Comparing Fuzzy Graphs
|
|
- Theodore Watkins
- 6 years ago
- Views:
Transcription
1 Comparing Fuzzy Graphs Michael R. Berthold! and Klaus-Peter Huber 2 1 Department of EECS Computer Science Division University of California at Berkeley Berkeley, CA 94720, USA bertholdclca. berkeley. edu 2 IRF (Prof. D. Schmid) Fakultiit fur Informatik U niversitat Karlsruhe P.O. Box 6980, Karlsruhe kphuberclira.ulta.de Abstract. This paper investigates techniques to compare two fuzzy graphs. Fuzzy graphs have raised increasing attention, because they not only allow an easy interpretation but in addition finding regions of interest or tolerating missing attributes can be done computationally very efficiently. This is of great interest in numerous applications, for example Intelligent Data Analysis, Metamodeling and others. In this paper a computationally efficient way to compare two fuzzy graphs is presented. 1 Introduction Fuzzy graphs [9J have recently raised increasing attention, especially in areas where understandable models are needed. In contrast to grid-based approaches fuzzy graphs allow to represent also complex relationships using only few elements, so-called fuzzy points. Since those models are often built from large amounts of data, a manual analysis is not feasible anymore. Also for applications where data is recorded online there is a need for continuous, automatic analysis. Recently an algorithm was proposed [1,41 that automatically builds a fuzzy graph from example data. Several properties of this approach make it well-suited for the automatic analysis of data. The usage of fuzzy concepts allows to hide information the user is not interested in (in/ormation granulation) and also offers an easy way to interpret the resulting fuzzy function in terms of fuzzy points or understandable if- then-rules. Also several operations on these fuzzy graphs can be done in computationally very efficient ways. In [2] for example, it was shown how missing values can be tolerated with almost no computational cost in a fuzzy environment. 234
2 In real applications it is very desirable to use the generated models for further analysis. For example finding extrema of the model function can be useful to determine parameter settings that should be avoided. Also the comparison of different models is of interest, to either judge the influence of modifications or simply the quality of the generated models itself. In theory the analysis of the models does not cause problems, but finding ways for the actual implementation is crucial for real applications. In the following it is discussed how fuzzy graphs can be compared to each other in a computationally efficient way. 2 Fuzzy Graphs In the following the concept of fuzzy graphs will be used to represent a system to approximate one output variable y depending on n input variables x, (1 ::; i ::; n). The typical fuzzy graph builds upon fuzzy points of the type if XI is Al and... and Xn is An then y is B where some of the input membership functions A, can be constant; that is, /-la, == 1. Thus different fuzzy points may only depend on a small subset of input variables. Simplifying this equation, using A = Al X. x An (x denotes the cartesian product), leads to: if ~ is A then y is B which 'can also be expressed as a fuzzy constraint on a joint variable (~,y); that is, (~,y) is A x B The membership function of Ax B is given using II as a conjunction operator which is usually defined as the minimum: or, more precisely I-'AxB(~' y) = J-IAI (xd /\... /\ PAn(Xn) /\ J-IB(Y) = min {J-IAI (XI)" ", PAn (Xn), /-lb{y)} Zadeh [8J uses the term fuzzy point to denote A x B. Often trapezoidal fuzzy points are used, which can be specified through the comers of their support- and core-region: < a, b, c, d >. The core-rectangle is defined through the lower left corner b and the upper right comer c. Similar the support-region is defined through a and d. 235
3 Figure 1: Intersection of a fuzzy graph with the cylindrical extension of A.. A collection of fuzzy points can now be regarded as forming a superposition of n fuzzy points: (x, y) is (AI X Bl Am X Bm) where + denotes the disjunction operator (usually defined as maximum). Zadeh calls this characterization of a dependency Fuzzy Graph, because the collection of rules can be seen as a coarse representation of a functional dependency f of y on x. This fuzzy graph f is thus defined through: m f = LAj x Bj ;=1 In the following we will concentrate on Fuzzy Graphs for the approximate representation of functions. The task of interpolation; that is, deriving a linguistic value B for y given an arbitrary linguistic value A for x and a fuzzy graph f: x is A f is Ei=IAj x Bj y is B This results in an intersection of the fuzzy graph f with a cylindrical extension of the input fuzzy set A. Figure 1 shows an example. The corresponding functional dependency can be computed through: J.LB ==f(a)(y) = sup{j.l/(x, y) /\ J.LA(X)} z = sup {(J.LAt XBI (x, y) V... V J.LA.xB. (x, V)) /\ J.LA(X)}., Note that individual rules do not depend on a common set of membership functions on the input variables because each fuzzy point is described through an individual set of membership functions. Therefore each fuzzy point can closely adapt to the underlying model function, making the resulting fuzzy graphs a very compact description, especially 236
4 compared to the approaches that use a "global grid", defined through only one set of membership functions for each input variable [3,5-7]. An algorithm that automatically constructs this kind of fuzzy graphs based on trapezoidal fuzzy points from example data was proposed in [1]. 3 Similarity of Fuzzy Graphs In technical applications fuzzy graphs may be used for model analysis or process control tasks. Often the generated fuzzy graph or fuzzy model is only validated or tested by some data sets using cross-validation, but this approach does not deliver insights into the behaviour. Therefore there is a need for structural methods to describe, compare and analyze several different fuzzy graphs, that may originate from different experiments or datasets. Here a way is presented to compare two fuzzy graphs. Comparing two fuzzy graphs should result in a degree of match. In most cases, however, it is also of interest if and how much the two graphs overlap. Therefore three different measurements are defined to compare two fuzzy graphs 11 and 12, based on their volume vol(j) := f 1l,{X,y)dxdy: - similarity: - overlap: - coverage: 2,vo/(11 nh) 8(11, h) := vo/(jd + vol(h) 0(1!:).= vol(fi n h) h 2 vol (h).= vol(fl n h) C(f J) h 2 vol(ft) where obviously O(Jb h) = C(h. 11); that is, if h overlaps 12, 12 is covered by It. Methods to efficiently compute the volume of one fuzzy point exist when trapezoidal membership functions are used, as is the case for the type of fuzzy graphs considered here: To compute the volume of the entire fuzzy graph the volumes of all fuzzy points are added up, ignoring possible overlaps. This is a similar approach to the Center of Gravity 237
5 Defuzzification, because regions of overlap are weighted proportional to the amount of overlap. The remaining problem, that is, the efficient computation of the intersection of two fuzzy graphs is relatively complicated, because the resulting fuzzy graph consists of fuzzy points that are not necessarily normalized or even trapezoidal. But for comparison of two fuzzy graphs it is sufficient to compute the volume of the intersection of both: For practical applications it is neccesary to compute this volume efficiently. For the precise calculation no efficient method is known, but a simple approximation can be used to compute the volume of the intersection of two fuzzy points, based on a granularization in several alpha-cuts. The alpha-cut for two intersecting fuzzy points p =< a, b, e, d > and p' =< a', b', c', d' > is equal to the rectangle: na(p,p') = [max{a + a(b - a), a' + a(b' - a ' )}, max{d - a(d - e), d' + a(d' - c')}] The correct solution for the volume of the intersection can be expressed as: 1/<-1 1 ) vol(p np') = lim L f (n(k+l)<(p,p') + -2 (n(k+l)'(p,p') - nk,(p,p'» <-+0 "",0 where the volume of the intersection is divided into l/f slices, whose volume is then added together. The correct solution is achieved by letting f go towards zero. For practical purposes a finite f can be chosen, depending on the desired accuracy. A nice property of.this approach is the ability to compute an upper bound for the resulting error, depending on the granularization f: 1/,-1 err.(pnp')::: L f (n(k+~).(p,p') - nk«p,p')) "=0 which approaches zero for f going towards zero, as should be expected. This approximation can then be used to compare two fuzzy graphs by adding up the intersection of all pairwise combinations of fuzzy points. Again, as in the computation of the volume of a fuzzy graph, areas of overlap are included multiple times. This methodology allows to compute measurements to compare two fuzzy graphs based on trapezoidal fuzzy points computationally efficient with an additional indicator of the maximum error of the used approximation. 238
6 4 Conclusions Since fuzzy graphs can be constructed from data and allow a compact representation of functions a structure based analysis is needed. Here, it was discussed how fuzzy graphs can be compared in a computationally efficient way. In addition to tolerating missing values which was presented in previous work, it is also possible to compute the volume of the. intersection of two fuzzy graphs efficiently when both graphs are based on trapezoidal fuzzy points. This allows to compute three different measures to compare two fuzzy graphs, namely similarity, overlap, and coverage. Acknowledgments M. Berthold was supported by a stipend of the "Gemeinsame Hochschulsonderprogramm III von Bund und Liindern" through the DAAD. Literature [1] Michael R. Berthold and Klaus-Peter Huber. Building fuzzy graphs from examples. In IEEE International Conference on Fuzzy Systems, 1, pages , September [2) Michael R. Berthold and Klaus-Peter Huber. Missing values and learning of fuzzy rules. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, [3] Charles M. Higgins and Rodney M. Goodman. Learning fuzzy rule-based neural networks for control. In Advances in Neural Information Processing Systems, 5, pages , California, Morgan Kaufmann. [4] Klaus-Peter Huber and Michael R. Berthold. Simulation data analysis using fuzzy graphs. In Xiaohui Liu, Paul Cohen, and Michael Berthold, editors, Advances in Intelligent Data Analysis - Reasoning about Data, LNCSI280, pages Springer Verlag, [5] Patrick K. Simpson. Fuzzy min-max neural networks - part 1: Classification. IEEE 1ransactions on Neural Networks, 3(5): , September [6J Patrick K. Simpson. Fuzzy min-max neural networks - part 2: Clustering. IEEE 7ransactions on Fuzzy Systems, 1(1):32-45, January [7J Li-Xin Wang and Jerry M. Mendel. Generating rules by learning from examples. In International Symposium on Intelligent Control, pages IEEE,
7 [8] Lotfi A. Zadeh. Soft computing and fuzzy logic. IEEE Software, pages 48~ 56, November [9] Lotfi A. Zadeh. Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs: A precis. Multi. Val. Logic, 1:1-38,
MISSING VALUES AND LEARNING OF FUZZY RULES MICHAEL R. BERTHOLD. Computer Science Division, Department of EECS
MISSING VALUES AND LEARNING OF FUZZY RULES MICHAEL R. BERTHOLD Computer Science Division, Department of EECS University of California, Bereley, CA 94720, USA email: Michael.Berthold@Informati.Uni-Karlsruhe.DE
More informationWhat is all the Fuzz about?
What is all the Fuzz about? Fuzzy Systems CPSC 433 Christian Jacob Dept. of Computer Science Dept. of Biochemistry & Molecular Biology University of Calgary Fuzzy Systems in Knowledge Engineering Fuzzy
More informationConstructing fuzzy graphs from examples
Constructing fuzzy graphs from examples Michael R. Berthold a, *, Klaus-Peter Huber b,1 a Berkeley Initiative in Soft Computing, Computer Science Division, Department of EECS, 329 Soda Hall, University
More informationWhat is all the Fuzz about?
What is all the Fuzz about? Fuzzy Systems: Introduction CPSC 533 Christian Jacob Dept. of Computer Science Dept. of Biochemistry & Molecular Biology University of Calgary Fuzzy Systems in Knowledge Engineering
More informationFuzzy Systems. Fuzzy Systems in Knowledge Engineering. Chapter 4. Christian Jacob. 4. Fuzzy Systems. Fuzzy Systems in Knowledge Engineering
Chapter 4 Fuzzy Systems Knowledge Engeerg Fuzzy Systems Christian Jacob jacob@cpsc.ucalgary.ca Department of Computer Science University of Calgary [Kasabov, 1996] Fuzzy Systems Knowledge Engeerg [Kasabov,
More informationLearning Fuzzy Rule-Based Neural Networks for Control
Learning Fuzzy Rule-Based Neural Networks for Control Charles M. Higgins and Rodney M. Goodman Department of Electrical Engineering, 116-81 California Institute of Technology Pasadena, CA 91125 Abstract
More informationNetworks for Control. California Institute of Technology. Pasadena, CA Abstract
Learning Fuzzy Rule-Based Neural Networks for Control Charles M. Higgins and Rodney M. Goodman Department of Electrical Engineering, 116-81 California Institute of Technology Pasadena, CA 91125 Abstract
More informationFUZZY BOOLEAN ALGEBRAS AND LUKASIEWICZ LOGIC. Angel Garrido
Acta Universitatis Apulensis ISSN: 1582-5329 No. 22/2010 pp. 101-111 FUZZY BOOLEAN ALGEBRAS AND LUKASIEWICZ LOGIC Angel Garrido Abstract. In this paper, we analyze the more adequate tools to solve many
More informationLecture notes. Com Page 1
Lecture notes Com Page 1 Contents Lectures 1. Introduction to Computational Intelligence 2. Traditional computation 2.1. Sorting algorithms 2.2. Graph search algorithms 3. Supervised neural computation
More informationRough Sets, Neighborhood Systems, and Granular Computing
Rough Sets, Neighborhood Systems, and Granular Computing Y.Y. Yao Department of Computer Science University of Regina Regina, Saskatchewan, Canada S4S 0A2 E-mail: yyao@cs.uregina.ca Abstract Granulation
More informationClassification with Diffuse or Incomplete Information
Classification with Diffuse or Incomplete Information AMAURY CABALLERO, KANG YEN Florida International University Abstract. In many different fields like finance, business, pattern recognition, communication
More informationReview of Fuzzy Logical Database Models
IOSR Journal of Computer Engineering (IOSRJCE) ISSN: 2278-0661, ISBN: 2278-8727Volume 8, Issue 4 (Jan. - Feb. 2013), PP 24-30 Review of Fuzzy Logical Database Models Anupriya 1, Prof. Rahul Rishi 2 1 (Department
More informationSome Properties of Intuitionistic. (T, S)-Fuzzy Filters on. Lattice Implication Algebras
Theoretical Mathematics & Applications, vol.3, no.2, 2013, 79-89 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2013 Some Properties of Intuitionistic (T, S)-Fuzzy Filters on Lattice Implication
More informationChapter 4 Fuzzy Logic
4.1 Introduction Chapter 4 Fuzzy Logic The human brain interprets the sensory information provided by organs. Fuzzy set theory focus on processing the information. Numerical computation can be performed
More informationMODELING FOR RESIDUAL STRESS, SURFACE ROUGHNESS AND TOOL WEAR USING AN ADAPTIVE NEURO FUZZY INFERENCE SYSTEM
CHAPTER-7 MODELING FOR RESIDUAL STRESS, SURFACE ROUGHNESS AND TOOL WEAR USING AN ADAPTIVE NEURO FUZZY INFERENCE SYSTEM 7.1 Introduction To improve the overall efficiency of turning, it is necessary to
More informationFuzzy Reasoning. Outline
Fuzzy Reasoning Outline Introduction Bivalent & Multivalent Logics Fundamental fuzzy concepts Fuzzification Defuzzification Fuzzy Expert System Neuro-fuzzy System Introduction Fuzzy concept first introduced
More informationIntroduction 2 Fuzzy Sets & Fuzzy Rules. Aleksandar Rakić Contents
Beograd ETF Fuzzy logic Introduction 2 Fuzzy Sets & Fuzzy Rules Aleksandar Rakić rakic@etf.rs Contents Characteristics of Fuzzy Sets Operations Properties Fuzzy Rules Examples 2 1 Characteristics of Fuzzy
More informationFUZZY INFERENCE SYSTEMS
CHAPTER-IV FUZZY INFERENCE SYSTEMS Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can
More informationFUZZY INFERENCE. Siti Zaiton Mohd Hashim, PhD
FUZZY INFERENCE Siti Zaiton Mohd Hashim, PhD Fuzzy Inference Introduction Mamdani-style inference Sugeno-style inference Building a fuzzy expert system 9/29/20 2 Introduction Fuzzy inference is the process
More informationInternational Journal of Scientific & Engineering Research, Volume 7, Issue 2, February ISSN
International Journal of Scientific & Engineering Research, Volume 7, Issue 2, February-2016 149 KEY PROPERTIES OF HESITANT FUZZY SOFT TOPOLOGICAL SPACES ASREEDEVI, DRNRAVI SHANKAR Abstract In this paper,
More informationFUNDAMENTALS OF FUZZY SETS
FUNDAMENTALS OF FUZZY SETS edited by Didier Dubois and Henri Prade IRIT, CNRS & University of Toulouse III Foreword by LotfiA. Zadeh 14 Kluwer Academic Publishers Boston//London/Dordrecht Contents Foreword
More informationChapter 7 Fuzzy Logic Controller
Chapter 7 Fuzzy Logic Controller 7.1 Objective The objective of this section is to present the output of the system considered with a fuzzy logic controller to tune the firing angle of the SCRs present
More informationSimilarity Measures of Pentagonal Fuzzy Numbers
Volume 119 No. 9 2018, 165-175 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Similarity Measures of Pentagonal Fuzzy Numbers T. Pathinathan 1 and
More informationA Brief Idea on Fuzzy and Crisp Sets
International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) A Brief Idea on Fuzzy and Crisp Sets Rednam SS Jyothi 1, Eswar Patnala 2, K.Asish Vardhan 3 (Asst.Prof(c),Information Technology,
More informationThe Travelling Salesman Problem. in Fuzzy Membership Functions 1. Abstract
Chapter 7 The Travelling Salesman Problem in Fuzzy Membership Functions 1 Abstract In this chapter, the fuzzification of travelling salesman problem in the way of trapezoidal fuzzy membership functions
More informationCHAPTER 4 FREQUENCY STABILIZATION USING FUZZY LOGIC CONTROLLER
60 CHAPTER 4 FREQUENCY STABILIZATION USING FUZZY LOGIC CONTROLLER 4.1 INTRODUCTION Problems in the real world quite often turn out to be complex owing to an element of uncertainty either in the parameters
More informationApproximation of Multiplication of Trapezoidal Epsilon-delta Fuzzy Numbers
Advances in Fuzzy Mathematics ISSN 973-533X Volume, Number 3 (7, pp 75-735 Research India Publications http://wwwripublicationcom Approximation of Multiplication of Trapezoidal Epsilon-delta Fuzzy Numbers
More informationANFIS: ADAPTIVE-NETWORK-BASED FUZZY INFERENCE SYSTEMS (J.S.R. Jang 1993,1995) bell x; a, b, c = 1 a
ANFIS: ADAPTIVE-NETWORK-ASED FUZZ INFERENCE SSTEMS (J.S.R. Jang 993,995) Membership Functions triangular triangle( ; a, a b, c c) ma min = b a, c b, 0, trapezoidal trapezoid( ; a, b, a c, d d) ma min =
More informationFUZZY SPECIFICATION IN SOFTWARE ENGINEERING
1 FUZZY SPECIFICATION IN SOFTWARE ENGINEERING V. LOPEZ Faculty of Informatics, Complutense University Madrid, Spain E-mail: ab vlopez@fdi.ucm.es www.fdi.ucm.es J. MONTERO Faculty of Mathematics, Complutense
More informationfuzzylite a fuzzy logic control library in C++
fuzzylite a fuzzy logic control library in C++ Juan Rada-Vilela jcrada@fuzzylite.com Abstract Fuzzy Logic Controllers (FLCs) are software components found nowadays within well-known home appliances such
More informationFuzzy Systems (1/2) Francesco Masulli
(1/2) Francesco Masulli DIBRIS - University of Genova, ITALY & S.H.R.O. - Sbarro Institute for Cancer Research and Molecular Medicine Temple University, Philadelphia, PA, USA email: francesco.masulli@unige.it
More informationAN APPROXIMATION APPROACH FOR RANKING FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE 1.INTRODUCTION
Mathematical and Computational Applications, Vol. 16, No. 3, pp. 588-597, 2011. Association for Scientific Research AN APPROXIMATION APPROACH FOR RANKING FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE
More informationAmerican International Journal of Research in Science, Technology, Engineering & Mathematics
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
More informationIntegration of Fuzzy Shannon s Entropy with fuzzy TOPSIS for industrial robotic system selection
JIEM, 2012 5(1):102-114 Online ISSN: 2013-0953 Print ISSN: 2013-8423 http://dx.doi.org/10.3926/jiem.397 Integration of Fuzzy Shannon s Entropy with fuzzy TOPSIS for industrial robotic system selection
More informationA New Method For Forecasting Enrolments Combining Time-Variant Fuzzy Logical Relationship Groups And K-Means Clustering
A New Method For Forecasting Enrolments Combining Time-Variant Fuzzy Logical Relationship Groups And K-Means Clustering Nghiem Van Tinh 1, Vu Viet Vu 1, Tran Thi Ngoc Linh 1 1 Thai Nguyen University of
More informationAvailable online at ScienceDirect. Procedia Computer Science 96 (2016 )
Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 96 (2016 ) 179 186 20th International Conference on Knowledge Based and Intelligent Information and Engineering Systems,
More informationFuzzy Transportation Problems with New Kind of Ranking Function
The International Journal of Engineering and Science (IJES) Volume 6 Issue 11 Pages PP 15-19 2017 ISSN (e): 2319 1813 ISSN (p): 2319 1805 Fuzzy Transportation Problems with New Kind of Ranking Function
More informationSimultaneous Perturbation Stochastic Approximation Algorithm Combined with Neural Network and Fuzzy Simulation
.--- Simultaneous Perturbation Stochastic Approximation Algorithm Combined with Neural Networ and Fuzzy Simulation Abstract - - - - Keywords: Many optimization problems contain fuzzy information. Possibility
More informationGranular Computing: A Paradigm in Information Processing Saroj K. Meher Center for Soft Computing Research Indian Statistical Institute, Kolkata
Granular Computing: A Paradigm in Information Processing Saroj K. Meher Center for Soft Computing Research Indian Statistical Institute, Kolkata Granular computing (GrC): Outline Introduction Definitions
More informationNeural Networks Lesson 9 - Fuzzy Logic
Neural Networks Lesson 9 - Prof. Michele Scarpiniti INFOCOM Dpt. - Sapienza University of Rome http://ispac.ing.uniroma1.it/scarpiniti/index.htm michele.scarpiniti@uniroma1.it Rome, 26 November 2009 M.
More informationUsing Decision Boundary to Analyze Classifiers
Using Decision Boundary to Analyze Classifiers Zhiyong Yan Congfu Xu College of Computer Science, Zhejiang University, Hangzhou, China yanzhiyong@zju.edu.cn Abstract In this paper we propose to use decision
More informationA Logic Language of Granular Computing
A Logic Language of Granular Computing Yiyu Yao and Bing Zhou Department of Computer Science University of Regina Regina, Saskatchewan, Canada S4S 0A2 E-mail: {yyao, zhou200b}@cs.uregina.ca Abstract Granular
More informationModeling the Real World for Data Mining: Granular Computing Approach
Modeling the Real World for Data Mining: Granular Computing Approach T. Y. Lin Department of Mathematics and Computer Science San Jose State University San Jose California 95192-0103 and Berkeley Initiative
More informationGenetic Tuning for Improving Wang and Mendel s Fuzzy Database
Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA - October 2009 Genetic Tuning for Improving Wang and Mendel s Fuzzy Database E. R. R. Kato, O.
More informationAssessment of Human Skills Using Trapezoidal Fuzzy Numbers (Part II)
American Journal of Computational and Applied Mathematics 05, 5(5): 54-58 DOI: 0.593/j.ajcam.050505.04 Assessment of Human Skills Using Trapezoidal Fuzzy Numbers (Part II) Michael Gr. Voskoglou Department
More informationChapter 2: FUZZY SETS
Ch.2: Fuzzy sets 1 Chapter 2: FUZZY SETS Introduction (2.1) Basic Definitions &Terminology (2.2) Set-theoretic Operations (2.3) Membership Function (MF) Formulation & Parameterization (2.4) Complement
More informationIJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 3, May
Optimization of fuzzy assignment model with triangular fuzzy numbers using Robust Ranking technique Dr. K. Kalaiarasi 1,Prof. S.Sindhu 2, Dr. M. Arunadevi 3 1 Associate Professor Dept. of Mathematics 2
More informationApplication of fuzzy set theory in image analysis. Nataša Sladoje Centre for Image Analysis
Application of fuzzy set theory in image analysis Nataša Sladoje Centre for Image Analysis Our topics for today Crisp vs fuzzy Fuzzy sets and fuzzy membership functions Fuzzy set operators Approximate
More informationSubsampling Conflicts to Construct Better Fuzzy Rules
Subsampling Conflicts to Construct Better Fuzzy Rules Michael R. Berthold Tripos, Inc. 601 Gateway Blvd., Suite 720 South San Francisco, CA 94080, USA email: berthold@tripos. com Abstract Many fuzzy rule
More informationRough Approximations under Level Fuzzy Sets
Rough Approximations under Level Fuzzy Sets W.-N. Liu J.T. Yao Y.Y.Yao Department of Computer Science, University of Regina Regina, Saskatchewan, Canada S4S 0A2 E-mail: [liuwe200, jtyao, yyao]@cs.uregina.ca
More informationIntroduction to Intelligent Control Part 3
ECE 4951 - Spring 2010 Introduction to Part 3 Prof. Marian S. Stachowicz Laboratory for Intelligent Systems ECE Department, University of Minnesota Duluth January 26-29, 2010 Part 1: Outline TYPES OF UNCERTAINTY
More informationRESULTS ON HESITANT FUZZY SOFT TOPOLOGICAL SPACES
ISSN 2320-9143 1 International Journal of Advance Research, IJOAR.org Volume 4, Issue 3, March 2016, Online: ISSN 2320-9143 RESULTS ON HESITANT FUZZY SOFT TOPOLOGICAL SPACES A. Sreedevi, Dr.N.Ravi Shankar
More informationAssessment of Human Skills Using Trapezoidal Fuzzy Numbers
American Journal of Computational and Applied Mathematics 2015, 5(4): 111-116 DOI: 10.5923/j.ajcam.20150504.03 Assessment of Human Skills Using Trapezoidal Fuzzy Numbers Michael Gr. Voskoglou Department
More informationTable of Contents. Recognition of Facial Gestures... 1 Attila Fazekas
Table of Contents Recognition of Facial Gestures...................................... 1 Attila Fazekas II Recognition of Facial Gestures Attila Fazekas University of Debrecen, Institute of Informatics
More informationOn Generalizing Rough Set Theory
On Generalizing Rough Set Theory Y.Y. Yao Department of Computer Science, University of Regina Regina, Saskatchewan, Canada S4S 0A2 E-mail: yyao@cs.uregina.ca Abstract. This paper summarizes various formulations
More informationRanking of Generalized Exponential Fuzzy Numbers using Integral Value Approach
Int. J. Advance. Soft Comput. Appl., Vol., No., July 010 ISSN 074-853; Copyright ICSRS Publication, 010.i-csrs.org Ranking of Generalized Exponential Fuzzy Numbers using Integral Value Approach Amit Kumar,
More informationA Triangular Fuzzy Model for Assessing Problem Solving Skills
Annals of Pure and Applied Mathematics Vol. 7, No., 04, 3-8 ISSN: 79-087X (P), 79-0888(online) Published on 9 September 04 www.researchmathsci.org Annals of A Triangular Fuzzy Model for Assessing Problem
More informationIntroduction to Fuzzy Logic and Fuzzy Systems Adel Nadjaran Toosi
Introduction to Fuzzy Logic and Fuzzy Systems Adel Nadjaran Toosi Fuzzy Slide 1 Objectives What Is Fuzzy Logic? Fuzzy sets Membership function Differences between Fuzzy and Probability? Fuzzy Inference.
More informationSpeed regulation in fan rotation using fuzzy inference system
58 Scientific Journal of Maritime Research 29 (2015) 58-63 Faculty of Maritime Studies Rijeka, 2015 Multidisciplinary SCIENTIFIC JOURNAL OF MARITIME RESEARCH Multidisciplinarni znanstveni časopis POMORSTVO
More informationFuzzy Logic : Introduction
Fuzzy Logic : Introduction Debasis Samanta IIT Kharagpur dsamanta@iitkgp.ac.in 23.01.2018 Debasis Samanta (IIT Kharagpur) Soft Computing Applications 23.01.2018 1 / 69 What is Fuzzy logic? Fuzzy logic
More information[Ch 6] Set Theory. 1. Basic Concepts and Definitions. 400 lecture note #4. 1) Basics
400 lecture note #4 [Ch 6] Set Theory 1. Basic Concepts and Definitions 1) Basics Element: ; A is a set consisting of elements x which is in a/another set S such that P(x) is true. Empty set: notated {
More informationFuzzy Sets and Systems. Lecture 1 (Introduction) Bu- Ali Sina University Computer Engineering Dep. Spring 2010
Fuzzy Sets and Systems Lecture 1 (Introduction) Bu- Ali Sina University Computer Engineering Dep. Spring 2010 Fuzzy sets and system Introduction and syllabus References Grading Fuzzy sets and system Syllabus
More informationON THEORY OF INTUITIONISTIC FUZZY SETS (OR VAGUE SETS)
International Journal of Fuzzy Systems On Theory and Rough of Intuitionistic Systems Fuzzy Sets (Or Vague Sets) 113 4(2), December 2011, pp. 113-117, Serials Publications, ISSN: 0974-858X ON THEORY OF
More informationLotfi Zadeh (professor at UC Berkeley) wrote his original paper on fuzzy set theory. In various occasions, this is what he said
FUZZY LOGIC Fuzzy Logic Lotfi Zadeh (professor at UC Berkeley) wrote his original paper on fuzzy set theory. In various occasions, this is what he said Fuzzy logic is a means of presenting problems to
More informationGEOG 5113 Special Topics in GIScience. Why is Classical set theory restricted? Contradiction & Excluded Middle. Fuzzy Set Theory in GIScience
GEOG 5113 Special Topics in GIScience Fuzzy Set Theory in GIScience -Basic Properties and Concepts of Fuzzy Sets- Why is Classical set theory restricted? Boundaries of classical sets are required to be
More informationMultiGrid-Based Fuzzy Systems for Function Approximation
MultiGrid-Based Fuzzy Systems for Function Approximation Luis Javier Herrera 1,Héctor Pomares 1, Ignacio Rojas 1, Olga Valenzuela 2, and Mohammed Awad 1 1 University of Granada, Department of Computer
More informationData Fusion for Magnetic Sensor Based on Fuzzy Logic Theory
2 Fourth International Conference on Intelligent Computation Technology and Automation Data Fusion for Magnetic Sensor Based on Fuzzy Logic Theory ZHU Jian, CAO Hongbing, SHEN Jie, LIU Haitao Shanghai
More informationFuzzy Set-Theoretical Approach for Comparing Objects with Fuzzy Attributes
Fuzzy Set-Theoretical Approach for Comparing Objects with Fuzzy Attributes Y. Bashon, D. Neagu, M.J. Ridley Department of Computing University of Bradford Bradford, BD7 DP, UK e-mail: {Y.Bashon, D.Neagu,
More informationIntroduction to Fuzzy Logic. IJCAI2018 Tutorial
Introduction to Fuzzy Logic IJCAI2018 Tutorial 1 Crisp set vs. Fuzzy set A traditional crisp set A fuzzy set 2 Crisp set vs. Fuzzy set 3 Crisp Logic Example I Crisp logic is concerned with absolutes-true
More informationIrregular Interval Valued Fuzzy Graphs
nnals of Pure and pplied Mathematics Vol 3, No, 03, 56-66 ISSN: 79-087X (P), 79-0888(online) Published on 0 May 03 wwwresearchmathsciorg nnals of Irregular Interval Valued Fuzzy Graphs Madhumangal Pal
More informationNETWORK FLOW WITH FUZZY ARC LENGTHS USING HAAR RANKING
NETWORK FLOW WITH FUZZY ARC LENGTHS USING HAAR RANKING S. Dhanasekar 1, S. Hariharan, P. Sekar and Kalyani Desikan 3 1 Vellore Institute of Technology, Chennai Campus, Chennai, India CKN College for Men,
More informationHARD, SOFT AND FUZZY C-MEANS CLUSTERING TECHNIQUES FOR TEXT CLASSIFICATION
HARD, SOFT AND FUZZY C-MEANS CLUSTERING TECHNIQUES FOR TEXT CLASSIFICATION 1 M.S.Rekha, 2 S.G.Nawaz 1 PG SCALOR, CSE, SRI KRISHNADEVARAYA ENGINEERING COLLEGE, GOOTY 2 ASSOCIATE PROFESSOR, SRI KRISHNADEVARAYA
More informationUnit V. Neural Fuzzy System
Unit V Neural Fuzzy System 1 Fuzzy Set In the classical set, its characteristic function assigns a value of either 1 or 0 to each individual in the universal set, There by discriminating between members
More informationVague Congruence Relation Induced by VLI Ideals of Lattice Implication Algebras
American Journal of Mathematics and Statistics 2016, 6(3): 89-93 DOI: 10.5923/j.ajms.20160603.01 Vague Congruence Relation Induced by VLI Ideals of Lattice Implication Algebras T. Anitha 1,*, V. Amarendra
More informationDiscrete Optimization. Lecture Notes 2
Discrete Optimization. Lecture Notes 2 Disjunctive Constraints Defining variables and formulating linear constraints can be straightforward or more sophisticated, depending on the problem structure. The
More informationA Learning Algorithm for Tuning Fuzzy Rules Based on the Gradient Descent Method
A Learning Algorithm for Tuning Fuzzy Rules Based on the Gradient Descent Method Yan Shi*, Masaharu Mizumoto*, Naoyoshi Yubazaki** and Masayuki Otani** *Division of Information and Computer Sciences Osaka
More informationAn Application of Fuzzy Matrices in Medical Diagnosis
Intern. J. Fuzzy Mathematical Archive Vol. 9, No. 2, 2015, 211-216 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 8 October 2015 www.researchmathsci.org International Journal of An Application of
More informationIntuitionistic Fuzzy Petri Nets for Knowledge Representation and Reasoning
Intuitionistic Fuzzy Petri Nets for Knowledge Representation and Reasoning Meng Fei-xiang 1 Lei Ying-jie 1 Zhang Bo 1 Shen Xiao-yong 1 Zhao Jing-yu 2 1 Air and Missile Defense College Air Force Engineering
More informationGeneralized Implicative Model of a Fuzzy Rule Base and its Properties
University of Ostrava Institute for Research and Applications of Fuzzy Modeling Generalized Implicative Model of a Fuzzy Rule Base and its Properties Martina Daňková Research report No. 55 2 Submitted/to
More informationThe Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets
EUSFLAT-LFA 20 July 20 Aix-les-Bains, France The Type- OWA Operator and the Centroid of Type-2 Fuzzy Sets Francisco Chiclana Shang-Ming Zhou 2 Centre for Computational Intelligence, De Montfort University,
More information2 Dept. of Computer Applications 3 Associate Professor Dept. of Computer Applications
International Journal of Computing Science and Information Technology, 2014, Vol.2(2), 15-19 ISSN: 2278-9669, April 2014 (http://ijcsit.org) Optimization of trapezoidal balanced Transportation problem
More informationDynamic Clustering of Data with Modified K-Means Algorithm
2012 International Conference on Information and Computer Networks (ICICN 2012) IPCSIT vol. 27 (2012) (2012) IACSIT Press, Singapore Dynamic Clustering of Data with Modified K-Means Algorithm Ahamed Shafeeq
More informationXI International PhD Workshop OWD 2009, October Fuzzy Sets as Metasets
XI International PhD Workshop OWD 2009, 17 20 October 2009 Fuzzy Sets as Metasets Bartłomiej Starosta, Polsko-Japońska WyŜsza Szkoła Technik Komputerowych (24.01.2008, prof. Witold Kosiński, Polsko-Japońska
More informationRanking Fuzzy Numbers Using Targets
Ranking Fuzzy Numbers Using Targets V.N. Huynh, Y. Nakamori School of Knowledge Science Japan Adv. Inst. of Sci. and Tech. e-mail: {huynh, nakamori}@jaist.ac.jp J. Lawry Dept. of Engineering Mathematics
More informationSolving Fuzzy Travelling Salesman Problem Using Octagon Fuzzy Numbers with α-cut and Ranking Technique
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X. Volume 2, Issue 6 Ver. III (Nov. - Dec.26), PP 52-56 www.iosrjournals.org Solving Fuzzy Travelling Salesman Problem Using Octagon
More informationOptimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm
Optimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm N. Shahsavari Pour Department of Industrial Engineering, Science and Research Branch, Islamic Azad University,
More informationFuzzy Modeling for Control.,,i.
Fuzzy Modeling for Control,,i. INTERNATIONAL SERIES IN INTELLIGENT TECHNOLOGIES Prof. Dr. Dr. h.c. Hans-Jiirgen Zimmermann, Editor European Laboratory for Intelligent Techniques Engineering Aachen, Germany
More informationX : U -> [0, 1] R : U x V -> [0, 1]
A Fuzzy Logic 2000 educational package for Mathematica Marian S. Stachowicz and Lance Beall Electrical and Computer Engineering University of Minnesota Duluth, Minnesota 55812-2496, USA http://www.d.umn.edu/ece/lis
More informationCOSC 6397 Big Data Analytics. Fuzzy Clustering. Some slides based on a lecture by Prof. Shishir Shah. Edgar Gabriel Spring 2015.
COSC 6397 Big Data Analytics Fuzzy Clustering Some slides based on a lecture by Prof. Shishir Shah Edgar Gabriel Spring 215 Clustering Clustering is a technique for finding similarity groups in data, called
More informationDejong Function Optimization by means of a Parallel Approach to Fuzzified Genetic Algorithm
Dejong Function Optimization by means of a Parallel Approach to Fuzzified Genetic Algorithm Ebrahim Bagheri, Hossein Deldari Department of Computer Science, University of New Bruswick Department of Computer
More informationExploring Domains of Approximation in R 2 : Expository Essay
Exploring Domains of Approximation in R 2 : Expository Essay Nicolay Postarnakevich August 12, 2013 1 Introduction In this paper I explore the concept of the Domains of Best Approximations. These structures
More informationGeneral network with four nodes and four activities with triangular fuzzy number as activity times
International Journal of Engineering Research and General Science Volume 3, Issue, Part, March-April, 05 ISSN 09-730 General network with four nodes and four activities with triangular fuzzy number as
More informationESSENTIALLY, system modeling is the task of building
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006 1269 An Algorithm for Extracting Fuzzy Rules Based on RBF Neural Network Wen Li and Yoichi Hori, Fellow, IEEE Abstract A four-layer
More informationIntelligent Methods in Modelling and Simulation of Complex Systems
SNE O V E R V I E W N OTE Intelligent Methods in Modelling and Simulation of Complex Systems Esko K. Juuso * Control Engineering Laboratory Department of Process and Environmental Engineering, P.O.Box
More informationBest proximation of fuzzy real numbers
214 (214) 1-6 Available online at www.ispacs.com/jfsva Volume 214, Year 214 Article ID jfsva-23, 6 Pages doi:1.5899/214/jfsva-23 Research Article Best proximation of fuzzy real numbers Z. Rohani 1, H.
More informationMultiple-Criteria Fuzzy Evaluation: The FuzzME Software Package
Multiple-Criteria Fuzzy Evaluation: The FuzzME Software Package Jana Talašová 1 Pavel Holeček 2 1., 2. Faculty of Science, Palacký University Olomouc tř. Svobody 26, 771 46 Olomouc, Czech Republic Email:
More informationInfluence of fuzzy norms and other heuristics on Mixed fuzzy rule formation
International Journal of Approximate Reasoning 35 (2004) 195 202 www.elsevier.com/locate/ijar Influence of fuzzy norms and other heuristics on Mixed fuzzy rule formation Thomas R. Gabriel, Michael R. Berthold
More informationApproximation of a Fuzzy Function by Using Radial Basis Functions Interpolation
International Journal of Mathematical Modelling & Computations Vol. 07, No. 03, Summer 2017, 299-307 Approximation of a Fuzzy Function by Using Radial Basis Functions Interpolation R. Firouzdor a and M.
More informationFUZZY LOGIC TECHNIQUES. on random processes. In such situations, fuzzy logic exhibits immense potential for
FUZZY LOGIC TECHNIQUES 4.1: BASIC CONCEPT Problems in the real world are quite often very complex due to the element of uncertainty. Although probability theory has been an age old and effective tool to
More informationRPKM: The Rough Possibilistic K-Modes
RPKM: The Rough Possibilistic K-Modes Asma Ammar 1, Zied Elouedi 1, and Pawan Lingras 2 1 LARODEC, Institut Supérieur de Gestion de Tunis, Université de Tunis 41 Avenue de la Liberté, 2000 Le Bardo, Tunisie
More information