Some Remarks on Hyperstructures their Connections with Fuzzy Sets and Extensions to Weak Structures

Piergiulio Corsini

Abstract


A brief excursus on the last results on Hyperstructures and their connections with Fuzzy Sets. At the end a calculation of the Fuzzy Grade of Hv-structures of order two.


Keywords


hyperstructure

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References


Ameri R., Nozari T., A connection between categories of (fuzzy) multialge-bras and (fuzzy) algebras, Italian Journal of Pure and Applied Mathematics, 27 (2010)

Ameri R., Shafiyan N., Fuzzy prime and primary hyperideals in hyperrings. Advances in Fuzzy Mathematics, n. 1-2. (2007)

Ameri R., Zahedi M.M., Hypergroup and join space induced by a fuzzy subset, PU.M.A. vol. 8, (2-3-4) (1997)

Ashrafi R., About some join spaces and hyperlattices, Italian Journal of Pure and Applied Mathematics, 10 (2001)

Ashrafi R., Zadeh A.H., Yavari, M., Hypergraphs and join spaces, Italian Journal of Pure and Applied Mathematics, 12 (2002)

Asokumar A., Velrajan M., Hyperring of matrices over regular hyperring, Italian Journal of Pure and Applied Mathematics, 23 (2008)

Asokumar A., Velrajan M., Characterization of regular hyperrings, Italian Journal of Pure and Applied Mathematics, 22 (2007)

Borzooei H. Harizavi, Isomorphismes theorems of Hyper K Algebras, Ital-ian Journal of Pure and Applied Mathematics, 21 (2007)

Corsini P., Join Spaces, Power Sets, Fuzzy Sets, Proc. Fifth International Congress on A.H.A., 1993, Iasi, Romania

Corsini P., Rough Sets, Fuzzy Sets and Join Spaces, Honorary Volume ded-icated to Prof. Emeritus Ioannis Mittas, Aristotle Univ. of Thessaloniki, 1990-2000, M. Konstantinidou, K. Serafimidis, G. Tsagas (Eds.)

Corsini P., Fuzzy sets, join spaces and factor spaces, PU.M.A., 11 (3) (2000)

Corsini P., Binary relations, interval structures and join spaces, J. Appl. Math. and Computing, Korean Soc. for Comput. and Appl. Math., 10 (2002)

Corsini P., On Chinese Hyperstructures, Proc. of the seventh Congress A.H.A., Taormina, 1999, Journal of Discrete Mathematical Sciences and Criptography, 6 (2003)

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., Fuzzy Sets, Join Spaces and Factor Spaces, PU.M.A., vol. 11. n. 3, (2000)

Corsini P., On the hypergroups associated with Binary Relations, Journal of Multiple-valued Logic, 5 (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, South-east Bulletin of Math., 27 (2003)

Corsini P., Hyperstructures associated with Ordered Sets, Bull. Greek Math. Soc., 48 (2003)

Corsini P., On the fuzzy grade of hypergroups, International Journal of Al-gebra and Statistics, vol. 1, n. 2, (2012)

Corsini P., Join Spaces, multivalued functions and soft sets, Proceedings of the International Conference on Algebra 2010, (ICA 2010), Universitas Gadjah Mada and the Southeast Asian Math.

Corsini P., Hypergroups associated with HX-groups, Analele Univ. Ovid-ius (Constanta), vol.2/2017

Corsini P. , HX-groups and Hypergroups, Analele Univ. Ovidius, Math Se-ries, n. 3, 2016

Corsini P., HX-hypergroups associated with the direct products of some Z/nZ, accepted by Algebraic Structures and their Applicaations, 2016

Corsini P., Bonansinga P., Sugli omomorfismi di semi-ipergruppi e di iper-gruppi, B.U.M.I., 1-B, (1982)

Corsini P., Borzooei R.A., Zahedi M.M., Some kinds of positive implicative hyper K-ideals, Journal of Discrete Mathematical Sciences and Criptogra-phy, Delhi, vol. 6, n. 1 (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, Iran J. of Fuzzy Systems, 1 (2004)

Corsini P., Cristea I., Fuzzy sets and non complete 1-hypergroups, An. St. Univ. Ovidius Constanta, 13 (1), (2005)

Corsini P., Davvaz B., New connections among multivalued functions, hy-perstructures and fuzzy sets, Jordan Journal of Mathematics and Statistics (JJMS), 3 (3) (2010)

Corsini P., Faisal Yousafzai F., Kostaq Hila, Anwar Zeb,Existence of non-associative algebraic hyper-strucures and related problems, Afrika Matem-atika, African Mathematical Union and Springer-Verlag, (2014)

Corsini P., Leoreanu V., Join Spaces associated with Fuzzy Sets, J. of Com-binatorics, Information and System Sciences, vol. 20, n. 1 (1995)

Corsini P., Leoreanu V., Hypergroups and binary relations, Algebra Uni-versalis, 43 (2000)

Corsini P., Leoreanu–Fotea V., Iranmanesh A., On the sequence of hyper-groups and membership functions determined by a hypergraph, J. Multiple Logic and Soft Computing, 14 (6) (2008)

Corsini P., Leoreanu–Fotea V., On the grade of a sequence of fuzzy sets and join spaces determined by a hypergraph, Southeast Asian Bulletin of Mathematics, 34, (2010)

Corsini P., Mahjoob R., Multivalued functions, fuzzy subsets and join spaces, Ratio Mathematica, 20, (2010)

Corsini P., Tofan I., On Fuzzy Hypergroups, PU.M.A., vol. 8, (1997)

Corsini P., Vougiouklis T., From groupoids to groups through hypergroups, Rend. Mat. Ser. VII, vol. 9 (1989)

Corsini P., Yaqoob N., Yousafai Faisal, On intra-regular left almost semi-hypergroups with pure left identity, Journal of Mathematics, An open ac-cess journal, Hindawi Publishing Corporation, in press, (2013)

Corsini P., Yin Y., Zhan J, Fuzzy Roughness of n-ary Hypergroups based on a complete residuated Lattice, Neural Comput. and Applications, (2011)

Cristea I., A property of the connection between fuzzy sets and hyper-groupoids, Italian Journal of Pure and Applied Mathematics, n. 21, (2007)

Cristea I., Aangheluta C., Fuzzy grade of the complete hypergroups, sub-mitted to Iranian Lournal of Fuzzy Systems (2011)

Cristea I., Hyperstructures and fuzzy sets endowed with two membership functions, Fuzzy Sets and Systems, 160, (2009)

Cristea I., Davvaz B., Atanassov’s intuitionistic fuzzy grade of hyper-groups, Information Sciences, 180 (2010)

Darafsheh M.R., Davvaz B., Hv-Ring of fractions, Italian Journal of Pure and Applied Mathematics, n. 5 (1999)

Davvaz B., Interval-valued fuzzy subhypergroups, Korean J. Comput. Appl. Math. 6, n.1. (1999)

Davvaz B., Corsini P., Generalized fuzzy polygroups, Iranian Journal of Fuzzy Systems, Vol.3. N-1. (2006)

Davvaz B., Corsini P., Redifined Hv- submodules and many valued impli-cations, Informations Sciences, 177, (2007)

Davvaz B., Corsini P. Leoreanu–Fotea V., Fuzzy n-ary polygroups, Com-puters and Mathematics, 57, (2009)

Davvaz B., Corsini P. Leoreanu-Fotea V., Atanassov’s intuitionistic (S; T )-fuzzy n-ary subhypergroups, Information Science, 179 (2009)

Davvaz B., Zhan J., Shum K.P., Generalized fuzzy polygroups endowed with interval valued membership functions Journal of intelligent fuzzy sys-tems, vol. 19, n. 3, (2008)

Feng Y., L-fuzzy and [ hyperoperations, Set-Valued Mathematics and Applications, 2 (2008)

Feng Y., On Fuzzy Corsini’s Hyperoperations, Journal of Applied Mathe-matics, Volume 12, Hindawi Publishing Corporation

Feng Y., Algebraic hyperstructures obtained from algebraic structures with fuzzy binary relations, Italian Journal of Pure and Applied Mathematics, n. 25, (2009)

Feng Y., The L-fuzzy hyperstructures (X; _; ^) and (X; ^; _), Italian Jour-nal of Pure and Applied Mathematics, n. 26, (2009)

Feng Y., p-Fuzzy hypergroups and p- fuzzy join spaces obtained from p - fuzzy hypergraphs, Italian Journal of Pure and Applied Mathematics, n. 27, (2010)

Feng Y., L-fuzzy and / hyperoperatios, Fuzzy Sets, Rough Sets, Multi-valued Operations and Applications, Vol. 1, n. 1, (2009)

Golmohamadian M. and Zahedi M.M, Hyper K-Algebras induced by a deterministic finite automaton. Italian Journal of Pure and Applied Mathe-matics, n. 27, (2010)

Hasankhani A., Zahedi M.M ., F -Hyperrings, Italian Journal of Pure and Applied Mathematics, n. 4, (1998)

Hasankhani A., Zahedi M.M., F-Hyperrings, Italian Journal of Pure and Applied Mathematics, n. 4, (1998)

Hoskova S., Quasi-order hypergroups and T hypergroups, International Journal of Mathematics and Analysis, Vol. 2. No. 1-3, Serials Publications, India (2006)

Hoskova S., Construction of hypergroups from ordered semigroups, Os-trava, VSB-Technicka Univerzita Ostrava, Czech Republic, (2006)

Hoskova S., Orders Hypergroups. The unique square root condition for Quasi-Order-Hypergroups, Set-Valued Mathematics and Applications, n. 1 (2008)

Jantosciak J., Homomorphisms, equivalences and reductions in hyper-groups, Riv. Mat. Pura e Applicata, n. 9, (1991)

Jantosciak J., Transposition Hypergroups: non commutative join spaces, Journal of Algebra, 187, (1997)

Jun Young Bae, Roh Eun Hwan, On strong Hyper K-ideals of HyperK-algebras, Italian Journal of Pure and Applied Mathematics, n. 10, (2001)

Kehagias Ath., An example of L-fuzzy join space, Circ. Mat. Palermo (2002)

Kellil R., and Bouaziz, F., New Investigations on HXGroups and Soft groups, accepted by Italian Journal of Pure and Applied Mathematics on October 13, 2017, n. 42

Kemprasit Y., Multiplicative interval semigroups on R admitting hyperring structure, Italian Journal of Pure and Applied Mathematics, 11 (2002)

Kemprasit Y., Transformation semigroups admitting hyperring structure, Italian Journal of Pure and Applied Mathematics, 10 (2001)

Kemprasit Y., Hyperring structure of some semigroups of linear transfor-mations, Italian Journal of Pure and Applied Mathematics, 13 (2003)

Konstantinidou–Serafimidou M., Distributive and complemented hyperlat-tices, Praktika tes Akademion Athenon. Math. Tomos 56, (1981)

Leoreanu V., On the heart of join spaces and of regular hypergroups, Riv. Mat, Pura e Appl., 17 (1995)

Leoreanu V., Direct limit and products of join spaces associated with rough sets, Honorary Volume dedicated to Prof. Emeritus Ioannis Mittas, Aristo-tle Univ. of Thessaloniki, 1999-2000

Leoreanu V., About hyperstructures associated with fuzzy sets of type 2, Italian Journal of Pure and Applied Mathematics, 17 (2005)

Leoreanu–Fotea V., Several types of n-ary hypergroups, Italian Journal of Pure and Applied Mathematics, 23 (2008)

Leoreanu–Fotea, V., Corsini P., Soft hypergroups, Critical Review, Society for Mathematics of Uncertainty. Creighton Univesity,- USA, July 2010, vol.

IV

Leoreanu–Fotea, V, Rosenberg I., Hypergroupoids determined by lattices, European Journal of Combinatorics, 31 (2010)

Li Hongxing, Duan Qinzhi and Wang Peizhuang, Hypergroup (I). Busefal, Vol. 23, (1985)

Li Hongxing, and Wang Peizhuang, Hypergroup, Busefal, (II), vol. 25, (1986). Li Hongxing,

Li Hongxing, HX-Groups, Busefal, Vol. 33, (1987)

Marty F., Sur une gen´eralization´ de la notion de groupe, IV Congres` des Mathematiciens´ Scandinaves, Stockholm, (1934)

Maturo A., A geometrical approach to the coherent conditional probabilily and its fuzzy extensions, Scientific Annals of A.S.V.M., “Ion Ionescu de la Brad”, Iasi XLIX. (2006)

Maturo A., On some structure of fuzzy numbers, Proceedings of 10th In-ternational A.H.A. Congress, Brno, (2008)

Maturo A., Join coherent previsions, Set-valued Mathematics and Applica-tions, n. 2, (2008)

Maturo A., Coherent conditional previsions, and geometric hyper-groupoids, Fuzzy Sets, Rough Sets, Multivalued Operations and Applica-tions, Vol.1, n. 1, (2009)

Mi Honghai, Uniform HX-groups, Busefal Vol. 47, (1991)

Mittas J., Hypergroupes canoniques, Math. Balk. t. 2, Beograd, (1972)

Mittas J., Generalized M-polysymmetric hypergroups. Proceedongs 10th International Congress on AHA, Brno, (2008)

Namnak C., Triphop N., Kemprasit Y., Homomorphisms of some multi-plicative Hyperrings, Set-valued Mathematics and Applications, 2 (2008)

Pawlak Z., Rough Sets. Theoretical Aspect of Reasoning about Data, Kluwer Academic Publishers, (1991)

Prenowitz W., Jantosciak J., Geometries and Join Spaces, J. Reine und angewandte Math., 257 (1972)

Rasovic S., Jancic, On a class of P -hyperrings, Mathematica Montesnigri, Vol. 18-19 (2006)

Rasovic S., About the hyperring of polynomials, Italian Journal of Pure and Applied Mathematics, 21 (2007)

Rasovic S., On a class of P 1 P 2 -hyperrings, and hypernear-rings, Set-Valued Mathematics and Applications, Vol. 1, n. 1, (2008)

Rasovic S., On a class of Chinese hyperrings, Italian Journal of Pure and Applied Mathematics, 28 (2011)

Rosenberg I., Hypergroups and join spaces determined by relations, Italian Journal of Pure and Applied Mathematics, 4 (1998)

Rosenberg I., Hypergroups induced by paths of a directed graph, Italian Journal of Pure and Applied Mathematics, 4 (1998)

Rosenfeld A., Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517

Sen M.K., Dasgupta U., H-Relation and its Associated Hyperstructures, Set-valued Mathematics and Applications, 2 (2008)

Serafimidis K., Kehagias Ath, Konstantinidou M., The L-fuzzy Corsini join hyperoperation, Italian Journal of Pure and Applied Mathematics, 12 (2002)

Serafimidis K., Konstantinidou M., Mittas J., Sur les hypergroupes canon-iques strictements reticules, Rivista di Matematica Pura e Applicata, 2 (1987)

Spartalis S., Hypergroupoids obtained from groupoids with binary rela-tions, Italian Journal of Pure and Applied Mathematics (Forum Editrice Universitaria Udinese), 16 (2004), 201-210

Spartalis S., The hyperoperation relation and the Corsini’s partial or not partial hypergroupoids (a classification), Italian Journal of Pure and Ap-plied Mathematics, 24 (2008)

Stefanescu M., Cristea I., On the fuzzy grade of hypergroups, Fuzzy Sets and Systems, 159 (2008)

Tofan I., Volf C., On some connections between hyperstructures and fuzzy sets, Italian Journal of Pure and Applied Mathematics, 7 (2000)

Torkzadeh L., Zahedi M.M., Dual commutative hyper K-ideals, Set-valued Mathematics and Applications, 1 (2008)

Yavary M., Corsini’s method and construction of Join Spaces, Italian Jour-nal of Pure and Applied Mathematics, 23 (2008)

Vougiouklis T., The fundamental relation in hyperrings. The general hyper-field, Proceedings of the Fourth International Congress AHA, (1990)

Vougiouklis T., On the hyperstructures with @-hopes, Proceedings 10th In-ternational Congress on AHA, Brno, (2008)

Zadeh L., Fuzzy Sets, Information and Control, 8 (1965)

Zahedi M.M., Ameri R., On the prime, primary and maximal subhyper-modules, Italian Journal of Pure and Applied Mathematics, 5 (1999)

Zhan J., Corsini P., L-Fuzzy Roughness in n-ary hypergroups, Accepted by Neural Computing and Applications, (2010)

Zhan J., Corsini P., L-Fuzzy Roughness in n-ary polygroups. Acepted by Acta Math. Sinica, (2010)

Zhan J., Davvaz B., Young Bae Jun, Generalized fuzzy algebraic hyper-systems, Accepted by Italian Journal of Pure and Applied Mathematics, (2010)

J. Zhan, B. Davvaz, K.P. Shum, A new view of fuzzy hyperquasigroups, Journal of Intelligent and Fuzzy Systems, on line date April 05, (2002)

Zang Zhenliang, The properties of HX-Groups, Italian Journal of Pure and Applied Mathematics, Vol. 2, (1997)

Zang Zhenliang, Classifications of HX-Groups and their chains of normal subgroups, Italian Journal of Pure and Applied Mathematics, Vol. 5, (1999).

Zhang Baojie, Li Hongxing, HX-type Chaotic (hyperchaotic) System Based on Fuzzy Inference Modeling, accepted by Italian Journal of Pure and Applied Mathematics, (2016)

Corsini P., Prolegomena of Hypergroup Theory, Aviani Editore, (1993)

Corsini P., Leoreanu V., Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, (2003)

Davvaz B., Leoreanu–Fotea, V., Hyperring Theory and Applications, Hadronic Press, (2008)

Davvaz B., Polygroup Theory and Related Systems. World Scientific Pub-lishing Co. Pte. Ltd., Hackensack, NJ, (2013)

Maturo, A., Tofan, I., Iperstrutture, Strutture Fuzzy e Applicazioni, dierre edizioni, (2001)

Prenowitz W., Jantosciak J., Join Geometries, Springer-Verlag UTM, (1979)

Shaefer G., A mathematical theory of evidence, Princeton University Press, (1976)

Vougiouklis T., Hyperstructures and their representations, Hadronic Press Inc. (1994)




DOI: http://dx.doi.org/10.23755/rm.v33i0.384

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