Fuzzy information processing

Guilherme A Barreto Ricardo Coelho (Eds.) Communications in Computer and Information Science Fuzzy Information Processing 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018 Fortaleza, Brazil, July 4–6, 2018 Proceedings 123 831 Communications in Computer and Information Science Commenced Publication in 2007 Founding and Former Series Editors: Alfredo Cuzzocrea, Xiaoyong Du, Orhun Kara, Ting Liu, Dominik Ślęzak, and Xiaokang Yang Editorial Board Simone Diniz Junqueira Barbosa Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil Phoebe Chen La Trobe University, Melbourne, Australia Joaquim Filipe Polytechnic Institute of Setúbal, Setúbal, Portugal Igor Kotenko St Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, St Petersburg, Russia Krishna M Sivalingam Indian Institute of Technology Madras, Chennai, India Takashi Washio Osaka University, Osaka, Japan Junsong Yuan University at Buffalo, The State University of New York, Buffalo, USA Lizhu Zhou Tsinghua University, Beijing, China 831 More information about this series at http://www.springer.com/series/7899 Guilherme A Barreto Ricardo Coelho (Eds.) • Fuzzy Information Processing 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018 Fortaleza, Brazil, July 4–6, 2018 Proceedings 123 Editors Guilherme A Barreto Department of Teleinformatics Engineering Federal University of Ceará Fortaleza, Ceará Brazil Ricardo Coelho Department of Statistics & Applied Mathematics Federal University of Ceará Fortaleza, Ceará Brazil ISSN 1865-0929 ISSN 1865-0937 (electronic) Communications in Computer and Information Science ISBN 978-3-319-95311-3 ISBN 978-3-319-95312-0 (eBook) https://doi.org/10.1007/978-3-319-95312-0 Library of Congress Control Number: 2018947460 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface In 1965, Lofti Asker Zadeh published the seminal paper “Fuzzy Sets” (Information and Control, 8, 338–353), which describe the first ideas about a formal mathematical modelling intended to bridge the gap between classic binary modelling and the subjective way that humans relate to day-to-day situations Despite these ideas being ambitious, this preliminary work inspired many researchers around the world and today his ideas are found in almost all branches of science According to the website Google Scholar, this seminal paper has been cited in more than 100,000 scholarly works, and many consumer products and software have been built based on its mathematical concepts Unfortunately, Professor Zadeh died in September 2017, and this book is a modest tribute to the generous, gentle continuous and always friendly support that the authors received over the years from Professor Lofti A Zadeh It can be noted that the research field of fuzzy sets and systems has undergone tremendous growth since 1965 This growth is in no small measure the result of the emergence of some important scientific societies in North America (North American Fuzzy Information Processing Society – NAFIPS – and IEEE Computational Intelligence Society – IEEE CIS), Europe (European Society for Fuzzy Logic and Technology – EUSFLAT), Asia (Japan Society for Fuzzy Theory and Intelligent Informatics – JSFTII), and South America, especially in Brazil, (Brazilian Society of Automatics – SBA – and Brazilian Society of Computational and Applied Mathematics – SBMAC) There is also a transnational scientific society (International Fuzzy Systems Association – IFSA) These societies promote scientific events in order to spread the state of the art, its applications, and technological advances A quick search in the Scopus database gives an idea of the number of published articles about fuzzy sets and systems By dividing time from 1965 until today into four periods, we obtain the following: (a) 4,754 published papers until 1990; (b) 27,773 published papers from 1991 to 2000; (c) 93,012 from 2001 to 2010; and (d) 105,604 from 2011 to the current date (May 2018) This search was made by using the words “Fuzzy Sets” or “Fuzzy Systems” or “Fuzzy Logic” as title, abstract, or keywords Among the societies mentioned, NAFIPS is the premier fuzzy society in North America, which was founded in 1981 The purpose of NAFIPS is “the promotion of the scientific study of, the development of an educational institution for the instruction in, and the dissemination of educational materials in the public interest including, but not limited to, theories and applications of fuzzy sets through publications, lectures, scientific meetings, or otherwise.” In this role, we understand the importance and necessity of developing a strong intellectual base and encouraging new and innovative applications In addition, we recognize our leading role in promoting interactions and technology transfer to other national and international organizations so as to bring the benefits of this technology to North America and the world The scientific event organized by the NAFIPS has been contributing for more than 30 editions to the VI Preface growth of the number of articles published in the fuzzy sets and systems field The first edition took place in the city of Logan, Utah, USA, in 1982, and it is held annually One of the objectives of NAFIPS is to expand the network of collaborators and enthusiasts of fuzzy thinking beyond the borders of North American countries The 37th North American Fuzzy Information Processing Society Annual Conference (NAFIPS 2018) was held during July 4–6, 2018, in the beautiful city of Fortaleza, capital of the state of Ceará, located on the sunny northeast coast of Brazil This event was held simultaneously with the 5th Brazilian Congress on Fuzzy Systems (CBSF 2018), bringing together researchers, engineers, and practitioners to share and present the latest achievements and innovations in the area of fuzzy information processing, to discuss thought-provoking developments and challenges, and to consider potential future directions Bearing this in mind, the NAFIPS 2018 meeting was the first edition of the meeting to be organized outside the USA, Canada, and Mexico NAFIPS 2018 had an international Program Committee including researchers from industry and academia worldwide The organization of NAFIPS 2018 and CBSF 2018 was the result of a joint action of the Brazilian Computational Intelligence Society (SBIC), the Brazilian Society of Computational and Applied Mathematics (SBMAC), the Federal University of Ceará (UFC), and the Brazilian funding agencies CAPES, process 88887.155510/2017-00, and CNPq, project 407666/2017-6, in addition to the executive boards of NAFIPS and CBSF This book is a collection of high-quality papers ranging over a large spectrum of topics, including theory and applications of fuzzy numbers and sets, fuzzy logic, fuzzy inference systems, fuzzy clustering, fuzzy pattern classification, neuro-fuzzy systems, fuzzy control systems, fuzzy modeling, fuzzy mathematical morphology, fuzzy dynamical systems, time series forecasting, and making decision under uncertainty We received 73 submissions from 11 countries, from which 54 papers were accepted The authors were from Brazil, Chile, Colombia, Czech Republic, India, Iran, Mexico, Romania, Spain, Turkey, and the USA Each submitted paper was reviewed by at least three independent referees The acceptance/rejection decision used the following criteria: every paper with two positive reviews was accepted, and those with two negative reviews were rejected Borderline papers, those with one positive and one negative review, were analyzed carefully by the conference chairs in order to evaluate the reasons given for acceptance or rejection Our final decision on these submissions took into account mainly the potential of each paper to foster fruitful discussions and the future development of the research on the theory and applications of fuzzy sets and systems in Brazil and, for extension, in the whole of Latin America We are enormously grateful to all reviewers for their goodwill in cooperating for the success of the aforementioned events We very much appreciate their willingness for hard work and prompt feedback, which certainly guaranteed the high quality of the technical program We wish NAFIPS a long life And we wish a long life for the Brazilian community, who organizes CBSF, with which we share this mutual congress June 2018 Guilherme A Barreto Ricardo Coelho Organization General Co-chairs Guilherme Barreto Ricardo Coelho Federal University of Ceará, Brazil Federal University of Ceará, Brazil Organizing Committee Fernando Gomide Guilherme Barreto Laecio Carvalho de Barros Patricia Melin Ricardo Coelho Weldon Lodwick Centro Acadêmico de Matemática Industrial University of Campinas, Brazil Federal University of Ceará, Brazil University of Campinas, Brazil Tijuana Institute of Technology, Mexico Federal University of Ceará, Brazil University of Colorado Denver, USA CAMI Web Masters Felipe Albuquerque Francisco Yuri Martins Federal University of Ceará, Brazil Federal University of Ceará, Brazil NAFIPS Officers Patricia Melin (President) Martine Ceberio (President-Elect) Christian Servin (Treasurer) Valerie Cross (Secretary) NAFIPS Board of Directors Ildar Batyrshin Ricardo Coelho Martine De Cock Scott Dick Juan Carlos Figueroa Garcia Weldon A Lodwick Marek Reformat Shahnaz Shahbazova Mark Wierman Dongrui Wu VIII Organization Program Committee Giovanni Acampora Plamen Angelov Krassimir Atanassov Adrian I Ban Guilherme Barreto Laecio Carvalho de Barros Ildar Batyrshin Fernando Bobillo Giovanni Bortolan Tadeusz Burczynski João Paulo Carvalho Oscar Castillo Martine Ceberio Wojciech Cholewa Ricardo Coelho Lucian Coroianu Valerie Cross Bernard de Baets Didier Dubois Robert Fuller Takeshi Furuhashi Fernando Gomide Wladyslaw Homenda Sungshin Kim Peter Klement Vladik Kreinovich Jonathan Lee Weldon A Lodwick Francesco Marcelloni Radko Mesiar Vesa Niskanen Fabrício Nogueira Vilem Novak Reinaldo Martinez Palhares Irina Perfilieva Henri Prade Radu Emil Precup Alireza Sadeghian Yabin Shao Andrzej Skowron Umberto Straccia Ricardo Tanscheit University of Naples Federico II, Italy Lancaster University, UK Bulgarian Academy of Science, Bulgaria University of Oradea, Romania Universidade Federal Ceará, Brazil University of Campinas, Brazil Instituto Politécnico Nacional, Mexico University of Zaragoza, Spain Institute of Neuroscience, IN-CNR, Italy Institute of Fundamental Technological Research, Poland Instituto Superior Tecnico/INESC-ID, Portugal Tijuana Institute of Technology, Mexico University of Texas at El Paso, USA Silesian University of Technology, Poland Universidade Federal Ceará, Brazil University of Oradea, Romania Miami University, USA Ghent University, Belgium Université Paul Sabatier, France Óbuda University, Hungary Nagoya University, Japan University of Campinas, Brazil Warsaw University of Technology, Poland Pusan National University, South Korea Johannes Kepler University, Austria University of Texas at El Paso, USA National Central University, Taiwan University of Colorado Denver, USA University of Pisa, Italy Slovak University of Technology, Slovakia University of Helsinki, Finland Universidade Federal Ceará, Brazil University of Ostrava, Czech Republic Federal University of Minas Gerais, Brazil University of Ostrava, Czech Republic Université Paul Sabatier, France Politehnica University of Timisoara, Romania Ryerson University, Canada Northwest University for Nationalities, China University of Warsaw, Poland Consiglio Nazionale delle Ricerche, ISTI-CNR, Italy Pontifícia Universidade Católica Rio de Janeiro, Brazil Organization Jose Luis Verdegay Yiyu Yao Hao Ying Fusheng Yu Slawomir Zadrozny M H Fazel Zarandi Guangquan Zhang Hans J Zimmermann University of Granada, Spain University of Regina, Canada Wayne State University, USA Beijing Normal University, China Polish Academy of Sciences, Poland Amirkabir University of Technology, Iran University of Technology Sydney, Australia RWTH Aachen University, Germany Additional Reviewers Jỗo Fernando Alcântara Aluizio Arẳjo Rodrigo Araújo Romis Attux Iury Bessa Arthur Braga Luiz Cordovil Pedro Coutinho Alexandre Evsukoff Carmelo J.A Bastos Filho Heriberto Román Flores João Paulo Pordeus Gomes Jose Manuel Soto Hidalgo Daniel Leite Adi Lin José Everardo Bessa Maia Sebastia Massanet Ajalmar Rêgo da Rocha Neto Rudini Sampaio Peter Sussner George Thé Marcos Eduardo Valle Bin Wang Zhen Zhang IX Differential Evolution Algorithm Using a Dynamic Crossover Parameter 587 experiments CR is dynamic by using the fuzzy system Experiments were only carried out with a number of dimensions of 10 and 30 with the same guidelines of the CEC 2015 competition Table Parameters of the experiments Parameters NP = 250 D = 10 and 30 F = 0.6 CR = 0.5 and dynamic GEN = 100000 and 300000 The results obtained with the original algorithm are shown in Table for number of dimensions of 10, the table contains the best and the worst result, the mean and the standard deviation Table Results for dimensions D = 10 Differential Evolution algorithm for D = 10 Best Worst Mean Std f1 3.21E+02 3.21E+02 3.21E+02 1.45E−01 f2 4.80E+02 5.64E+02 5.28E+02 2.01E+01 f3 2.42E+03 3.50E+03 2.97E+03 2.41E+02 f4 1.52E+05 1.37E+08 2.92E+07 2.78E+07 f5 7.14E+02 8.01E+02 7.53E+02 2.18E+01 f6 7.48E+04 1.39E+07 4.39E+06 4.13E+06 Table shows the results for number of dimensions of 30 and contains the best and the worst result, the mean and the standard deviation Table Results for dimensions D = 30 Differential Evolution algorithm for D = 30 Best Worst Mean Std f1 3.21E+02 3.21E+02 3.21E+02 7.28E−02 f2 9.31E+02 1.13E+03 1.05E+03 4.21E+01 f3 8.62E+03 1.09E+04 9.93E+03 4.54E+02 f4 7.26E+07 1.09E+09 4.44E+08 2.51E+08 f5 1.14E+03 4.05E+03 2.07E+03 5.89E+02 f6 1.33E+07 4.65E+08 1.43E+08 5.89E+02 588 P Ochoa et al Tables and represent the results obtained with a dynamic CR parameter for 10 and 30 dimensions respectively and contains the best and the worst result, the mean and the standard deviation Table Results with CR dynamic for D = 10 D E with CR dynamic for D = 10 Best Worst Mean f1 5.15E−01 2.12E+01 1.62E+01 f2 8.23E+00 1.55E+02 1.01E+02 f3 1.76E+01 2.89E+03 2.16E+03 f4 1.69E+04 1.12E+08 2.22E+07 f5 4.65E−01 1.12E+02 4.45E+01 f6 3.86E+04 1.55E+07 4.38E+06 Std 8.83E+00 5.36E+01 8.63E+02 2.68E+07 3.25E+01 3.73E+06 Table Results with CR dynamic for D = 10 D E with CR dynamic for D = 30 Best Worst Mean f1 2.18E−01 2.15E+01 2.07E+01 f2 1.00E+02 7.44E+02 6.43E+02 f3 2.36E−01 1.02E+04 6.70E+03 f4 5.04E+01 7.58E+08 2.41E+08 f5 3.70E−01 1.75E+03 5.61E+02 f6 9.63E+01 3.67E+08 9.88E+07 Std 3.86E+00 1.13E+02 4.48E+03 2.45E+08 6.36E+02 1.05E+08 Table represents a comparison between the original method and the proposed method where CR is dynamic, and a comparison of the best results obtained for the number or dimensions of 10 and 30 is made Table Comparison between DE and DE with dynamic CR Comparison between DE and DE with dynamic CR D = 10 D = 30 Original Proposed Original Proposed f1 3.21E+02 5.15E−01 5.15E−01 2.18E−01 f2 4.80E+02 8.23E+00 9.41E+01 1.00E+02 f3 2.42E+03 1.76E+01 1.65E+03 2.36E−01 f4 1.52E+05 1.69E+04 5.94E+05 5.04E+01 f5 7.14E+02 4.65E−01 1.67E+01 3.70E−01 f6 7.48E+04 3.86E+04 3.86E+04 9.63E+01 Differential Evolution Algorithm Using a Dynamic Crossover Parameter 589 Figures and show graphically the comparison of the best results between the original algorithm and the proposed method, and Fig shows the results for dimensions of 10 and Fig shows the results for dimensions of 30 Fig Graphic to D = 10 Fig Graphic to D = 30 We can notice graphically that the proposed method has better results than the original algorithm for both comparisons, the separation between the two methods is clearly shown Conclusions The study carried out with the experimentation of at least functions of CEC 2015 gives us an idea of the behavior of the CR parameter in the algorithm, with the obtained results we can notice that we are on the right track although we cannot yet affirm that the fuzzy system used is the optimal one since we need more experimentation and a statistical test to be able to demonstrate the improvement of the algorithm 590 P Ochoa et al We can rescue the following points the use of the diversity variable helps the algorithm to obtain better results We can also state that the use of the diversity variable helps the algorithm to obtain better results until now, we lack more experimentation, the goal is to use the whole set of the CEC 2015 benchmark functions and thus to make a comparison of our proposed method and the winning algorithm of the CEC 2015 benchmark functions competition and carry out the corresponding statistical test As future work, we can consider extending to use type-2 fuzzy logic, and also deal with applications of optimizing neural networks [18, 19] References Amador-Angulo, L., Castillo, O.: Statistical analysis of type-1 and interval type-2 fuzzy logic in dynamic parameter adaptation of the BCO In: IFSA-EUSFLAT, pp 776–783, June 2015 (2015) Amador-Angulo, L., Castillo, O.: A new fuzzy bee colony optimization with dynamic adaptation of parameters using interval type-2 fuzzy logic for tuning fuzzy controllers Soft Comput 22(2), 1–24 (2016) Awad, N., Ali, M.Z., Reynolds, R.G.: A differential evolution algorithm with success-based parameter adaptation for CEC 2015 learning-based optimization In: 2015 IEEE Congress on Evolutionary 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Environment to explore future consequences of actions planned within a strategic scenario context in terms of KPIs displayed in a Balanced ScoreCard (BSC) control board Corporation’s Strategy Map is required to plan the Knowledge Identification and Capture Activity (KICA) required to obtain the knowledge to be represented in the FN’s Nodes Rule Bases KICA produces linguistic variables as well as the qualitative relationships amongst them A FN appears as a natural solution to model the knowledge distributed within the members participating in all analysis and decision making tasks along the organization As an example an application done for a Utility Corporation is included Introduction Since BSC officially appeared [1] it has become an important corporate control tool However the feedback it provides through the KPIs takes a good time after an action has been taken This occurs because the time constants involved in a corporate dynamics are rather long ranging from weeks to months depending of the strategic deep of decisions and the corresponding actions This paper presents an enhancement of the BSC control strategy by means of a knowledge based computing model representing the corporate dynamics and implementing a Model Reference Adaptive Control (MRAC) strategy [3] Since the Strategy Map [4] displays the inner causality in an organization’s dynamic it is used to conduct the KICA required to identify the involved linguistic variables and the qualitative relationships amongst them The model is constructed using a FN which stores the knowledge gathered through a KICA This model is used to provide the What If? Environment to test different strategic scenarios and to identify the best actions to be taken on order to obtain desired KPI’s values in a given time horizon FN have already been used and reported [6, 7] as a tool to build Expert Systems using distributed knowledge © Springer International Publishing AG, part of Springer Nature 2018 G A Barreto and R Coelho (Eds.): NAFIPS 2018, CCIS 831, pp 592–599, 2018 https://doi.org/10.1007/978-3-319-95312-0_52 Corporate Control with a Fuzzy Network 593 BSC Control Structure The current BSC control loop is displayed in Fig No matter how good the measurement system is the values entered for the KPIs in the BSC Board will reflect the consequences of the taken actions only after a good amount of time since the time constants involved in the corporate dynamics are some times weeks or even months long The What If? Environment introduced here allows to test groups of actions, in fact, whole strategies, to examine the future KPI’s values and so to determine the best strategy in terms of future KPI’s values Fig Current BSC control loop structure Model Reference Adaptive Control Structure The What If? Environment is obtained using the mentioned MRAC control strategy and this is showed in Fig The Corporate Model allows to test actions showing future KPI’s values in the BSC Model Board Fig MRAC structure with What If? environment 594 G Pérez Hoyos Once the structure depicted in Fig is constructed all that is needed is a good Simulation Barnacle to start testing strategies and actions to be input to the model in order to observe over the BSC Model Board the resultant KPIs in the specified time horizon Corporate Model Figure shows a typical FN structure for the corporate model Fig Corporate model The FN structure is distributed along the four BSC Perspectives: Financial Perspective (FP), Customer Perspective (CP), Internal Perspective (IP) and Learning and Grow Perspective (LGP) Every Node in the FN is separately created and tuned using the MRAC interface included in the MANAGEMENT Block (Fig 2) Design parameters for each node are determined through the tuning procedure using criteria obtained in the KICA Figure shows the structure of a Fuzzy System (FS) in every node with the design parameters for every module Depending on the particular dynamic associated to a company the FN could be either Feedforward or Recurrent Corporate Control with a Fuzzy Network 595 The Rule Base for every Node will contain the fuzzy rules obtained after analyzing the results obtained with the KICA The nodes producing the KIP’s values are explicitly shown All the fuzzy rules for every node contain the time as a linguistic variable in the Antecedent Rule k is then explicitly written as (1) Although the Inputs go into nodes in the Learning and Growing Perspective in Fig 3, inputs can actually go into any node in any perspective Rk: IF X1 is LX1 AND … AND Xm is LXm AND Time is LT THEN Y1 is LY1 AND AND Yn is LYn ð1Þ Where: X1 … Xm are the inputs to the node and Y1 … Yn are the outputs, LXi e fL, M, Hg; LYi e fL, M, Hg LT e fVS, S, M, L, VLg With: L = Low, H = High, VS = Very Short, S = Short, M = Medium, L = Long, VL = Very Long Although only one layer is shown for the FN in each perspective, it is the particular dynamics for each corporation’s value-creating processes which determines the FN’s nodes structure for every perspective The particular FN structure constructed for any particular organization will reflect the particular dynamics and the inner causality within the value-creating processes in that corporation The What If? Environment The User Interface also contains the simulation environment so that managers and/or planners can perform the simulation tasks required to test any strategy This environment keeps the record of all simulations to facilitate the supervision tasks required to identify the best strategies When a corporation has a comprehensive and well maintained Data Base with a few years of data, rules can be identified using a mining procedure with the help of Adaptive (Trainable) Fuzzy Systems [3] This capability is built in the UNFUZZY tool [5] used for the developments reported in [6, 7] Implementing this MRAC strategy with What If? Environment requires the committed participation of all members in the organization KEA in particular requires the open and patient collaboration since many times it is necessary to go over some particular subjects in order to clearly identify the linguistic variables as well as the nature of relationships MRAC with What If? Environment was implemented in a local utility It is currently used in the planning tasks and it has been taken as a pilot experience to scout new possibilities The task force organized for this accomplishment is now working on model refinement to include risks, using the experience gathered in a recent work [7] 596 G Pérez Hoyos Fig Node’s structure with design parameters This means identifying the associated risks to every strategic goal and to actually acquire the heuristics associated to its assessment This approach intends to reach the point where we can modify the fuzzy rules for the KPI nodes in the corporate model to include risk values The BSC Boards, Corporate Board as well as Model Board, will also be modified to include the column corresponding to risk values Utility Company Application The example presented in this paper is an application developed for a Utility Corporation Figure shows the strategy map for this utility, where the inputs are also indicated As a result of KICA the input and output linguistic variables for every process in the map were identified as well as the proper fuzzy relationship relating each input-output pair in order to elaborate the fuzzy rules for every node Identifying the proper fuzzy rules includes detecting the adequate set of Qualifying Linguistic Terms (QLT) as well as the Trend relationships, i.e whether a variable appearing in the consequent of a particular fuzzy rule is growing or decaying when a variable in the antecedent is growing Corporate Control with a Fuzzy Network 597 Fig Strategy map Fuzzy Network Architecture Figure shows the final FN designed architecture Five layers were required in order to implement the network using UNFUZZY [5], a software tool to implement and simulate FS and FN, developed at Universidad Nacional de Colombia Fig FN architecture 598 G Pérez Hoyos Functionality, input/output variables, rules and fuzzy system parameters for every node are not included in this paper since the confidentiality agreement signed with the company prevent us from doing so In [7] they were included explicitly because that was not an industrial application with a signed contract but an academic research work For all the nodes the fuzzy inference employed was Mandani (Minimum), membership functions employed were the standard L, Lambda (Triangle) and Gamma Functions, available in most Fuzzy Systems software tools Defuzzification was done with Center of Gravity DeDuzzifier The Time Horizon selected for a particular simulation exercise is entered as input linguistic variable to every one of the nodes The antecedent for every rule in the corresponding Rule Base will contain the component time is LT, where LT  fVery Short, Short, Medium, Long, Very Longg As it was stated before Besides the inputs to the nodes in the following layer, The outputs of the nodes in every layer include the Key Performance Indexes (KPIs) that go to BSC simulation Board Then Layer outputs include the KPIs related to the Training and Selection Processes, Layer outputs include the KPIs related to corporate Empowerment, Layer outputs include KPIs related to Quality Control and Layer outputs include KPIs related to Positioning and Growth Conclusions and Final Recommendations • The Corporate Model constructed after the KICA using a Fuzzy Network is a good example of a working asset obtained through capitalizing organization knowledge • A Fuzzy Network is a versatile way to model corporate knowledge since this is distributed all over the people working in analysis and decision making activities within the organization’s value-creating processes • A What If? Environment provides the BSC corporate control strategy a powerful tool to explore different strategic scenarios Using different action scenarios and different time horizons to detect the best possible results in terms of KPIs requires a great deal of expertise achieved through consistently using this tool • Identifying the risks associated to every strategic goal as well as the associated heuristic to its assessment would allow to add the Risk column to the BSC Board, adding Risk Management to the MRAC STRATEGY References Kaplan, R.S., Norton, D.P.: The Strategy Focused Organization, How Balanced Scorecard Companies Thrive in the New Business Environment Harvard Business School Publishing Corporation, Brighton (2001) Shastry, S., Bodson, M.: Adaptive Control: Stability, Convergence and Robustness Dover Publications, Mineola (2011) Corporate Control with a Fuzzy Network 599 Wang, L.-X.: Adaptive Fuzzy Systems and Control PTR Prentice Hall, Englewood Cliffs (1994) Kaplan, R.S., Norton, D.P.: Strategy Maps, Converting Intangible Assets into Tangible Outcomes Harvard Business School Publishing Corporation, Boston (2004) Duarte, O., Pérez, G.: UNFUZZY: fuzzy logic system analysis, design simulation and implementation software In: Proceedings of the 1999 EUSFLAT-ESTYLF Joint Conference, Mallorca (1999) Perez, G.: A fuzzy logic based expert system for short term energy negotiations In: Proceedings of the 18th Conference of the North American Fuzzy Information Processing Society, NAFIPS IEEE (1999) Perez, G.: Pipeline risk assessment using a fuzzy systems network In: Proceedings of the IFSA (World Congress) - NAFIPS (Annual Meeting) 2013, IFSA-NAFIPS IEEE (2013) Perez, V.: FuzzyNet, A Software Tool to Implement Fuzzy Networks (to be published) Author Index Abdolkarimzadeh, Mona 559 Agostini, Lucas 206 Albuquerque, Renan Fonteles 385 Alcântara, João 179 Andrade, João P B 61 Argou, Amanda 119 Avila, Anderson 206 Ballini, R 361 Barros, Laécio C 84, 132, 489 Barros, Lắcio 192 Bassanezi, Rodney C 408, 431, 477 Bedregal, Benjamín 167, 217, 265, 302, 348 Behrooz, Mehrnaz 24 Bertato, Fábio 192 Borges, Eduardo N 144 Botelho, Silvia S C 144 Braga, Arthur P de S 385 Brito, Abner 192 Bueno, Jéssica C S 144 Bustince, Humberto 144, 155 Bustos-Tellez, Camilo Alejandro 538 Castiblanco, Fabián 96 Castillo, Oscar 559, 569, 580 Castillo-Lopez, Aitor 155 Cecconello, Moiseis S 408 Chalco-Cano, Yurilev 450 Chen, Shangye 230 Coniglio, Marcelo 192 Costa, Lidiane 217 Cross, Valerie 230 da da da de de de de de Costa, Tiago Mendonỗa 450 Rocha Neto, Ajalmar R 398 Silva Melo, José Carlos 49 Almeida Nogueira, Jordana 49 Barros, Laécio Carvalho 108, 450 Campos Souza, Paulo Vitor 13 Campos, Gustavo A L 61 Moraes, Ronei Marcos 49 de Oliveira Serra, Ginalber Luiz 336 de Oliveira, Paulo D L 385 de Oliveira, Valeriano Antunes 500 de Sá, Laisa Ribeiro 49 de Souza Júnior, Amauri H 398 De Souza Leite Cuadros, Marco Antônio 243 de Souza, Aline Cristina 290 Dias, Camila Alves 144 Dias, Madson L D 398 Dilli, Renato 119 Dimuro, Graỗaliz Pereira 144, 155, 302 Diniz, Geraldo L 419 Diniz, Michael M 431 Drews Junior, Paulo Lilles Jorge 144 DuBois, André 206 Esmi, Estevão 84, 108, 132 Esterline, Albert Fazel Zarandi, M H 559 Feitosa, Samuel 206 Fernandéz, Javier 144, 155 Fernandez, Marcial P 61 Figueroa-García, Juan Carlos 253, 538 Florêncio, José A V 398 Franco, Camilo 96 Galindo-Arevalo, Eiber Arley 253 Gamarra, Daniel Fernando Tello 243 Gebreyohannes, Solomon Gomes, Luciana T 431, 477 Gomide, Fernando 37, 361 Homaifar, Abdollah Jonsson, Claudio M 489 Karimoddini, Ali Kearfott, Ralph Baker 508 Kreinovich, Vladik 530, 551 602 Author Index Lagunes, Marylu L 569 Laureano, Estevão 192 Leal, Ulcilea 439 Liu, Dun 508 Lodwick, Weldon A 489 Lopes Moura, Renato 374 Loureiro, Tibério C J 61 Lucca, Giancarlo 144 Maciel, L 361 Mafalda, Marcelo 243 Maqui-Huamán, Gino G 439 Marco-Detchart, Cedric 155 Mascarenhas, W F 519 Matzenauer, Mônica 217 Melin, Patricia 569 Menezes Jr., Evanizio M 419 Mezzomo, Ivan 265 Milfont, Thadeu 265 Mizukoshi, Marina Tuyako 464 Močkoř, Jiří 72 Montero, Javier 96 Pinto, Érico Augusto Nunes Pinto, Nilmara J B 132 Pires, Danúbia Soares 336 Porto, Alisson 37 324 Reis, Ricardo A 324 Reiser, Renata 119, 206, 217 Rodríguez, J Tinguaro 96 Sangalli, Mateus 278 Santiago, Regivan 302, 314, 348 Santos, Helida 302, 348 Schnitman, Leizer 324 Servin, Christian 530 Sesma-Sara, Mikel 155 Silva, Geraldo Nunes 450 Silva, Geraldo 439 Soria, José 569, 580 Sussner, Peter 84, 374 Tenjo-García, Jhoan Sebastian 538 Torres, Luiz Carlos Bambirra 13 Neto, Afonso B L 61 Ochoa, Patricia 580 Oliveira, Jônathas D S 477 Paiva, Rui 314 Palmeira, Eduardo 167 Paraiba, Lourival C 489 Pedro, Francielle Santo 108 Peixoto, Magda S 489 Perdomo-Tovar, Jairo Andres 253 Pereira, Chryslayne M 408 Pérez Hoyos, Gustavo 592 Pilla, Maurício 206 Pinheiro, Jocivania 302, 314, 348 Valdez, Fevrier 569 Valle, Marcos Eduardo 278, 290 Vargas, Rogério R 167 Viana, Henrique 179 Vieira, R 361 Villanueva, Fabiola Roxana 500 Wasques, Vinícius F 84, 132 Welfer, Daniel 243 Yamin, Adenauer 119, 217 Zapata, Francisco 551 Zarandi, Mohammad Hossein Fazel 24 ... applications of fuzzy numbers and sets, fuzzy logic, fuzzy inference systems, fuzzy clustering, fuzzy pattern classification, neuro -fuzzy systems, fuzzy control systems, fuzzy modeling, fuzzy mathematical... More information about this series at http://www.springer.com/series/7899 Guilherme A Barreto Ricardo Coelho (Eds.) • Fuzzy Information Processing 37th Conference of the North American Fuzzy Information. .. a type-1 fuzzy number In the fuzzy inference engine, fuzzy logic principles are used to map fuzzy input sets in X1 × .×Xp , that flow through an IF-THEN rule (or a set of rules), into fuzzy output