Issue:Generalized Atanassov's intuitionistic fuzzy index. Construction method

shortcut

http://ifigenia.org/wiki/issue:eusflat-2009-478-482

Title of paper: Generalized Atanassov's intuitionistic fuzzy index. Construction method Author(s): Edurne Barrenechea Dpt. Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, s/n, 31006 Pamplona (Spain) edurne.barrenechea@unavarra.es Humberto Bustince Dpt. Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, s/n, 31006 Pamplona (Spain) bustince@unavarra.es Miguel Pagola Dpt. Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, s/n, 31006 Pamplona (Spain) miguel.pagola@unavarra.es Javier Fernandez Dpt. Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, s/n, 31006 Pamplona (Spain) fcojavier.fernandez@unavarra.es Josean Sanz Dpt. Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, s/n, 31006 Pamplona (Spain) joseantonio.sanz@unavarra.es Presented at: Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009 Published in: Conference proceedings, pages 478-482 Download:  PDF (168  Kb, File info) Abstract: In this work we introduce the concept of Generalized Atanassov's Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and we propose a construction method with automorphisms. Finally, we study some special properties of the generalized Atanassov’s intuitionistic fuzzy index. Keywords: Atanassov's Intuitionistic Fuzzy Index, Fuzzy Implication Operator, Automorphisms References: K. T. Atanassov. Intuitionistic fuzzy sets. In: V. Sgurev, ed., VII ITKR’s Session, Sofia, June 1983 (deposed in Central Science and Technical Library, Bulgarian Academy of Sciences, 1697/84, in Bulgarian). K. T. Atanassov. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems,20:87–96, 1986. K. Atanassov, G. Gargov. Elements of Intuitionistic Fuzzy Logic. Part I. Fuzzy Sets and Systems,95:39-52, 1998. P. Burillo, H. Bustince. Orderings in the referential set induced by an intuitionistic fuzzy relation. Notes on Intuitionistic Fuzzy Sets, 1:93-103, 1995. H. Bustince, P. Burillo, V.Mohedano. About Intuitionistic Fuzzy Implication Operators. JCIS 2002, Research Triangle Park, 109–113, North Carolina, USA, 2002. H. Bustince, P. Burillo, F. Soria. Automorphisms, Negations and Implication Operators. Fuzzy Sets and Systems, 134:209-229, 2003. H. Bustince, E. Barrenechea, V. Mohedano. Intuitionistic Fuzzy Implication Operators. An expression and main properties. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(3):387–406, 2004. H. Bustince, V. Mohedano, E. Barrenechea, M. Pagola. A study of the Intuitionistic Fuzzy S-Implication. First Properties. Procesos de Toma de Decisiones, modelado y Agregaci´on de Preferencias, 141–150, Eds.:E. Herrera-Viedma, 2005. H. Bustince, M. Pagola, P. Melo-Pinto, E. Barrenechea, P. Couto, Image Threshold Computation by modelizing Knowledge/Unknowledge by means of Atanassov’s Intuitionistic Fuzzy Sets. Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision, 621–638, Eds.: H. Bustince, F. Herrera, J. montero, (Springer-Verlag), 2008. H. Bustince, E. Barrenechea, M. Pagola. Generation of interval-valued fuzzy and Atanassov’s intuitionistic fuzzy connectives from fuzzy connectives and from Kα operators: Laws for conjunctions and disjunctions, amplitude. International Journal of Intelligent Systems, 23(6):680-714, 2008. H. Bustince, E. Barrenechea, M. Pagola, J. Fernandez, J. Olagoitia, P. Melo-Pinto, P. Couto. Contrast computing using Atanassov’s intuitionistic fuzzy sets. In Proc. 8th International FLINS Conference on Computational Intelligence in Decision and Control ,Madrid: 259–264, 2008. C. Cornelis, G. Deschrijver. The Compositional Rule of Inference in an Intuitionistic Fuzzy Logic Setting. In Proc. 6th ESSLLI Students Session, 2001. C. Cornelis, G. Deschrijver, E. Kerre. Classification of Intuitionistic Fuzzy Implicators: an Algebraic Approach. In Proc. 6th Joint Conf. Information Sciences, Research Triangle Park, USA: 105–108, 2002. G. Deschrijver, C. Cornelis, E. Kerre. On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems, 12(1):45-61, 2004. J. Fodor, M. Roubens. Fuzzy Preference Modelling and Multicriteria Decision Support. Theory and Decision. Kluwer Academic Publishers, 1994. A. Pankowska, M. Wygralak. On hesitation degrees in IF-set theory. In: LNAI 3070, Springer, 338–343, 2004. A. Pankowska, M. Wygralak. General If-sets with triangular norms and their applications to group decision making. Information Sciences, 176:2713–2754, 2006. P. Smets, P. Magrez. Implication in fuzzy logic. International Journal of Approximate Reasoning, 1:327-347, 1987. E. Trillas. Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica, III(1):47-59, 1979 (in Spanish). Reprinted (English version) in: Advances of Fuzzy Logic. S. Barro et altri-Universidad de Santiago de Compostela, 31-43,1998. E. Trillas, C. Alsina, J.M. Terricabras. Introducción a la lógica borrosa, ArielMatemática, 1995. M. Wygralak. Representing incomplete knowledge about fuzzy sets. In Proc. 5th Eusflat Conf., Ostrava, Czech Rep.: Vol.II, 287–292, 2007. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.