, y) < T(x, y) < T3(x, y) for all x, y ~ [0, 1]. While many of the results in this paper hold for arbitrary T-norms, we will primarily be concerned with the Lukasiewicz T-norm T~, the product, and the minimum. Associated with each T-norm is a dual T-conorm S defined by S(x,y) = 1- T(1-x, 1--y). The T-conorm S is the disjunction that corresponds to the conjunction T. An exposition of the general properties of T-norms can be found in [1-3]. A fuzzy rule specifies an approximate conditional relationship between the elements in a universe U and those in a universe W. The relationship is indicated by a statement of the form "if X is A then Z is C" where the antecedent A is a fuzzy set over U and the consequent C is a fuzzy set over W. Fuzzy rule-based inference combines the relationship with input indicating the current state of U to produce an estimate C' of the state of W. The input is given by a fuzzy set A' over U. The use of fuzzy sets to describe the input permits the representation of imprecision in the speci- fication of the current state of knowledge of U. A fuzzy set is said to be normal if there is at least one element that has the maximal membership value 1. Normality implies that some element in the universe is completely compatible with the concept defined by the fuzzy set. A fuzzy set A is said to be precise if /zA(Ui) = 1 for some ug and tzA(U j) = 0 for all j ¢ i. Throughout this paper, A, B, and C will repre- sent fuzzy sets over the domains U = {u 1.... , un}, V = {v I ..... Urn}, and W = {w 1..... wp}, respectively. Table 1. T-Norms and T-Conorms T-norm T-conorm T3(x , y) = min(x, y) S3(x , y) = max(x, y) Tz(x, y) = xy Sz(x, y) = x + y - xy Ta(x,y) = max(x + y - 1,0) Sl(x,y) = min(1, x + y) To(x, y) = (10 ifxy=l So(x, y) = (1 ifx+y>0 otherwise. 0 otherwise 238 Valerie Cross and Thomas Sudkamp 3. COMPOSITIONAL INFERENCE The generalization of inference from bivalued logic to fuzzy logic employs a generalization of the deductive law modus ponens. Following the standard pattern of logical deduction, generalized modus ponens has the form if X is A then Z is C XisA' Z is C' producing an output fuzzy set C'. Formally, the relationship specified by the rule "if X is A then Z is C" is given by an implication relation RA _~ c over the Cartesian product U × W. An element R A __, c(U, w) indicates the degree to which the truth or presence of u implies that of w. As an extension of logical deduction, tZc,(W) = 1 whenever lZA,(U) = 1 and R A _, c(U, w) = 1. A decrease in the certainty of u or of the degree of the implication of w by u is accompa- nied by a decrease in the implied support for w. An entry R A _~ c(U, w) in the implication relation may be thought of as defining a rule "if u then w" whose strength is R A _~ c(U, w). The support for w given input tt,4,(u) is obtained by combining the degree to which u is true with the strength of the implication of w from u. The implied support T(l£A(u), R A_,c(u,w)) is the conjunction of txA,(u) and R A_~c(u,w), where the T-norm T is called the evaluator of the implication. The most frequently used compositional T-norms are the minimum and the product [4]. These choices provide alternative philosophies for determining support from uncertain inferential information. The standard fuzzy-set conjunction min assigns support based on the weaker of the two conjuncts. Employing the product is similar to support generation with certainty factors [5]: the support for the consequent is affected both by the degree of support for the premise and by the strength of the implication. The interpretation of the entries RA-.c(Ui, W), i = 1,..., n, as rules may be considered to produce a element wise "rule base" If u I then w if u, then w pertaining to w.
Load more

Recommended publications
  • The State of the Art in Developing Fuzzy Ontologies: a Survey
    The State of the Art in Developing Fuzzy Ontologies: A Survey Zahra Riahi Samani1, Mehrnoush Shamsfard2, 1Faculty of Computer Science and Engineering, Shahid Beheshti University Email:[email protected] 1Faculty of Computer Science and Engineering, Shahid Beheshti University Email:[email protected] Abstract Conceptual formalism supported by typical ontologies may not be sufficient to represent uncertainty information which is caused due to the lack of clear cut boundaries between concepts of a domain. Fuzzy ontologies are proposed to offer a way to deal with this uncertainty. This paper describes the state of the art in developing fuzzy ontologies. The survey is produced by studying about 35 works on developing fuzzy ontologies from a batch of 100 articles in the field of fuzzy ontologies. 1. Introduction Ontology is an explicit, formal specification of a shared conceptualization in a human understandable, machine- readable format. Ontologies are the knowledge backbone for many intelligent and knowledge based systems [1, 2]. However, in some domains, real world knowledge is imprecise or vague. For example in a search engine one may be interested in ”an extremely speedy, small size, not expensive car”. Classical ontologies based on crisp logic are not capable of handling this kind of knowledge. Fuzzy ontologies were proposed as a combination of fuzzy theory and ontologies to tackle such problems. On the topic of fuzzy ontology, we studied about 100 research articles which can be categorized into four main categories. The first category includes the research works on applying fuzzy ontologies in a specific domain- application to improve the performance of the application such as group decision making systems [3] or visual video content analysis and indexing [4].The ontology development parts of the works in this category were done manually or were not of much concentration.
    [Show full text]
  • The Orthogonality Between Complex Fuzzy Sets and Its Application to Signal Detection
    Article The Orthogonality between Complex Fuzzy Sets and Its Application to Signal Detection Bo Hu 1 ID , Lvqing Bi 2 and Songsong Dai 3,* ID 1 School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, China; [email protected] 2 School of Electronics and Communication Engineering, Yulin Normal University, Yulin 537000, China; [email protected] 3 School of Information Science and Engineering, Xiamen University, Xiamen 361005, China * Correspondence: [email protected]; Tel.: +86-592-258-0135 Academic Editor: Hsien-Chung Wu Received: 25 July 2017; Accepted: 25 August 2017; Published: 31 August 2017 Abstract: A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect to complex fuzzy complement, complex fuzzy union, complex fuzzy intersection, and complex fuzzy inference methods. Finally, an example application of signal detection demonstrates the utility of the orthogonality of complex fuzzy sets. Keywords: orthogonality; complex fuzzy sets; complex fuzzy operations; complex fuzzy inference 1. Introduction Complex fuzzy sets [1] are an important extension of fuzzy set theory. In recent years, complex fuzzy sets have been successfully used in complex fuzzy inference systems for various applications, such as time series prediction [2–8], function approximation [9–11], and image restoration [12,13]. A complex fuzzy set A on a universe of discourse U is a mapping from U to the unit disc in the complex plane.
    [Show full text]
  • Zerohack Zer0pwn Youranonnews Yevgeniy Anikin Yes Men
    Zerohack Zer0Pwn YourAnonNews Yevgeniy Anikin Yes Men YamaTough Xtreme x-Leader xenu xen0nymous www.oem.com.mx www.nytimes.com/pages/world/asia/index.html www.informador.com.mx www.futuregov.asia www.cronica.com.mx www.asiapacificsecuritymagazine.com Worm Wolfy Withdrawal* WillyFoReal Wikileaks IRC 88.80.16.13/9999 IRC Channel WikiLeaks WiiSpellWhy whitekidney Wells Fargo weed WallRoad w0rmware Vulnerability Vladislav Khorokhorin Visa Inc. Virus Virgin Islands "Viewpointe Archive Services, LLC" Versability Verizon Venezuela Vegas Vatican City USB US Trust US Bankcorp Uruguay Uran0n unusedcrayon United Kingdom UnicormCr3w unfittoprint unelected.org UndisclosedAnon Ukraine UGNazi ua_musti_1905 U.S. Bankcorp TYLER Turkey trosec113 Trojan Horse Trojan Trivette TriCk Tribalzer0 Transnistria transaction Traitor traffic court Tradecraft Trade Secrets "Total System Services, Inc." Topiary Top Secret Tom Stracener TibitXimer Thumb Drive Thomson Reuters TheWikiBoat thepeoplescause the_infecti0n The Unknowns The UnderTaker The Syrian electronic army The Jokerhack Thailand ThaCosmo th3j35t3r testeux1 TEST Telecomix TehWongZ Teddy Bigglesworth TeaMp0isoN TeamHav0k Team Ghost Shell Team Digi7al tdl4 taxes TARP tango down Tampa Tammy Shapiro Taiwan Tabu T0x1c t0wN T.A.R.P. Syrian Electronic Army syndiv Symantec Corporation Switzerland Swingers Club SWIFT Sweden Swan SwaggSec Swagg Security "SunGard Data Systems, Inc." Stuxnet Stringer Streamroller Stole* Sterlok SteelAnne st0rm SQLi Spyware Spying Spydevilz Spy Camera Sposed Spook Spoofing Splendide
    [Show full text]
  • Fuzzy Relational Maps and Neutrosophic Relational Maps
    University of New Mexico UNM Digital Repository Faculty and Staff Publications Mathematics 2004 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS Florentin Smarandache University of New Mexico, [email protected] W.B. Vasantha Kandasamy [email protected] Follow this and additional works at: https://digitalrepository.unm.edu/math_fsp Part of the Algebraic Geometry Commons, Analysis Commons, and the Set Theory Commons Recommended Citation W.B. Vasantha Kandasamy & F. Smarandache. FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS. Church Rock: Hexis, 2004. This Book is brought to you for free and open access by the Mathematics at UNM Digital Repository. It has been accepted for inclusion in Faculty and Staff Publications by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected], [email protected], [email protected]. W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXIS Church Rock 2004 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, India e-mail: [email protected] web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: [email protected] HEXIS Church Rock 2004 1 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 1346, Ann Arbor MI 48106-1346, USA Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co.
    [Show full text]
  • A Fuzzy-Rule Based Ontology for Urban Object Recognition
    A Fuzzy-rule Based Ontology for Urban Object Recognition Stella Marc-Zwecker, Khalid Asnoune and Cedric´ Wemmert ICube Laboratory, BFO team, University of Strasbourg, CNRS, Illkirch Cedex, Strasbourg, France Keywords: Ontologies, OWL, SWRL, Fuzzy Logic, Urban Object Recognition, Satellite Images. Abstract: In this paper we outline the principles of a methodology for semi-automatic recognition of urban objects from satellite images. The methodology aims to provide a framework for bridging the semantic gap problem. Its principle consists in linking abstract geographical domain concepts with image segments, by the means of ontologies use. The imprecision of image data and of qualitative rules formulated by experts geographers are handled by fuzzy logic mechanisms. We have defined fuzzy rules, implemented in SWRL (Semantic Web Rule Language), which allow classification of image segments in the ontology. We propose some fuzzy classification strategies, which are compared and evaluated through an experimentation performed on a VHR image of Strasbourg region. 1 INTRODUCTION of cognitive vision. Their approach relies on an on- tology of visual concepts, such as colour and texture, In the domain of knowledge representation for image which can be seen as an intermediate layer between recognition, we outline the principles of a method- domain knowledge and image processing procedures. ology for semi-automatic extraction of urban objects However, this kind of learning system requires that from Very High Resolution (VHR) satellite images. the expert produces examples for each of the concepts This methodology relies on the design and implemen- he is looking for.(Athanasiadis et al., 2007) present a tation of ontologies, which are an effective tool for framework for both image segmentation and object domain’s knowledge formalization and exploitation labeling using an ontology in the domain of multime- (Gruber, 1993) and for the implementation of reason- dia analysis.
    [Show full text]
  • Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic
    NASA Conference Publication 10111 Proceedings of the Third - _ International Workshop on Neural Networks and T_ Fuzzy Logic , k ('_ASA-CP-1OIII-Vol-2) PRQCEEOINGS N93-22206 i]F ThE TH[_O INTERNATIONAL WORKSHOP --THRU-- ON NEURAL NETWORKS AND FUZZY LOGIC, N93-22223 V_LU_E 2 (NASA) i83 p Unclas Volume II G3/63 0150400 a workshop held at ,nson Space Center Houston, Texas June 1 - 3, 1992 p_ _q_r NASA Conference Publication 10111 Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic Volume II Christopher J. Culbert, Editor NASA Lyndon B. Johnson Space Center Houston, Texas Proceedings of a workshop held at Lyndon B. Johnson Space Center Houston, Texas June 1 - 3, 1992 National Aeronautics and Space Administration January 1993 THIRD INTERNATIONAL WORKSHOP ON NEURAL NETWORKS AND FUZZY LOGIC Program Schedule Monday June 1, 1992 7:30-8:00 Registration 8:00-8:30 Robed T. Savely, Chief Scientist, Information Systems Directorate, NASA/Lyndon B. Johnson Space Center, Houston, TX. Welcoming Remarks. 8:30-9:30 Jon Erickson, Chief Scientist, Automation and Robotics Division, NASNLyndon B. Johnson Space Center, Houston, TX. Space Exploration Needs for Supervised Intelligent Systems. 9:30-9:45 Break Plenary Speakers 9:45-10:30 Piero P. Bonnisone, General Electric, Fuzzy Logic Controllers: A Knowledge-Based Systems Perspective. 10:30-11:15 Robed Farber, Los Alamos National Laboratory, Efficiently Modeling Neural Networks on Massively Parallel Computers. 11:15-1:00 Lunch pRLI_EOING P.._SE BLANK NOT RLMIED iii. w 1:00-1:30 Lawrence O. Hall and Steve G. Romaniuk, University of South Florida, Learning Fuzzy Information in a Hybrid Connectionist, Symbolic Model.
    [Show full text]
  • Fuzzy Sets, Fuzzy Logic and Their Applications • Michael Gr
    Fuzzy Sets, Fuzzy Logic and Their Applications • Michael Gr. Voskoglou • Michael Gr. Fuzzy Sets, Fuzzy Logic and Their Applications Edited by Michael Gr. Voskoglou Printed Edition of the Special Issue Published in Mathematics www.mdpi.com/journal/mathematics Fuzzy Sets, Fuzzy Logic and Their Applications Fuzzy Sets, Fuzzy Logic and Their Applications Special Issue Editor Michael Gr. Voskoglou MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editor Michael Gr. Voskoglou Graduate Technological Educational Institute of Western Greece Greece Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Mathematics (ISSN 2227-7390) (available at: https://www.mdpi.com/journal/mathematics/special issues/Fuzzy Sets). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03928-520-4 (Pbk) ISBN 978-3-03928-521-1 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Preface to ”Fuzzy Sets, Fuzzy Logic and Their Applications” ...................
    [Show full text]
  • An Introduction to Fuzzy & Annotated Semantic Web Languages Arxiv
    An Introduction to Fuzzy & Annotated Semantic Web Languages∗ Umberto Straccia ISTI - CNR, Pisa, ITALY [email protected] Abstract We present the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may generalise them to so-called annotation domains, that cover also e.g. temporal and provenance extensions. 1 Introduction Managing uncertainty and fuzziness is growing in importance in Semantic Web re- search as recognised by a large number of research efforts in this direction [279, 285, 287, 288, 291]. Semantic Web Languages (SWL) are the languages used to provide a formal description of concepts, terms, and relationships within a given domain, among which the OWL 2 family of languages [221], triple languages RDF & RDFS [64] and rule languages (such as RuleML [138], Datalog± [68] and RIF [237]) are major players. While their syntactic specification is based on XML [313], their semantics is based arXiv:1811.05724v1 [cs.AI] 14 Nov 2018 on logical formalisms: briefly, • RDFS is a logic having intensional semantics and the logical counterpart is ρdf [219]; ∗This is an updated version of [291] and acts as accompanying material to my invited talk and slides at the 2018 Artificial Intelligence International Conference (A2IC-18). 1 • OWL 2 is a family of languages that relate to Description Logics (DLs) [4]; • rule languages relate roughly to the Logic Programming (LP) paradigm [177]; • both OWL 2 and rule languages have an extensional semantics.
    [Show full text]
  • Fuzzy Inference Systems for Risk Appraisal in Military Operational Planning Curtis B
    Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-21-2019 Fuzzy Inference Systems for Risk Appraisal in Military Operational Planning Curtis B. Nelson Follow this and additional works at: https://scholar.afit.edu/etd Part of the Operations and Supply Chain Management Commons Recommended Citation Nelson, Curtis B., "Fuzzy Inference Systems for Risk Appraisal in Military Operational Planning" (2019). Theses and Dissertations. 2311. https://scholar.afit.edu/etd/2311 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. FUZZY INFERENCE SYSTEMS FOR RISK APPRAISAL IN MILITARY OPERATIONAL PLANNING THESIS Curtis B. Nelson, Major, USA AFIT-ENS-MS-19-M-141 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A. APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Army, United States Air Force, Department of Defense, or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENS-MS-19-M-141 FUZZY INFERENCE SYSTEMS FOR RISK APRAISAL IN MILITARY OPERATIONAL PLANNING THESIS Presented to the Faculty Department of Operational Sciences Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command In Partial Fulfillment of the Requirements for the Degree of Master of Science in Operations Research Curtis B.
    [Show full text]
  • A Fuzzy Model for Representing Uncertain, Subjective and Vague Temporal Knowledge in Ontologies
    A Fuzzy Model for Representing Uncertain, Subjective and Vague Temporal Knowledge in Ontologies G´abor Nagyp´aland Boris Motik FZI Research Center for Information Technologies at the University of Karlsruhe? Haid-und-Neu-Str. 10-14 76131 Karlsruhe, Germany fnagypal,[email protected] http://www.fzi.de Abstract. Time modeling is a crucial feature in many application do- mains. However, temporal information often is not crisp, but is uncertain, subjective and vague. This is particularly true when representing histori- cal information, as historical accounts are inherently imprecise. Similarly, we conjecture that in the Semantic Web representing uncertain temporal information will be a common requirement. Hence, existing approaches for temporal modeling based on crisp representation of time cannot be applied to these advanced modeling tasks. To overcome these difficulties, in this paper we present fuzzy interval-based temporal model capable of representing imprecise temporal knowledge. Our approach naturally subsumes existing crisp temporal models, i.e. crisp temporal relation- ships are intuitively represented in our system. Apart from presenting the fuzzy temporal model, we discuss how this model is integrated with the ontology model to allow annotating ontology definitions with time specifications. 1 Introduction Time modeling is a crucial feature in many application domains, such as medicine, history, criminal and financial applications. Its importance is shown by the nu- merous works in the area of temporal databases [1, 2] and temporal reasoning [3]. Our experience from the EU-IST sponsored VICODI project1 supports this claim fully. The main aim of this project is to develop an ontology of European history used for semantical indexing of historical documents.
    [Show full text]
  • The Implementation of Intelligent Oos Networking by the Development
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2003 The Implementation of Intelligent QoS Networking by the Development and Utilization of Novel Cross-Disciplinary Soft Computing Theories and Techniques Ahmed Shawky Moussa Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES THE IMPLEMENTATION OF INTELLIGENT QoS NETWORKING BY THE DEVELOPMENT AND UTILIZATION OF NOVEL CROSS-DISCIPLINARY SOFT COMPUTING THEORIES AND TECHNIQUES By AHMED SHAWKY MOUSSA A Dissertation submitted to the Department of Computer Science In partial fulfillment of the requirements for The degree of Doctor of Philosophy Degree Awarded: Fall Semester, 2003 The members of the committee approve the dissertation of Ahmed Shawky Moussa Defended on September 19, 2003. ______________________ Ladislav Kohout Major Professor ______________________ Michael Kasha Outside Committee Member ______________________ Lois Wright Hawkes Committee Member ______________________ Ernest McDuffie Committee Member ______________________ Xin Yuan Committee Member The Office of Graduate Studies has verified and approved the above named committee members ii Optimization is not just a technique, or even a whole science; it is an attitude and a way of life. My mother’s life is a great example of optimization, making the best out of every thing, sometimes out of nothing. She has also been the greatest example of sacrifice, dedication, selfishness, and many other qualities, more than can be listed. I dedicate this work and all my past and future works to the strongest person I have ever known, the one who taught me, by example, what determination is, Fawkeya Ibrahim, my mother.
    [Show full text]
  • Fuzzy Inference Engi
    Blending Methodologies for Optimizing Fuzzy Inference Engine Designs Rob Chapman, Adam F. Gobi and Witold Pedrycz Department of Electrical and Computer Engineering University of Alberta Edmonton, AB T6G 2V4 {rchapman,gobia,pedrycz}@ece.ualberta.ca Abstract -- The software paradigm of writing sequential pro- the rooms, but you can not easily change the number of rooms, gramming tasks executed on a single processor has pervaded turrets or add other novel structures. computers since their dawning. In spite of progress, sequential Our development platform is a granular computer (GC): a execution of certain algorithms remain limited by this paradigm. flexible architecture and methodology for combining software In particular, fuzzy control systems involve fuzzy set operations programs and hardware engines in programmable hardware. which require significant amounts of vector and matrix computa- This ability to blend the domains of software and hardware, as tion. This computation can be considered an inherently parallel task, and performing these operations in software results in ineffi- well as program with data, will be exploited later in the paper. cient execution, severely limiting the use of fuzzy operations in The GC model for programming is a simplified, parameter- real-time systems where fast responses are required. This paper ized processor with no instruction set. As part of a design, will explore solutions to this problem using software, hardware instructions and instruction sequences, known as primitives, and finally a hybrid approach with a proposed computing archi- are either created or included from a library set, and are used to tecture and platform known as a granular computer (GC). construct sequential programs.
    [Show full text]