ORIGINAL_ARTICLE
Cover Vol.6, No.2, June 2009 (IJFS)
http://ijfs.usb.ac.ir/article_2897_523834bf7d1d175e7c59916a7f074f37.pdf
2009-06-29T11:23:20
2017-12-11T11:23:20
0
10.22111/ijfs.2009.2897
ORIGINAL_ARTICLE
A NOTE ON EVALUATION OF FUZZY LINEAR REGRESSION
MODELS BY COMPARING MEMBERSHIP FUNCTIONS
Kim and Bishu (Fuzzy Sets and Systems 100 (1998) 343-352) proposeda modification of fuzzy linear regression analysis. Their modificationis based on a criterion of minimizing the difference of the fuzzy membershipvalues between the observed and estimated fuzzy numbers. We show that theirmethod often does not find acceptable fuzzy linear regression coefficients andto overcome this shortcoming, propose a modification. Finally, we present twonumerical examples to illustrate efficiency of the modified method.
http://ijfs.usb.ac.ir/article_203_91984c1c552a9c8428c6600866e5cadd.pdf
2009-06-10T11:23:20
2017-12-11T11:23:20
1
6
10.22111/ijfs.2009.203
Fuzzy linear regression
Fuzzy number
Least-squares method.
This paper is supported in part by Fuzzy Systems and Applications Center of Excellence
Shahid Bahonar University of Kerman
Kerman
I.R. of Iran
H.
Hassanpour
hhassanpur@birjand.ac.ir
true
1
Department of Mathematics, University of Birjand, Birjand, Iran
Department of Mathematics, University of Birjand, Birjand, Iran
Department of Mathematics, University of Birjand, Birjand, Iran
AUTHOR
H. R.
Malek
maleki@sutech.ac.ir
true
2
Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Iran
Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Iran
Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Iran
LEAD_AUTHOR
M. A.
Yaghoobi
yaghoobi@mail.uk.ac.ir
true
3
Department of Statistics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Statistics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Statistics, Shahid Bahonar University of Kerman,
Kerman, Iran
AUTHOR
[1] A. Abdalla and J. J. Buckley, Monte Carlo methods in fuzzy linear regression, Soft Computing,
1
11 (2007), 991-996.
2
[2] S. Abbasbandy and M. Alavi, A method for solving fuzzy linear systems, Iranian Journal of
3
Fuzzy Systems, 2(2) (2005), 37-44.
4
[3] S. M. Abu Nayeem and M. Pal, The p-center problem on fuzzy networks and reduction of
5
cost, Iranian Journal of Fuzzy Systems, 5(1) (2008), 1-26.
6
[4] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model,
7
Iranian Journal of Fuzzy Systems, 5(2) (2008), 1-19.
8
[5] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
9
Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-22.
10
[6] S. H. Choi and J. J. Buckley, Fuzzy regression using least absolute deviation estimators, Soft
11
Computing, 12(3) (2008), 257-263.
12
[7] C. Kao and C. L. Chyu, A fuzzy linear regression model with better explanatory power, Fuzzy
13
Sets and Systems, 126 (2002), 401-409.
14
[8] C. Kao and C. L. Chyu, Least-squares estimates in fuzzy regression analysis, European Journal
15
of Operational Research, 148 (2003), 426-435.
16
[9] B. Kim and R. R. Bishu, Evaluation of fuzzy linear regression models by comparing membership
17
functions, Fuzzy Sets and Systems, 100 (1998), 343-352.
18
[10] H. Lee and H. Tanaka, Upper and lower approximation models in interval regression using
19
regression quantile techniques, European Journal of Operational Research, 116 (1999), 653-
20
[11] MATLAB 7.0, The Mathworks, (www.mathworks.com).
21
[12] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression models with least
22
square errors, Applied Mathematics and Computation, 163 (2005), 977-989.
23
[13] J. Mohammadi and S. M. Taheri, Pedomodels fitting with fuzzy least squares regression,
24
Iranian Journal of Fuzzy Systems, 1(29) (2004), 45-62.
25
[14] M. Sakawa and H. Yano, Fuzzy linear regression and its applications, In: J. Kacprzyk and
26
M. Fedrizzi (Eds.), Studies in fuzziness, fuzzy regression analysis, Omnitech Press, Warsaw,
27
Poland, (1992), 61-80.
28
[15] M. R. Safi, H. R. Maleki and E. Zaeimazad, A note on Zimmermann method for solving
29
fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-46.
30
[16] E. Shivanian, E. Khorram and A. Ghodousian, Optimization of linear objective function subject
31
to fuzzy relation inequalities constraints with Max-average composition, Iranian Journal
32
of Fuzzy Systems, 4(2) (2007), 15-30.
33
[17] S. M. Vaezpour and F. Karimi, t-Best approximation in fuzzy normed spaces, Iranian Journal
34
of Fuzzy Systems, 5(2) (2008), 93-99.
35
[18] H. C. Wu, Fuzzy linear regression model based on fuzzy scalar product, Soft Computing, 12
36
(2008), 469-477.
37
[19] M. A. Yaghoobi and M. Tamiz, A Short note on the relationship between goal programming
38
and fuzzy programming for vectormaximum problems, Iranian Journal of Fuzzy Systems, 2
39
(2) (2005), 31-36.
40
[20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
41
ORIGINAL_ARTICLE
DIRECTLY INDECOMPOSABLE RESIDUATED LATTICES
The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are directly indecomposable. We apply these results toprove some properties of the Boolean center of a residuated lattice and alsodefine the algebras on subintervals of residuated lattices.
http://ijfs.usb.ac.ir/article_204_3e6b6b9895e27badb0b800d0bb818256.pdf
2009-06-10T11:23:20
2017-12-11T11:23:20
7
18
10.22111/ijfs.2009.204
Residuated lattice
Complementary factor congruence
Boolean center
Directly indecomposable algebra
Subdirectly irreducible algebra
Normal filter
Lavinia Corina
Ciungu
lavinia_ciungu@math.pub.ro
true
1
Polytechnical University of Bucharest, Splaiul Independentei
313, Bucharest, Romania
Polytechnical University of Bucharest, Splaiul Independentei
313, Bucharest, Romania
Polytechnical University of Bucharest, Splaiul Independentei
313, Bucharest, Romania
LEAD_AUTHOR
[1] P. Bahls, J. Cole, N. Galatos, P. Jipsen and C. Tsinakis, Cancellative residuated lattices,
1
Algebra Universalis, 50 (2003), 83-106.
2
[2] M. Bakhshi, M. M. Zahedi and R. A. Borzooei, Fuzzy (positive,weak) implicative BCK-ideals,
3
Iranian Journal of Fuzzy Systems, 2 (2004), 63-73.
4
[3] A. S. Boroumand and Y. B. Jun, Redefined fuzzy subalgebras of BCI/BCK-algebras, Iranian
5
Journal of Fuzzy Systems, 2 (2008), 63-70.
6
[4] S. Burris and H. P. Sankappanavar, A course in universal algebra, Springer-Verlag, New
7
York, 1981.
8
[5] L. C. Ciungu, Classes of residuated lattices, Annals of University of Craiova, Math. Comp.
9
Sci. Ser., 33 (2006), 189-207.
10
[6] L. C. Ciungu, Some classes of pseudo-MTL algebras, Bull. Math. Soc. Sci. Math. Roumanie,
11
Tome, 50(98) (2007), 223-247.
12
[7] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BL-algebras: Part I, Multiple Valued
13
Logic, 8 (2002), 673-714.
14
[8] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BL-algebras: Part II, Multiple Valued
15
Logic, 8 (2002), 715-750.
16
[9] A. Dvure˘censkij and M. Hy˘cko, Algebras on subintervals of BL algebras, pseudo-BL algebras
17
and bounded residuated R`-monoids, Mathematica Slovaca, 56 (2006), 125-144.
18
[10] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated lattices: an algebraic glimpse at
19
substructural logics, Elsevier, 2007.
20
[11] G. Georgescu, L. Leu˘stean and V. Preoteasa, Pseudo-hoops, Journal of Multiple-Valued Logic
21
and Soft Computing, 11 (2005), 153-184.
22
[12] G. Gr¨atzer, Lattice theory, W. H. Freeman and Company, San Francisco, 1979.
23
[13] A. Hasankhani and H. Saadat, Some quotiens on a BCK-algebra generated by a fuzzy set,
24
Iranian Journal of Fuzzy Systems, 2 (2004), 33-43.
25
[14] A. Iorgulescu, Classes of pseudo-BCK algebras - Part I, Journal of Multiple-Valued Logic
26
and Soft Computing, 12 (2006), 71-130.
27
[15] A. Iorgulescu, Classes of pseudo-BCK algebras - Part II, Journal of Multiple-Valued Logic
28
and Soft Computing, 12 (2006), 575-629.
29
[16] A. Iorgulescu, Algebras of logic as BCK algebras, ASE Ed., Bucharest, 2008.
30
[17] P. Jipsen and C. Tsinakis, A survey of residuated lattices, In: Ordered Algebraic Structures,(
31
J.Martinez, ed) Kluwer Academic Publishers, Dordrecht, 2002, 19-56.
32
[18] T. Kowalski and H. Ono, Residuated lattices: an algebraic glimpse at logics without contraction,
33
Japan Advanced Institute of Science and Technology, 2001.
34
[19] L. Liu and K. Li, Fuzzy filters of BL-algebras, Information Science, 173 (2005), 141-154.
35
ORIGINAL_ARTICLE
UNIFORM AND SEMI-UNIFORM TOPOLOGY ON GENERAL
FUZZY AUTOMATA
In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of a general fuzzy automaton. We then constructa semi-uniform structure on , the set of all nite words on , the set ofinput symbols of a general fuzzy automaton and, nally, using these semi-uniform structures, we construct two topologies on Q and and discuss theirproperties.
http://ijfs.usb.ac.ir/article_205_ec6fce5c69b2892bbfa26aecd7e61bf8.pdf
2009-06-10T11:23:20
2017-12-11T11:23:20
19
29
10.22111/ijfs.2009.205
(General) Fuzzy automata
(Uniform) Topology
Response function
Compatibility
Transitivity
M.
Horry
mohhorry@yahoo.com
true
1
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
LEAD_AUTHOR
M. M.
Zahedi
zahedi mm@mail.uk.ac.ir
true
2
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
AUTHOR
[1] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
1
of Approximate Reasoning, 38 (2005), 175-214.
2
[2] I. M. Hanafy, A. M. Abd El-Aziz and T. M. Salman, Semi -compactness in Intuitionistic
3
Fuzzy Topological Spaces, Iranian Journal of Fuzzy Systems, 3(2) (2006), 53-62.
4
[3] K. D. Joshi, Introduction to general topology, New Age International Publisher, India, 1997.
5
[4] Y. B. Jun and H. S. Kim, Uniform structure in positive implicative algebras, International
6
Mathematical Journal, 2 (2002), 215-218.
7
[5] S. P. Li, Z. Fang and J. Zhao, P2-Connectedness in L-Topological Spaces, Iranian Journal of
8
Fuzzy Systems, 2(1) (2005), 29-36.
9
[6] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,
10
Cha-pman and Hall/CRC, London/Boca Raton, FL, 2002.
11
[7] D. S. Malik and J. N. Mordeson, Fuzzy discrete structures, Physica-Verlag, New York, 2000.
12
[8] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: au-
13
tomata, rnns, and dynamic fuzzy systems, Proc. IEEE, 87(9) (1999), 1623-1640.
14
[9] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy nite-state automata can be determinis-
15
tically encoded into recurrent neural networks, IEEE Trans. Fuzzy Syst. 5(1) (1998), 76-89.
16
[10] W. Page, Topological uniform structures, Dover Publication, Inc. New York, 1988.
17
[11] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
18
to pattern classif ication, Ph.D. dissertation Purdue University, IN, 1967.
19
[12] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
20
[13] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (General) topology on max-min general
21
fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 51-68.
22
ORIGINAL_ARTICLE
IDEALS OF PSEUDO MV-ALGEBRAS BASED ON VAGUE SET
THEORY
The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension property for a vague ideal is discussed.
http://ijfs.usb.ac.ir/article_206_79b54ac844b28e6231f9bb14b4e1d8da.pdf
2009-06-10T11:23:20
2017-12-11T11:23:20
31
45
10.22111/ijfs.2009.206
Pseudo MV-algebra
(implicative
prime) vague ideal
Young Bae
Jun
skywine@gmail.com
true
1
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660-701, Korea
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660-701, Korea
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660-701, Korea
AUTHOR
Chul Hwan
Park
skyrosemary@gmail.com
true
2
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
LEAD_AUTHOR
[1] R. Biswas, Vague groups, Internat. J. Comput. Cognition, 4(2) (2006), 20-23.
1
[2] H. Bustince and P. Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems,
2
79 (1996), 403-405.
3
[3] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics,
4
23 (1993), 610-614.
5
[4] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic, 6 (2001), 95-135.
6
[5] A. Lu and W. Ng, Vague sets or intuitionistic fuzzy set for handling vague data: which one
7
is better?, Lecture Notes in Computer Science, 3716 (2005), 401-466.
8
[6] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. Online, e-2005
9
(2005), 363-369.
10
[7] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
11
ORIGINAL_ARTICLE
ON FUZZY HYPERIDEALS OF $\Gamma$-HYPERRINGS
The aim of this paper is the study of fuzzy $\Gamma$-hyperrings. In thisregard the notion of -fuzzy hyperideals of $\Gamma$-hyperrings are introduced andbasic properties of them are investigated. In particular, the representationtheorem for $\nu$-fuzzy hyperideals are given and it is shown that the image of a-fuzzy hyperideal of a $\Gamma$-hyperring under a certain conditions is two-valued.Finally, the product of $\nu$-fuzzy hyperideals are studied.
http://ijfs.usb.ac.ir/article_209_038442a0be35ebc015994bc4e8bb6f0e.pdf
2009-06-11T11:23:20
2017-12-11T11:23:20
47
59
10.22111/ijfs.2009.209
$Gamma$- hyperring
($nu$-fuzzy) hyperideal
Fuzzy polygroup
Canonical hypergroup
Fuzzy product
Reza
Ameri
ameri@umz.ac.ir
true
1
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
LEAD_AUTHOR
Hossein
Hedayati
h.hedayati@umz.ac.ir
true
2
Department of Basic Sciences,, Babol University of Technology,
Babol, Iran
Department of Basic Sciences,, Babol University of Technology,
Babol, Iran
Department of Basic Sciences,, Babol University of Technology,
Babol, Iran
AUTHOR
A.
Molaee
true
3
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
AUTHOR
[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2
1
(2005), 37-47.
2
[2] R. Ameri and H. Hedayati, Fuzzy isomorphism and quotient of fuzzy subpolygroups, Quasigroups
3
and Related Systems, 13 (2005), 175-184.
4
[3] R. Ameri and M. M. Zahedi, Hyperalgebraic systems, Italian Journal of Pure and Applied
5
Mathematics, 13 (1999), 21-32.
6
[4] W. E. Barnes, On the -rings of Nobusawa, Pacific J. Math., 13 (1966), 411-422.
7
[5] P. Corsini, Prolegomena of hypergroup theory, Second Edition Aviani editor, 1993.
8
[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publications,
9
[7] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. of Combinatorics,
10
Information and System Sciences, 20(13) (1995), 293-303.
11
[8] B. Davvaz, On Hypernear-rings and fuzzy hyperideals, J. Fuzzy Math., 7 (1999), 745-753
12
[9] W. A. Dudek, B. Davvaz and Y. B. Jun, On intuitionistic fuzzy sub-quasihypergroups of
13
quasihypergroups, Inform. Sci. (in press).
14
[10] H. Hedayati and R. Ameri, Fuzzy k-hyperideals, Int. J. Pu. Appl. Math. Sci., 2(2) (2005),
15
[11] H. Hedayati and R. Ameri, On fuzzy closed, invertible and reflexive subsets of hypergroups,
16
Italian Journal of Pure and Applied Mathematics, (to appear).
17
[12] Y. B. Jun and C. Y. Lee, Fuzzy -rings, Pusan Kyongnam Math. J. (presently, Esat Asian
18
Math. J.), 8(2) (1992), 163-170.
19
[13] M. Krasner, Approximation des corps values complete de characteristique p=0 par ceux de
20
characteristique 0, Colloque dAlgebra Superieure, C.B.R.M., Bruxelles, 1956.
21
[14] M. Krasner, A class of hyperrings and hyperfields, Intern. J. Math. Math. Sci., 6(2) (1983),
22
[15] W. J. Liu, Fuzzy invariants subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1987),
23
[16] F. Marty, Surnue generalization de la notion e group, 8iem Course Math. Scandinaves Stockholm,
24
1934, 45-49.
25
[17] C. G. Massouros, Methods of construting hyperfields, International Journal of Mathematics
26
and Mathematical Sciences, 8(4) (1985), 725-728.
27
[18] C. G. Massouros, Free and cyclic hypermodules, Annali di Matematica Pura ed Applicata, 4
28
(1988), 153-166.
29
[19] N. Nobusawa, On a generaliziton of the ring theory, Osaka J. Math., 1 (1964), 81-89.
30
[20] M. A. Ozturk, M. Uckun and Y. B. Jun, ”Fuzzy ideals in gamma-rings”, Turk J. Math., 27
31
(2003), 369-374.
32
[21] I. G. Rosenberg, Hypergroups and join spaces determined by relations, Italian J. of Pure and
33
Applied Math., 24 (1998), 93-101.
34
[22] T. Vougiuklis, Hyperstructures and their representations, Hardonic Press Inc., 1994.
35
[23] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
36
[24] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J.
37
of Fuzzy Mathematics, 3(1) (1995), 1-15.
38
[25] M. M. Zahedi and R. Ameri, On the prime, primary and maximal subhypermodules, Italian
39
Journal of Pure and Applied Mathematics, 5 (1999), 61-80.
40
ORIGINAL_ARTICLE
HYPERGROUPS AND GENERAL FUZZY AUTOMATA
In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an $H_{nu}$- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible and “principal and strongly connected, as appliedto them and use these concepts to construct a quasi-order hypergroup on aninvertible general fuzzy automaton. Finally, we derive relationships betweenthe properties of an invertible general fuzzy automaton and the induced hypergroup.
http://ijfs.usb.ac.ir/article_211_e7bd1dc99e2c18d86e95ab19cc9bdb1b.pdf
2009-06-11T11:23:20
2017-12-11T11:23:20
61
74
10.22111/ijfs.2009.211
(General) Fuzzy automata
(Quasi-order) Hypergroup
Invertibility
Connectedness
Mohammad
Horry
mohhorry@yahoo.com
true
1
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
LEAD_AUTHOR
Mohammad Mehdi
Zahedi
zahedi mm@mail.uk.ac.ir
true
2
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
AUTHOR
[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems,
1
2(1) (2005), 37-47.
2
[2] M. A. Arbib, From automata theory to brain theory, International Journal of Man-Machin
3
Studies, 7(3) (1975), 279-295.
4
[3] W. R. Ashby, Design for a brain, Chapman and Hall, London, 1954.
5
[4] D. Ashlock, A. Wittrock and T. Wen, Training finite state machines to improve PCR primer
6
design, in: Proceedings of the 2002 Congress on Evolutionary Computation (CEC) 20, 2002.
7
[5] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1993.
8
[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,
9
Advances in Mathematics, 2003.
10
[7] P. Corsini and I. Cristea, Fuzzy grade I.P.S hypergroups of order 7, Iranian Journal of Fuzzy
11
Systems, 1(2) (2004), 15-32.
12
[8] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
13
of Approximate Reasoning, 38 (2005), 175-214.
14
[9] B. R. Gaines and L. J. Kohout, The logic of automata, International Journal of General
15
Systems, 2 (1976), 191-208.
16
[10] Y. M. Li and W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership
17
valuesin lattice-ordered monoids, Fuzzy Sets and Systems, 156 (2005), 68-92.
18
[11] R. Maclin and J. Shavlik, Refing domain theories expressed as finite-state automata, in:
19
L.B.G. Collins (Ed.), Proceedings of the 8th International Workshop on Machine Learning
20
(ML’91), Morgan Kaufmann, San Mateo CA, 1991.
21
[12] R. Maclin and J. Shavlik, Refing algorithm with knowledge-based neural networks: improving
22
the choufasma algorithm for protein folding, in: S. Hanson, G. Drastal and R. Rivest (Eds.),
23
Computational Learning Theory and Natural Learning Systems, MIT Press, Cambridge, MA,
24
[13] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, Theory and Applications,
25
Chapman and Hall/CRC, London/Boca Raton, FL, 2002.
26
[14] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: automata,
27
rnns, and dynamical fuzzy systems, Proceeding of IEEE, 87(9) (1999), 1623-1640.
28
[15] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy finite-state automata can be deterministically
29
encoded into recurrent neural networks, IEEE Transactions on Fuzzy Systems, 5(1)
30
(1998), 76-89.
31
[16] B. Tucker (Ed.), The computer science and engineering handbook, CRC Press, Boca Raton,
32
[17] J. Virant and N. Zimic, Fuzzy automata with fuzzy relief, IEEE Transactions on Fuzzy Systems,
33
3(1) (1995), 69-74.
34
[18] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
35
to pattern classification, Ph.D. dissertation, Purdue University, Lafayette, IN, 1967.
36
[19] M. Ying, A formal model of computing with words, IEEE Transactions on Fuzzy Systems,
37
10(5) (2002), 640-652.
38
[20] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
39
[21] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (General) topology on max-min general
40
fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 51-68.
41
ORIGINAL_ARTICLE
APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS
The concept of soft sets, introduced by Molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and soft deductive systems are introduced, and their basic propertiesare investigated. The relations between soft Hilbert algebras, soft Hilbertabysmal algebras and soft Hilbert deductive algebras are also derived.
http://ijfs.usb.ac.ir/article_212_0e2304d1bdfe452ab84730ecc265a358.pdf
2009-06-11T11:23:20
2017-12-11T11:23:20
75
86
10.22111/ijfs.2009.212
Hilbert algebra
Soft set
Soft Hilbert algebra
Soft Hilbert abysmal
algebra
Soft Hilbert deductive algebra
(trivial
whole) soft Hilbert algebra
Soft subalgebra
Soft
abysm
Soft deductive system
Young Bae
Jun
skywine@gmail.com
true
1
Department of Mathematics Education (and RINS), Gyeongsang National
University, Chinju 660-701, Korea
Department of Mathematics Education (and RINS), Gyeongsang National
University, Chinju 660-701, Korea
Department of Mathematics Education (and RINS), Gyeongsang National
University, Chinju 660-701, Korea
AUTHOR
Chul Hwan
Park
skyrosemary@gmail.com
true
2
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
LEAD_AUTHOR
[1] H. Akta¸s and N. C¸ aˇgman, Soft sets and soft groups, Inform. Sci., 177 (2007), 2726-2735.
1
[2] A. Borumand Saeid and Y. B. Jun, Redefined fuzzy subalgebras of BCK/BCI-algebras, Iranian.
2
J. Fuzzy Systems, 5(2) (2008), 63-70.
3
[3] R. A. Borzooei and Y. B. Jun, Intuitionistic fuzzy hyper BCK-ideals of hyper BCK-algerbas,
4
Iranian. J. Fuzzy Systems, 1(1) (2004), 65-78.
5
[4] D. Busneag, A note on deductive systems of a Hilbert algebra, Kobe J. Math., 2 (1985),
6
[5] D. Busneag, Hilbert algebras of fractions and maximal Hilbert algebras of quotients, Kobe J.
7
Math., 5 (1988), 161-172.
8
[6] I. Chajda, The lattice of deductive systems on Hilbert algebras, SEA Bull. Math., 26 (2002),
9
21–26.
10
[7] I. Chajda, R. Halaˇs and Y. B. Jun, Annihilators and deductive systems in commutative
11
Hilbert algebras, Comment. Math. Univ. Carolinae, 43(3) (2002), 407-417.
12
[8] D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parametrization reduction of soft
13
sets and its applications, Comput. Math. Appl., 49 (2005), 757-763.
14
[9] B. Davvaz, Roughness based on fuzzy ideals, Inform. Sci., 176 (2006), 2417-2437.
15
[10] B. Davvaz and P. Corsini On (, )-fuzzy Hv-ideals of Hv-rings Iranian. J. Fuzzy Systems,
16
5(2) (2008), 35-48.
17
[11] A. Diego, Sur les alg´ebres de Hilbert, Collection de Logigue Math. Ser. A (Ed. Hermann,
18
Paris), 21 (1966), 1-52.
19
[12] Y. B. Jun, Deductive systems of Hilbert algebras, Math. Jpn., 43(1) (1996), 51-54.
20
[13] Y. B. Jun, Commutative Hilbert algebras, Soochow J. Math., 22(4) (1996), 477-484.
21
[14] Y. B. Jun, S. Y. Kim and E. H. Roh, The abysm of a Hilbert algebra, Sci. Math. Jpn., 65(1)
22
(2007),135-140.
23
[15] Y. B. Jun, M. A. ¨Ozt¨urk and C. H. Park, Intuitionistic nil radicals of intuitionistic fuzzy
24
ideals and Euclidean intuitionistic fuzzy ideals in rings, Inform. Sci., 177 (2007), 4662-4677.
25
[16] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras,
26
Inform. Sci., 178 (2008), 2466-2475.
27
[17] D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, Soft sets theory-based optimization, J.
28
Comput. Syc. Sci. Internat., 46(6) (2007), 872-880.
29
[18] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003),
30
[19] P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making
31
problem, Comput. Math. Appl., 44 (2002), 1077-1083.
32
[20] D. Molodtsov, Soft set theory-First results, Comput. Math. Appl., 37 (1999), 19-31.
33
[21] Z. Pawlak, Rough sets: theoretical aspects of reasoning about data, Kluwer Academic, Boston,
34
MA, (1991).
35
[22] Z. Pawlak and A. Skowron, Rudiments of rough sets, Inform. Sci., 177 (2007), 3-27.
36
[23] Z. Pawlak and A. Skowron, Rough sets: some extensions, Inform. Sci., 177 (2007), 28-40.
37
[24] Z. Pawlak and A. Skowron, Rough sets and Boolean reasoning, Inform. Sci., 177 (2007),
38
[25] L. Torkzadeh, M. Abbasi and M. M. Zahedi Some results of intuitionistic fuzzy weak dual
39
hyper K-ideals, Iranian J. Fuzzy Systems, 5(1) (2008), 65-78.
40
[26] L. A. Zadeh, From circuit theory to system theory, Proc. Inst. Radio Eng., 50 (1962) 856-865.
41
[27] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
42
[28] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)- an outline, Inform. Sci.,
43
172 (2005) 1-40.
44
ORIGINAL_ARTICLE
Persian-translation Vol.6, No.2 June 2009
http://ijfs.usb.ac.ir/article_2898_d4ce05cba0daff7238f4983b1147268f.pdf
2009-06-29T11:23:20
2017-12-11T11:23:20
89
95
10.22111/ijfs.2009.2898