(Intuitionistic) Fuzzy Grade of a Hypergroupoid: A Survey of Some Recent Researches

Authors

  • Irina Cristea Centre for Systems and Information Technologies University of Nova Gorica, Slovenia

Keywords:

(Intuitionistic) Fuzzy Grade, Join Space, I.p.s. Hy- pergroup, Complete Hypergroup.

Abstract

This paper aims to present a short survey on two numerical functions determined by a hypergroupoid, called the fuzzy grade and the intuitionistic fuzzy grade of a hypergroupoid. It starts with the main construction of the sequences of join spaces and (intuitionistic) fuzzy sets associated with a hypergroupoid. After some computations of the above grades, we discuss some similarities and differences between the two grades for the complete hypergroups and for the i.p.s. hypergroups. We conclude with some open problems.

References

R. Ameri, M.M. Zahedi, Hypergroup and join space induced by a fuzzy subset, Pure Math. Appl., 8 (1997).

C. Angheluta, I. Cristea, Fuzzy grade of complete hypergroups, Iran. J. Fuzzy Syst., in press.

C. Angheluta, I. Cristea, Atanassov's intuitionistic fuzzy grade of the complete hypergroups, J. Mult.-Valued Logic Soft Comput., in press.

M. Asghari-Larimi, I. Cristea, Atanassov's intuitionistic fuzzy index of hypergroupoids, Ratio Math., in press.

K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), no.1, 87-96.

K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Sys-tems, 33 (1989), no.1, 37-45.

K. Atanassov, New operations de ned over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994), no.2, 137-142.

K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Studies in Fuzziness and Soft Computing, 35, Physica-Verlag, Hei-delberg, 1999.

P. Burillo, H. Bustince, Construction theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 84 (1996), no.3, 271-281.

H. Bustince, P. Burillo, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78 (1996), no. 3, 305316.

P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1993.

P. Corsini, Join spaces, power sets, fuzzy sets, Algebraic hyperstruc-tures and applications (Iasi, 1993), 4552, Hadronic Press, Palm Har-bor, FL, 1994.

P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. Math., 27 (2003), no.2, 221-229.

P. Corsini, I. Cristea, Fuzzy grade of i.p.s. hypergroups of order less or equal to 6, Pure Math. Appl., 14 (2003), 275-288.

P. Corsini, I. Cristea, Fuzzy grade of i.p.s. hypergroups of order 7, Iran. J. Fuzzy Syst., 1(2004), no. 2, 15-32.

P. Corsini, V. Leoreanu, Join Spaces Associated with Fuzzy Sets, J. Combin. Inform. Syst. Sci., 20(1995), no.1-4, 293-303.

P. Corsini, V. Leoreanu, Applications of hyperstructure theory, Ad-vances in Mathematics (Dordrecht), 5, Kluwer Academic Publishers, Dordrecht, 2003.

P. Corsini, V. Leoreanu-Fotea, On the grade of a sequence of fuzzy sets and join spaces determined by a hypergraph, Southeast Asian Bull. Math., 34(2010), no.2, 231-242.

P. Corsini, V. Leoreanu-Fotea, A. Iranmanesh, On the sequence of hypergroups and membership functions determined by a hypergraph,

J. Mult.-Valued Logic Soft Comput., 14(2008), no.6, 565-577.

P. Corsini, R. Mahjoob, Multivalued functions, fuzzy subsets and join spaces, Ratio Math., 20(2010), 1-41.

I. Cristea, Complete Hypergroups, 1-Hypergroups and Fuzzy Sets, An. St. Univ. Ovidius Constanta, 10(2002), no.2, 25-38.

I. Cristea, A property of the connection between fuzzy sets and hyper-groupoids, Ital. J. Pure Appl. Math., 21(2007), 73-82.

I. Cristea, About the fuzzy grade of the direct product of two hyper-groupoids, Iran. J. Fuzzy Syst., 7(2)(2010), 95-108.

I. Cristea, B. Davvaz, Atanassov's intuitionistic fuzzy grade of hyper-groups, Inform. Sci., 180 (2010), no.8, 1506-1517.

B. Davvaz, E. Hassani Sadrabadi, I. Cristea, Atanassov's intuitionistic fuzzy grade of i.p.s. hypergroups of order less than or equal to 6, Iran.

J. Fuzzy Syst., 9(2012), vol.4, 71-97.

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Published

2012-12-18

Issue

Vol. 23 (2012)

Section

Volume 23-2012

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