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MULTIVALUED FUNCTIONS, FUZZY SUBSETS AND JOIN SPACES
Abstract
One has considered the Hypergroupoid Η Γ = < H;ο Γ > associated with a multivalued function Γ from H to a set D, defined as follows:
∀ x ∈ H, x ο Γ x = ⎨y⏐ Γ(y) ∩ Γ(x) ≠ ∅⎬ ,
∀ (y,z) ∈ H 2 , y ο Γ z = y ο Γ y ∪ z ο Γ z ,
and one has calculated the fuzzy grade ∂(Η Γ ) for several functions Γ defined on sets H, such that ⎮H⎮ ∈ ⎨3, 4, 5, 6, 8, 9, 16⎬.
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Ameri R. and Zahedi M.M., Hypergroup and join space induced by a fuzzy subset, PU.M.A. vol. 8, (1997)
Ameri R. and Shafiiyan, Fuzzy Prime and Primary Hyperideals of Hyperrings, Advances in Fuzzy Math., n. 1-2, Research India Publications (2007)
Ameri R., Hedayati H, Molaee A., On fuzzy hyperideals of Γ-hyperrings, Iranian J. of Fuzzy Systems, vol. 6, n. 2, (2009)
Bakhshi M., Mashinki M., Borzooei R.A., Representation Theorem for some Algebraic Hyperstructures, International Review of Fuzzy Mathematics (IRFM), vol. 1, n.1, (2006)
Borzooei R.A., Jun Young Bae, Intuitionistic Fuzzy Hyper BCK- Ideals of BCK- Algebras, Iranian J. of Fuzzy Systems, vol. 1, n.1, (2004)
Borzooei R.A, Zahedi M.M., Fuzzy structures on hyper K-algebras, International J. of Uncertainty Fuzzyness and Knowledge-Based Systems 112, (2), (2000)
Corsini P., Prolegomena of hypergroup theory, Aviani Editore (1993)
Corsini P., Join Spaces, Power Sets, Fuzzy Sets, Proc. Fifth International Congress on A.H.A. 1993, Iasi. Romania, Hadronic Press, (1994)
Corsini P., Rough Sets, Fuzzy Sets and Join Spaces, Honorary Volume dedicated to Prof. Emeritus Ioannis Mittas, Aristotle Univ. of Thessaloniki, 1999-2000, Editors M. Konstantinidou, K. Serafimidis, G. Tsagas
Corsini P., On Chinese Hyperstructures, Proc. of the Seventh Congress A.H.A., Taormina, 1999, Journal of Discrete Mathematical Sciences & Criptography, vol. 6 (2003)
Corsini P., Fuzzy sets, join spaces and factor spaces, PU.M.A. vol. 11, n. 3, (2000)
Corsini P., Properties of hyperoperations associated with fuzzy sets and with factor spaces, International Journal of Sciences and Technology, Kashan University, vol. 1, n. 1, (2000)
Corsini P., Binary Relations, Interval Structures and Join Spaces, Korean J.Math Comput. Appl. Math., 9(1) (2002)
Corsini P., A new connection between Hypergroups and Fuzzy Sets, Southeast Asian Bulletin of Math., 27. (2003)
Corsini P., Hyperstructures associated with ordered sets, Bull. Greek. Math. Soc. vol. 48, (2003)
Corsini P., Cristea I., Fuzzy grade of i.p.s. hypergroups of order less or equal to 6, PU.M.A. vol. 14, n. 4, (2003)
Corsini P., Cristea I., Fuzzy grade of i.p.s. hypergroups of order 7, Iranian J.of Fuzzy Systems, vol. 1, n. 2 (2004)
Corsini P., Cristea I., Fuzzy sets and non complete 1-hypergroups, An. St. Univ. Ovidius Constanta, 13(1), (2005)
Corsini P. and Leoreanu V., Applications of Hyperstructure Theory, Kluwer Academic Publishers, Advances in Mathematics, n. 5, (2003)
Corsini P. and Leoreanu V., Join Spaces associated with Fuzzy Sets, J. of Combinatorics, Information and System Sciences, vol. 20, n.1. (1995)
Corsini P., Leoreanu V., Fuzzy Sets and Join Spaces associated with Rough Sets, Circolo Matematico di Palermo, S. II, T. LI, (2002)
Corsini P. and Leoreanu-Fotea V., On the grade of a sequence of fuzzy sets and join spaces determined by a hypergraph, accepted by Southeast Asian Bulletin of Mathematics (2007)
Corsini P., Leoreanu-Fotea V., Iranmanesh A., On the sequence of hypergroups and membership functions determined by a hypergraph, J. of Multiple Valued Logic and Soft Computing, vol. 14, issue 6, (2008)
Corsini P., Tofan I., On Fuzzy Hypergroups, PU.M.A. vol. 8, n. 1, (1997)
Cristea I., Complete Hypergroups, 1-Hypergroups and Fuzzy Sets, An. St. Univ. Ovidius Constanta, Vol. 10(2), (2002)
Cristea I., A property of the connection between Fuzzy Sets and Hypergroupoids, Italian Journal of Pure and Applied Mathematics, Vol. 21, (2007)
Cristea I., On the fuzzy subhypergroups of some particular complete hypergroup (II), accepted by Proc. of the 10th International Congress on A.H.A., Brno, Czech Republic (2008)
Cristea I., Hyperstructures and fuzzy sets endowed with two membership functions, Fuzzy Sets and Systems, 160, (2009)
Davvaz B., Interval-valued fuzzy subhypergroups, Korean J.Comput. Appl. Math., 6, n. 1, (1999)
Davvaz B., Fuzzy hyperideals in semihypergroups, Italian J. of Pure and Appl. Math., 8, (2000)
Davvaz B., Fuzzy Hv-submodules, Fuzzy Sets and Systems, 117, (2001)
Davvaz B., Interval-valued ideals of a hyperring, Italian J. of Pure and Applied Math., 10, (2001)
Davvaz B., Corsini P., Generalized fuzzy sub-hyperquasigroups of hyperquasigroups, Soft Computing, 10(11), (2006)
Davvaz B., Corsini P., Fuzzy n-ary hypergroups, J. of Intelligent and Fuzzy Systems, 18 (4), (2007)
Davvaz B, Leoreanu-Fotea V., On a product of Hv–submodules, International J.of Fuzzy Systems, v.19 (2), (2008)
Davvaz B., Corsini P, Leoreanu-Fotea V., Atanassov's intuitionistic (S,T)-fuzzy n-ary subhypergroups and their properties, Information Sciences, 179 (2009)
Dramalidis A, Vougiouklis T., Two Fuzzy geometric-like hyperoperations defined on the same set, Proc. of the 9th International Congress on A.H.A., (2005), University of Mazandaran, Babolsar, Iran, Journal of Basic Sciences, 2008, vol.4, n.1
Feng Yuming, Algebraic hyperstructures obtained from algebraic structures with fuzzy binary relations. , Italian J. of Pure and Applied Math. 25, (2009)
Feng Yuming, L-fuzzy * and / hyperoperations, Fuzzy Seys, Rough Sets and Multivalued Operations and Applications, International Sciences Press n.1, (2009)
Feng Yuming, The L-fuzzy hyperstructures (X, ٨, V) and (X, ٧, Λ), Italian J. of Pure and Applied Math. 26, (2009)
Feng Yuming, P-Fuzzy Hypergroupoids associated with the product of Fuzzy Hypergraphs, accepted by Italian J. of Pure and Applied Math., (2009)
Feng Yuming, Interval-valued Fuzzy Hypergraphs and Interval-valued Fuzzy Hyperoperations, accepted by Italian J. of Pure and Applied Math., (2009)
Horry M., Zahedi M.M., Hypergroups and fuzzy general automata, Iranian J. of Fuzzy Systems, vol. 6, n. 2, (2009)
Horry M., Zahedi M.M., Join Spaces and Max-Min general fuzzy automata, Italian J. of Pure and Applied Math. 26, (2009)
Kehagias Ath., An example of L-Fuzzy Join Space, Rendiconti del Circolo Mat. di Palermo, vol. 51, (2002)
Kehagias Ath., Lattice-Fuzzy Meet and Join Hyperoperations, Proc. 8th International Congress on A.H.A., Samothraki 2002, Edited by T. Vougiouklis, Spanidis Press
Kehagias Ath., L-fuzzy Join and Meet Hyperoperations and the Associated L-fuzzy Hyperalgebras, Rendiconti del Circolo Mat. di Palermo, vol. 52, (2003)
Kehagias Ath., Serafimidis K, The L-Fuzzy Nakano Hypergroup, Information Sciences, vol. 169 (2005)
Kyung Ho Kim, B. Davvaz, Eun Hwan Ro, On fuzzy hyper R-subgroups of hypernear-rings, Italian J. of Pure and Applied Math.20, (2006)
Leoreanu V., Direct limit and inverse limit of join spaces associated with rough sets, Honorary Volume dedicated to Prof. Emeritus Ioannis Mittas, Aristotle Univ. of Thessaloniki, 1999-2000
Leoreanu V., Direct limit and inverse limit of join spaces associated with fuzzy sets, PU.M.A. vol. 11, n. 3, (2000)
Leoreanu V., About hyperstructures associated with fuzzy sets of type 2, Italian Journal of Pure and Applied Mathematics, n. 17, (2005)
Leoreanu-Fotea V., Leoreanu L., About a sequence of hyperstructures associated with a rough set, accepted by Southeast Asian Bulletin of Mathematics (2007)
Leoreanu-Fotea V., Fuzzy rough n-ary subhypergroups, Iranian Journal of Fuzzy Systems, vol. 5, n. 2, (2008)
Leoreanu-Fotea V., Fuzzy hypermodules, Computers and Mathematics with Applications, vol. 57, issue 3, (2009)
Leoreanu-Fotea V.,Davvaz B., Roughness in n-ary hypergroups, Information Sciences, 178. (2008)
Leoreanu-Fotea V., Rosenberg Ivo, Homomorphisms of hypergroupoids associated with L-fuzzy sets, accepted by Journal of Multiple Valued Logic Soft Comput. (2008)
Leoreanu-Fotea V., Davvaz B., Fuzzy Hyperrings, Fuzzy Sets and Systems, vol.160, issue 16 (2008)
Maturo A. A geometrical approach to the coherent conditional probability and its fuzzy extensions, Scientific Annals of University of A. S. V. M., "Ion Ionescu de la Brad",Iasi XLIX, (2006)
Maturo A., Alternative Fuzzy Operations and Applications to Social Sciences, International Journal of Intelligent Systems, to appear.
Maturo A., Squillante M., and Ventre A.G.S., (2006a), Consistency for assessments of uncertainty evaluations in non-additive settings in: Amenta, D'Ambra, Squillante and Ventre, Metodi, modelli e tecnologie dell’informazione a supporto delle decisioni, Franco Angeli, Milano.
Maturo A., Squillante M., and Ventre A. G. S., (2006b), Consistency for nonadditive measures: analytical and algebraic methods, in B. Reusch (ed.), Computational Intelligence, Theory and Applications, in Advances in Soft Computing, Springer, Berlin, Heidelberg, New York.
Maturo A., Squillante M., and Ventre A. G. S., (2009), Coherence for fuzzy Measures and Applications to Decision Making, Proceeding of the Intern. Conference on Preferences and Decisions, Trento, 6th-8-th april 2009.
Maturo A., Squillante M., and Ventre A. G. S., (2009), Decision Making, Fuzzy Measures, and Hyperstructures, IV meeting on Dynamics of Social and Economic systems, April 14-18, 2009, Argentina, submitted to Advances and Applications in Statistical Sciences.
Maturo A., On some structures of fuzzy numbers, accepted for publication in Proceedings of 10th International AHA Congress Brno, 3 - 9. 9. 2008.
Maturo A., Tofan I., Iperstrutture, strutture fuzzy ed applicazioni, Pubblicazioni Progetto Internazionale Socrates, Italia-Romania, San Salvo. Dierre Edizioni
Prenowitz W and Jantosciak J., Geometries and Join Spaces, J. reine und angewandte Math. 257, (1972)
Serafimidis K., Konstantinidou M., Kehagias Ath., L - Fuzzy Nakano Hyperlattices, Proc. 8th International Congress on A.H.A., Samothraki (2002), Spanidis Press
Serafimidis K., Kehagias Ath., Konstantinidou M., The L-Fuzzy Corsini Join Hyperoperation, Italian Journal of Pure and Applied Mathematics, n. 12, (2003)
Stefanescu M., Cristea I., On the Fuzzy Grade of Hypergroups, Fuzzy Sets and Systems, (2008)
Tofan I., Volf C., On some connections between hyperstructures and fuzzy sets, Italian Journal of Pure and Applied Mathematics, n. 7, (2000)
Zadeh L.A., Fuzzy Sets, Information and Control, 8, (1965)
Zahedi M.M., Bolurian M., Hasankhani A., On polygroups and fuzzy subpolygroups, J. of Fuzzy Mathematics, vol. 3, n.1, (1995)
Zahedi, MM, Hasankhani, A, F-polygroups (II), Information Sciences, v 89, n 3-4, Mar, 1996,
M. M. Zahedi, L. Torkzadeh: Intuitionistic Fuzzy Dual Positive Implicative Hyper K- Ideals. WEC (5) 2005
Zhan Janming, Davvaz B., Shum K.P., A new view of hypermodules, Acta Mathematica Sinica, English Series 23(8), (2007)
Zhan Janming, Davvaz B., Shum K.P., On fuzzy isomorphism theorems of hypermodules, Soft Computing, 11, (2007)
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