2009
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Cover Vol.6, No.2, June 2009 (IJFS)
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A NOTE ON EVALUATION OF FUZZY LINEAR REGRESSION
MODELS BY COMPARING MEMBERSHIP FUNCTIONS
A NOTE ON EVALUATION OF FUZZY LINEAR REGRESSION
MODELS BY COMPARING MEMBERSHIP FUNCTIONS
2
2
Kim and Bishu (Fuzzy Sets and Systems 100 (1998) 343352) 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.
1
Kim and Bishu (Fuzzy Sets and Systems 100 (1998) 343352) 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.
1
6
H.
Hassanpour
H.
Hassanpour
Department of Mathematics, University of Birjand, Birjand, Iran
Department of Mathematics, University of
Iran
hhassanpour@birjand.ac.ir
H. R.
Malek
H. R.
Malek
Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Iran
Faculty of Basic Sciences, Shiraz University
Iran
maleki@sutech.ac.ir
M. A.
Yaghoobi
M. A.
Yaghoobi
Department of Statistics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Statistics, Shahid Bahonar
Iran
yaghoobi@mail.uk.ac.ir
Fuzzy linear regression
Fuzzy number
Leastsquares 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
[[1] A. Abdalla and J. J. Buckley, Monte Carlo methods in fuzzy linear regression, Soft Computing,##11 (2007), 991996.##[2] S. Abbasbandy and M. Alavi, A method for solving fuzzy linear systems, Iranian Journal of##Fuzzy Systems, 2(2) (2005), 3744.##[3] S. M. Abu Nayeem and M. Pal, The pcenter problem on fuzzy networks and reduction of##cost, Iranian Journal of Fuzzy Systems, 5(1) (2008), 126.##[4] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model,##Iranian Journal of Fuzzy Systems, 5(2) (2008), 119.##[5] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,##Iranian Journal of Fuzzy Systems, 3(1) (2006), 122.##[6] S. H. Choi and J. J. Buckley, Fuzzy regression using least absolute deviation estimators, Soft##Computing, 12(3) (2008), 257263.##[7] C. Kao and C. L. Chyu, A fuzzy linear regression model with better explanatory power, Fuzzy##Sets and Systems, 126 (2002), 401409. ##[8] C. Kao and C. L. Chyu, Leastsquares estimates in fuzzy regression analysis, European Journal##of Operational Research, 148 (2003), 426435.##[9] B. Kim and R. R. Bishu, Evaluation of fuzzy linear regression models by comparing membership##functions, Fuzzy Sets and Systems, 100 (1998), 343352.##[10] H. Lee and H. Tanaka, Upper and lower approximation models in interval regression using##regression quantile techniques, European Journal of Operational Research, 116 (1999), 653##[11] MATLAB 7.0, The Mathworks, (www.mathworks.com).##[12] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression models with least##square errors, Applied Mathematics and Computation, 163 (2005), 977989.##[13] J. Mohammadi and S. M. Taheri, Pedomodels fitting with fuzzy least squares regression,##Iranian Journal of Fuzzy Systems, 1(29) (2004), 4562.##[14] M. Sakawa and H. Yano, Fuzzy linear regression and its applications, In: J. Kacprzyk and##M. Fedrizzi (Eds.), Studies in fuzziness, fuzzy regression analysis, Omnitech Press, Warsaw,##Poland, (1992), 6180.##[15] M. R. Safi, H. R. Maleki and E. Zaeimazad, A note on Zimmermann method for solving##fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 3146.##[16] E. Shivanian, E. Khorram and A. Ghodousian, Optimization of linear objective function subject##to fuzzy relation inequalities constraints with Maxaverage composition, Iranian Journal##of Fuzzy Systems, 4(2) (2007), 1530.##[17] S. M. Vaezpour and F. Karimi, tBest approximation in fuzzy normed spaces, Iranian Journal##of Fuzzy Systems, 5(2) (2008), 9399.##[18] H. C. Wu, Fuzzy linear regression model based on fuzzy scalar product, Soft Computing, 12##(2008), 469477.##[19] M. A. Yaghoobi and M. Tamiz, A Short note on the relationship between goal programming##and fuzzy programming for vectormaximum problems, Iranian Journal of Fuzzy Systems, 2##(2) (2005), 3136.##[20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
DIRECTLY INDECOMPOSABLE RESIDUATED LATTICES
DIRECTLY INDECOMPOSABLE RESIDUATED LATTICES
2
2
The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the noncommutative 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.
1
The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the noncommutative 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.
7
18
Lavinia Corina
Ciungu
Lavinia Corina
Ciungu
Polytechnical University of Bucharest, Splaiul Independentei
313, Bucharest, Romania
Polytechnical University of Bucharest, Splaiul
Romania
lavinia_ciungu@math.pub.ro
residuated lattice
Complementary factor congruence
Boolean center
Directly indecomposable algebra
Subdirectly irreducible algebra
Normal filter
[[1] P. Bahls, J. Cole, N. Galatos, P. Jipsen and C. Tsinakis, Cancellative residuated lattices,##Algebra Universalis, 50 (2003), 83106.##[2] M. Bakhshi, M. M. Zahedi and R. A. Borzooei, Fuzzy (positive,weak) implicative BCKideals,##Iranian Journal of Fuzzy Systems, 2 (2004), 6373.##[3] A. S. Boroumand and Y. B. Jun, Redefined fuzzy subalgebras of BCI/BCKalgebras, Iranian##Journal of Fuzzy Systems, 2 (2008), 6370.##[4] S. Burris and H. P. Sankappanavar, A course in universal algebra, SpringerVerlag, New##York, 1981.##[5] L. C. Ciungu, Classes of residuated lattices, Annals of University of Craiova, Math. Comp.##Sci. Ser., 33 (2006), 189207.##[6] L. C. Ciungu, Some classes of pseudoMTL algebras, Bull. Math. Soc. Sci. Math. Roumanie,##Tome, 50(98) (2007), 223247.##[7] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BLalgebras: Part I, Multiple Valued##Logic, 8 (2002), 673714.##[8] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BLalgebras: Part II, Multiple Valued##Logic, 8 (2002), 715750.##[9] A. Dvure˘censkij and M. Hy˘cko, Algebras on subintervals of BL algebras, pseudoBL algebras##and bounded residuated R`monoids, Mathematica Slovaca, 56 (2006), 125144.##[10] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated lattices: an algebraic glimpse at##substructural logics, Elsevier, 2007.##[11] G. Georgescu, L. Leu˘stean and V. Preoteasa, Pseudohoops, Journal of MultipleValued Logic##and Soft Computing, 11 (2005), 153184.##[12] G. Gr¨atzer, Lattice theory, W. H. Freeman and Company, San Francisco, 1979.##[13] A. Hasankhani and H. Saadat, Some quotiens on a BCKalgebra generated by a fuzzy set,##Iranian Journal of Fuzzy Systems, 2 (2004), 3343.##[14] A. Iorgulescu, Classes of pseudoBCK algebras  Part I, Journal of MultipleValued Logic##and Soft Computing, 12 (2006), 71130.##[15] A. Iorgulescu, Classes of pseudoBCK algebras  Part II, Journal of MultipleValued Logic##and Soft Computing, 12 (2006), 575629.##[16] A. Iorgulescu, Algebras of logic as BCK algebras, ASE Ed., Bucharest, 2008.##[17] P. Jipsen and C. Tsinakis, A survey of residuated lattices, In: Ordered Algebraic Structures,(##J.Martinez, ed) Kluwer Academic Publishers, Dordrecht, 2002, 1956.##[18] T. Kowalski and H. Ono, Residuated lattices: an algebraic glimpse at logics without contraction,##Japan Advanced Institute of Science and Technology, 2001.##[19] L. Liu and K. Li, Fuzzy filters of BLalgebras, Information Science, 173 (2005), 141154.##]
UNIFORM AND SEMIUNIFORM TOPOLOGY ON GENERAL
FUZZY AUTOMATA
UNIFORM AND SEMIUNIFORM TOPOLOGY ON GENERAL
FUZZY AUTOMATA
2
2
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 maxmin general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semiuniform structures on a nonempty set X and construct a semiuniformstructure on the set of states of a general fuzzy automaton. We then constructa semiuniform structure on , the set of all nite words on , the set ofinput symbols of a general fuzzy automaton and, nally, using these semiuniform structures, we construct two topologies on Q and and discuss theirproperties.
1
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 maxmin general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semiuniform structures on a nonempty set X and construct a semiuniformstructure on the set of states of a general fuzzy automaton. We then constructa semiuniform structure on , the set of all nite words on , the set ofinput symbols of a general fuzzy automaton and, nally, using these semiuniform structures, we construct two topologies on Q and and discuss theirproperties.
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29
M.
Horry
M.
Horry
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
mohhorry@yahoo.com
M. M.
Zahedi
M. M.
Zahedi
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
zahedi mm@mail.uk.ac.ir
(General) Fuzzy automata
(Uniform) Topology
Response function
compatibility
Transitivity
[[1] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal##of Approximate Reasoning, 38 (2005), 175214.##[2] I. M. Hanafy, A. M. Abd ElAziz and T. M. Salman, Semi compactness in Intuitionistic##Fuzzy Topological Spaces, Iranian Journal of Fuzzy Systems, 3(2) (2006), 5362.##[3] K. D. Joshi, Introduction to general topology, New Age International Publisher, India, 1997.##[4] Y. B. Jun and H. S. Kim, Uniform structure in positive implicative algebras, International##Mathematical Journal, 2 (2002), 215218.##[5] S. P. Li, Z. Fang and J. Zhao, P2Connectedness in LTopological Spaces, Iranian Journal of##Fuzzy Systems, 2(1) (2005), 2936.##[6] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,##Chapman and Hall/CRC, London/Boca Raton, FL, 2002.##[7] D. S. Malik and J. N. Mordeson, Fuzzy discrete structures, PhysicaVerlag, New York, 2000.##[8] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: au##tomata, rnns, and dynamic fuzzy systems, Proc. IEEE, 87(9) (1999), 16231640.##[9] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy nitestate automata can be determinis##tically encoded into recurrent neural networks, IEEE Trans. Fuzzy Syst. 5(1) (1998), 7689.##[10] W. Page, Topological uniform structures, Dover Publication, Inc. New York, 1988.##[11] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept##to pattern classif ication, Ph.D. dissertation Purdue University, IN, 1967.##[12] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338353.##[13] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (General) topology on maxmin general##fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 5168.##]
IDEALS OF PSEUDO MVALGEBRAS BASED ON VAGUE SET
THEORY
IDEALS OF PSEUDO MVALGEBRAS BASED ON VAGUE SET
THEORY
2
2
The notion of vague ideals in pseudo MValgebras 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.
1
The notion of vague ideals in pseudo MValgebras 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.
31
45
Young Bae
Jun
Young Bae
Jun
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660701, Korea
Department of Mathematics Education and (RINS),
Korea
skywine@gmail.com
Chul Hwan
Park
Chul Hwan
Park
Department of Mathematics, University of Ulsan, Ulsan 680749,
Korea
Department of Mathematics, University of
Korea
skyrosemary@gmail.com
Pseudo MValgebra
(implicative
prime) vague ideal
[[1] R. Biswas, Vague groups, Internat. J. Comput. Cognition, 4(2) (2006), 2023.##[2] H. Bustince and P. Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems,##79 (1996), 403405.##[3] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics,##23 (1993), 610614.##[4] G. Georgescu and A. Iorgulescu, Pseudo MValgebras, Multi. Val. Logic, 6 (2001), 95135.##[5] A. Lu and W. Ng, Vague sets or intuitionistic fuzzy set for handling vague data: which one##is better?, Lecture Notes in Computer Science, 3716 (2005), 401466.##[6] A. Walendziak, On implicative ideals of pseudo MValgebras, Sci. Math. Jpn. Online, e2005##(2005), 363369.##[7] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338353.##]
ON FUZZY HYPERIDEALS OF $Gamma$HYPERRINGS
ON FUZZY HYPERIDEALS OF $Gamma$HYPERRINGS
2
2
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 afuzzy hyperideal of a $Gamma$hyperring under a certain conditions is twovalued.Finally, the product of $nu$fuzzy hyperideals are studied.
1
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 afuzzy hyperideal of a $Gamma$hyperring under a certain conditions is twovalued.Finally, the product of $nu$fuzzy hyperideals are studied.
47
59
Reza
Ameri
Reza
Ameri
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic
Iran
ameri@umz.ac.ir
Hossein
Hedayati
Hossein
Hedayati
Department of Basic Sciences,, Babol University of Technology,
Babol, Iran
Department of Basic Sciences,, Babol University
Iran
h.hedayati@umz.ac.ir
A.
Molaee
A.
Molaee
Department of Mathematics, Faculty of Basic Sciences, University of
Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic
Iran
$Gamma$ hyperring
($nu$fuzzy) hyperideal
Fuzzy polygroup
Canonical hypergroup
Fuzzy product
[[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2##(2005), 3747.##[2] R. Ameri and H. Hedayati, Fuzzy isomorphism and quotient of fuzzy subpolygroups, Quasigroups##and Related Systems, 13 (2005), 175184.##[3] R. Ameri and M. M. Zahedi, Hyperalgebraic systems, Italian Journal of Pure and Applied##Mathematics, 13 (1999), 2132.##[4] W. E. Barnes, On the rings of Nobusawa, Pacific J. Math., 13 (1966), 411422.##[5] P. Corsini, Prolegomena of hypergroup theory, Second Edition Aviani editor, 1993.##[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publications,##[7] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. of Combinatorics,##Information and System Sciences, 20(13) (1995), 293303.##[8] B. Davvaz, On Hypernearrings and fuzzy hyperideals, J. Fuzzy Math., 7 (1999), 745753##[9] W. A. Dudek, B. Davvaz and Y. B. Jun, On intuitionistic fuzzy subquasihypergroups of##quasihypergroups, Inform. Sci. (in press).##[10] H. Hedayati and R. Ameri, Fuzzy khyperideals, Int. J. Pu. Appl. Math. Sci., 2(2) (2005),##[11] H. Hedayati and R. Ameri, On fuzzy closed, invertible and reflexive subsets of hypergroups,##Italian Journal of Pure and Applied Mathematics, (to appear).##[12] Y. B. Jun and C. Y. Lee, Fuzzy rings, Pusan Kyongnam Math. J. (presently, Esat Asian##Math. J.), 8(2) (1992), 163170.##[13] M. Krasner, Approximation des corps values complete de characteristique p=0 par ceux de##characteristique 0, Colloque dAlgebra Superieure, C.B.R.M., Bruxelles, 1956.##[14] M. Krasner, A class of hyperrings and hyperfields, Intern. J. Math. Math. Sci., 6(2) (1983),##[15] W. J. Liu, Fuzzy invariants subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1987),##[16] F. Marty, Surnue generalization de la notion e group, 8iem Course Math. Scandinaves Stockholm,##1934, 4549. ##[17] C. G. Massouros, Methods of construting hyperfields, International Journal of Mathematics##and Mathematical Sciences, 8(4) (1985), 725728.##[18] C. G. Massouros, Free and cyclic hypermodules, Annali di Matematica Pura ed Applicata, 4##(1988), 153166.##[19] N. Nobusawa, On a generaliziton of the ring theory, Osaka J. Math., 1 (1964), 8189.##[20] M. A. Ozturk, M. Uckun and Y. B. Jun, ”Fuzzy ideals in gammarings”, Turk J. Math., 27##(2003), 369374.##[21] I. G. Rosenberg, Hypergroups and join spaces determined by relations, Italian J. of Pure and##Applied Math., 24 (1998), 93101.##[22] T. Vougiuklis, Hyperstructures and their representations, Hardonic Press Inc., 1994.##[23] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338353.##[24] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J.##of Fuzzy Mathematics, 3(1) (1995), 115.##[25] M. M. Zahedi and R. Ameri, On the prime, primary and maximal subhypermodules, Italian##Journal of Pure and Applied Mathematics, 5 (1999), 6180.##]
HYPERGROUPS AND GENERAL FUZZY AUTOMATA
HYPERGROUPS AND GENERAL FUZZY AUTOMATA
2
2
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 quasiorder hypergroup on aninvertible general fuzzy automaton. Finally, we derive relationships betweenthe properties of an invertible general fuzzy automaton and the induced hypergroup.
1
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 quasiorder hypergroup on aninvertible general fuzzy automaton. Finally, we derive relationships betweenthe properties of an invertible general fuzzy automaton and the induced hypergroup.
61
74
Mohammad
Horry
Mohammad
Horry
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
mohhorry@yahoo.com
Mohammad Mehdi
Zahedi
Mohammad Mehdi
Zahedi
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
zahedi mm@mail.uk.ac.ir
(General) Fuzzy automata
(Quasiorder) Hypergroup
Invertibility
Connectedness
[[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems,##2(1) (2005), 3747.##[2] M. A. Arbib, From automata theory to brain theory, International Journal of ManMachin##Studies, 7(3) (1975), 279295.##[3] W. R. Ashby, Design for a brain, Chapman and Hall, London, 1954.##[4] D. Ashlock, A. Wittrock and T. Wen, Training finite state machines to improve PCR primer##design, in: Proceedings of the 2002 Congress on Evolutionary Computation (CEC) 20, 2002.##[5] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1993.##[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,##Advances in Mathematics, 2003.##[7] P. Corsini and I. Cristea, Fuzzy grade I.P.S hypergroups of order 7, Iranian Journal of Fuzzy##Systems, 1(2) (2004), 1532.##[8] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal##of Approximate Reasoning, 38 (2005), 175214.##[9] B. R. Gaines and L. J. Kohout, The logic of automata, International Journal of General##Systems, 2 (1976), 191208.##[10] Y. M. Li and W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership##valuesin latticeordered monoids, Fuzzy Sets and Systems, 156 (2005), 6892.##[11] R. Maclin and J. Shavlik, Refing domain theories expressed as finitestate automata, in:##L.B.G. Collins (Ed.), Proceedings of the 8th International Workshop on Machine Learning##(ML’91), Morgan Kaufmann, San Mateo CA, 1991.##[12] R. Maclin and J. Shavlik, Refing algorithm with knowledgebased neural networks: improving##the choufasma algorithm for protein folding, in: S. Hanson, G. Drastal and R. Rivest (Eds.),##Computational Learning Theory and Natural Learning Systems, MIT Press, Cambridge, MA,##[13] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, Theory and Applications,##Chapman and Hall/CRC, London/Boca Raton, FL, 2002.##[14] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: automata,##rnns, and dynamical fuzzy systems, Proceeding of IEEE, 87(9) (1999), 16231640.##[15] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy finitestate automata can be deterministically##encoded into recurrent neural networks, IEEE Transactions on Fuzzy Systems, 5(1)##(1998), 7689.##[16] B. Tucker (Ed.), The computer science and engineering handbook, CRC Press, Boca Raton,##[17] J. Virant and N. Zimic, Fuzzy automata with fuzzy relief, IEEE Transactions on Fuzzy Systems,##3(1) (1995), 6974. ##[18] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept##to pattern classification, Ph.D. dissertation, Purdue University, Lafayette, IN, 1967.##[19] M. Ying, A formal model of computing with words, IEEE Transactions on Fuzzy Systems,##10(5) (2002), 640652.##[20] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338353.##[21] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (General) topology on maxmin general##fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 5168.##]
APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS
APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS
2
2
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.
1
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.
75
86
Young Bae
Jun
Young Bae
Jun
Department of Mathematics Education (and RINS), Gyeongsang National
University, Chinju 660701, Korea
Department of Mathematics Education (and
Korea
skywine@gmail.com
Chul Hwan
Park
Chul Hwan
Park
Department of Mathematics, University of Ulsan, Ulsan 680749,
Korea
Department of Mathematics, University of
Korea
skyrosemary@gmail.com
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
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