Bustince, H. and Montero de Juan, Francisco Javier and Barrenechea, E. and Pagola, M.
(2008)
*Laws for Conjunctions and Disjunctions in Interval Type 2 Fuzzy Sets.*
In
2008 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS.
IEEE Xplore Digital Library, 1-5
.
IEEE, Hong Kong, Peoples R China, pp. 1615-1620.
ISBN 978-1-4244-1818-3

PDF
Restringido a Repository staff only hasta 2020. 141kB |

Official URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4630587

## Abstract

In this paper we study in depth certain properties of interval type 2 fuzzy sets. In particular we recall a method to construct different interval type 2 fuzzy connectives starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore we analyze the properties: idempotency, absorption, and distributiveness.

Item Type: | Book Section |
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Additional Information: | IEEE International Conference on Fuzzy Systems. |

Uncontrolled Keywords: | Connectives; Inference; Conorms; Systems; Norms |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 16906 |

References: | C. Alsina, E. Trillas and L. Valverde, “On some Logical Connectives for Fuzzy Sets Theory”, Journal of Mathematical Analysis and Applications,vol. 93, pp. 15–26, 1983. T. Arnauld, S.Tano, “Interval-valued fuzzy backward reasoning”, IEEE Transactions on Fuzzy Systems, 3(4)(1995), 425-437. K. Atanassov , “Intuitionistic fuzzy sets”, VII ITKR’s Session, Deposed in Central Sci. Techn. Library of Bulg. Acd. of Sciences, Sofia, pp.1684–1697, 1983. K. Atanassov, “ Intuitionistic fuzzy sets. Theory and Applications”,Physica-Verlag, Heidelberg, 1999). E. Barrenechea, Image Processing with Interval-valued Fuzzy Sets.Edge Detection. Contrast, Ph. D. Dissertation,Universidad Publica de Navarra, 2005. P. Burillo and H. Bustince, “Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets”, Fuzzy Sets and Systems, vol. 78, pp.305–016, 1996. P. Burillo and H. Bustince, “Orderings in the referential set induced by an intuitionistic fuzzy relation”, Notes on IFS, vol. 1, pp. 93–103, 1995. P. Burillo and H. Bustince, “Construction theorems for intuitionistic fuzzy sets”, Fuzzy Sets and Systems, vol. 84, pp. 271–281, 1996. [9] H. Bustince and P. Burillo, “Interval-valued fuzzy relations in a set structure”, The Journal of Fuzzy Mathematics, vol. 4, pp. 765–785,1996. H. Bustince, “Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets”, International Journal of Approximate Reasoning, vol. 23,pp. 137–209, 2000. H. Bustince and P. Burillo, “Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning”, Fuzzy Sets and Systems, vol. 113, pp. 205–219, 2000. H. Bustince and P. Burillo, “Structures on Intuitionistic Fuzzy Relations”,Fuzzy Sets and Systems, vol. 78, pp. 293–303, 1996. H. Bustince, J. Kacprzyk and V. Mohedano, “Intuitionistic Fuzzy Generators.Application to Intuitionistic Fuzzy Complementation”, Fuzzy Sets and ystems, vol. 114, pp. 485–504, 2000. H. Bustince, J. Montero, M. Pagola, E. Barrenechea and D. Gomez “A survey of interval-valued fuzzy sets,” in (Chapter 21) Handbook of Granular Computing, Edited by J. Wiley & Sons, 2008. H. Bustince, F. Herrera and J. Montero, Editors, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, Springer Verlag,Berlin, 2007. S.M. Chen, W.H. Hsiao, W.T. Jong, “Bidirectional approximate reasoning based on interval-valued fuzzy sets”, Fuzzy Sets and Systems,vol. 91, pp. 339–353, 1997. C. Cornelis, G. Deschrijver and E. Kerre, “Classification of Intuitionistic Fuzzy Implicators: an Algebraic Approach”, Proc. of the 6th Joint Conference on Information Sciences, Research Triangle Park, North Carolina, USA, 2002, pp. 105–108. C. Cornelis, G. Deschrijver and E. Kerre, “Intuitionistic Fuzzy Connectives Revisited”, Proc. of the Ninth International Conference IPMU 2002, Annecy-France July 2002, pp. 1839–1844. G. Deschrijver,C. Cornelis and E.E. Kerre, “On the representation of Intuitionistic Fuzzy T-Norms and T-Conorms”, IEEE Transactions on Fuzzy Systems, vol. 12, pp. 45–61, 2004. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York: Academic, 1980. F. Esteva, E. Trillas and X. Domingo, “Weak and strong negation function for fuzzy set theory”, Proc. Eleventh IEEE International Symposium on Multivalued Logic, Norman, Oklahoma, 1981, pp. 23–27. J. Fodor and M. Roubens,“Fuzzy Preference Modelling and Multicriteria Decision Support”, in: Theory and Decision Library, Kluwer Academic Publishers, 1994. J. Fodor, “On fuzzy implication operators”, Fuzzy Sets and Systems,vol. 42, pp. 293–300, 1991. M.B. Gorzalczany, “A method of inference in approximate reasoning based on interval-valued fuzzy sets”, Fuzzy Sets and Systems, vol. 21,pp. 1–17, 1987. M.B. Gorzalczany, “Interval-valued fuzzy controller based on verbal model of object”, Fuzzy Sets and Systems, vol. 28, pp. 45–53, 1988. M.B. Gorzalczany, “Interval-valued fuzzy inference involving uncertain (inconsistent) conditional propositions”, Fuzzy Sets and Systems,vol. 29, pp. 235–240, 1989. M.B. Gorzalczany, “An interval-valued fuzzy inference method. Some basic properties”, Fuzzy Sets and Systems, vol. 31, pp. 243–251, 1989. S. Jenei, “A more efficient method for defining fuzzy connectives”,Fuzzy Sets and Systems, vol. 90, pp. 25–35, 1997. J.M. Mendel, Robert I. Bob John, “Type-2 fuzzy sets made simple”,IEEE Transactions on Fuzzy Systems, vol. 10, pp. 117–127, 2002. J.M. Mendel, H. Wu, “Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems”, IEEE Transactions on Fuzzy Systems, vol. 14, pp. 781–792, 2006. J.M. Mendel, “Uncertain Rule-Based Fuzzy Logic Systems”, Editor Prentice-Hall, Upper Saddle River, NJ, 2001. J.M. Mendel, “Advances in type-2 fuzzy sets and systems”, Information Sciences, vol. 177, pp. 84–110, 2007. J. Montero, D. Gomez and H. Bustince, “On the relevance of some families of fuzzy sets”, Fuzzy Sets and Systems, vol. 158, pp. 2429–2442, 2007. S. V.Ovchinnikov, M. Roubens, “On strict preference relations”, Fuzzy Sets and Systems, vol. 43, pp. 319–326, 2001. R. Sambuc, “Function Φ-Flous, Application a l’aide au Diagnostic en Pathologie Thyroidienne”, These de Doctorat en Medicine, Marseille,1975. E. Trillas, “Sobre funciones de negaci´on en la teor´ıa de conjuntos difusos”, Stochastica, vol. III-1, pp. 47–59, 1979 (in Spanish). Reprinted (English version) in: Advances f Fuzzy Logic, Edited by S. Barro et altri-Universidad de Santiago de Compostela, pp. 31–43, 1998. E. Trillas, C. Alsina, J.M. Terricabras, “Introducci ´on a la l´ogica borrosa”, Ariel Matem´atica, 1995. E. Trillas, L. Valverde, “On mode and implication in approximate reasoning”, in: Approximate reasoning in Expert Systems, Edited by M.M. Gupta, A. Kandel, W. Bandler, J.B. Kiszka, North-Holland,Amsterdam, 157–166 , 1985. I.B. Turksen, “Interval valued fuzzy sets based on normal forms”,Fuzzy Sets and Systems, vol. 20, pp. 191–210, 1986. I.B. Turksen, , Z. Zhong “An approximate analogical reasoning schema based on similarity measures and interval-valued fuzzy sets,”, Fuzzy Sets and Systems, vol. 34, pp. 323–346, 1990. I.B. Turksen “Interval-valued fuzzy sets and compensatory AND”,Fuzzy Sets and Systems, vol. 51, pp. 295–307, 1992. S. Weber, “A general concept of fuzzy connectives,negations and implications based on t-norms and t-conorms”, Fuzzy sets and Systems,vol. 11, 115–134, 1983. L. A. Zadeh. “Fuzzy Sets”, Information Control, vol. 8, pp. 338–353,1965. L. A. Zadeh, “Outline of a new approach to analysis of complex systems and decision processes”, IEEE Transactions on Systems, Man,and Cybernetics, vol. 3, pp. 28–44, 1973. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning I”, Information Sciences, vol. 8, pp. 199–249,1975. |

Deposited On: | 29 Oct 2012 10:53 |

Last Modified: | 07 Feb 2014 09:38 |

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