IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.2903 unavailable Cover Vol.5, No.2, June 2008 30 06 2008 5 2 0 0 02 01 2017 02 01 2017 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_2903.html

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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.322 Research Paper ESTIMATING THE PARAMETERS OF A FUZZY LINEAR REGRESSION MODEL ESTIMATING THE PARAMETERS OF A FUZZY LINEAR REGRESSION MODEL Arabpour A. R. Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran Tata M. Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran 08 06 2008 5 2 1 19 08 01 2007 08 08 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_322.html

Fuzzy linear regression models are used to obtain an appropriate linear relation between a dependent variable and several independent variables in a fuzzy environment. Several methods for evaluating fuzzy coefficients in linear regression models have been proposed. The first attempts at estimating the parameters of a fuzzy regression model used mathematical programming methods. In this thesis, we generalize the metric defined by Diamond and use it as a criterion to estimate these parameters. Our method, is not only computationally easy to handle, but, when compared with earlier methods, has a smaller the sum of errors of estimation.

Fuzzy linear regression Least squares method Estimate
 P. Diamond,Fuzzy least squares, Information Sciences, 46 (1988), 141-157.  D. H. Hong and C. Hwang,Support vector fuzzy regression machines, Fuzzy Sets and Systems, 138(2003), 271-281.  C. Kao and C. Chyu,A fuzzy linear regression model with better explanatory power, Fuzzy Sets and Systems,126 (2002), 401-409.  C. Kao and C. Chyu,Least-squares estimates in fuzzy regression analysis, European J. Oper. Res.,148 (2003), 426-435.  N. Kim , R. R. Bishu,Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems, 100 (1998), 343-353.  M. L. Puri and D. A. Ralescu,Fuzzy random variables, J. Math. Anal. Appl., 114 (1986),  M. Sakawa and H. Yano,Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 47 (1992), 173-181.  H. Tanaka,Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems, 24(1987), 363-375.  H. Tanaka, I. Hayashi and J.Watada,Possibilistic linear regression analysis with fuzzy model, European J. Oper. Res.,40 (1989), 389-396.  H. Tanaka and H. Lee,Interval regression analysis by quadratic programming approach, IEEE Trans. Systems Man Cybrnet.,6(4)(1988), 473-481.  H. Tanaka , S. Uegima and K. Asai,Linear regression analysis with fuzzy model. IEEE Trans. Systems Man Cybrnet.,12(6)(1982), 903-907.  H. Tanaka and J. Watada,Possibilistic systems and their application to the linear regression model, Fuzzy Sets and Systems, 27(1988), 275-289.  M. Yang and T. Lin,Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 126 (2002), 389-399.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.325 Research Paper GENERATING FUZZY RULES FOR PROTEIN CLASSIFICATION GENERATING FUZZY RULES FOR PROTEIN CLASSIFICATION G. MANSOORI EGHBAL COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN ZOLGHADRI MANSOOR J. COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN KATEBI SERAJ D. COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN MOHABATKAR HASSAN BIOLOGY DEPARTMENT, COLLEGE OF SCIENCE, SHIRAZ UNIVERSITY, SHIRAZ, IRAN BOOSTANI REZA COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN SADREDDINI MOHAMMAD H. COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN 08 06 2008 5 2 21 33 08 06 2007 08 09 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_325.html

This paper considers the generation of some interpretable fuzzy rules for assigning an amino acid sequence into the appropriate protein superfamily. Since the main objective of this classifier is the interpretability of rules, we have used the distribution of amino acids in the sequences of proteins as features. These features are the occurrence probabilities of six exchange groups in the sequences. To generate the fuzzy rules, we have used some modified versions of a common approach. The generated rules are simple and understandable, especially for biologists. To evaluate our fuzzy classifiers, we have used four protein superfamilies from UniProt database. Experimental results show the comprehensibility of generated fuzzy rules with comparable classification accuracy.

Amino acid sequence Protein classification Fuzzy rule-based classifier
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.331 Research Paper ON ( $alpha, beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS ON ( $alpha, beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS Davvaz B. Department of Mathematics, Yazd University, Yazd, Iran Corsini P. Dipartimento di Matematica e Informatica, Via delle Scienze 206, 33100 Udine, Italy 08 06 2008 5 2 35 47 08 01 2007 08 06 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_331.html

Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and useful generalization of ordinary fuzzy Hv-ideals, we discuss some fundamental aspects of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals. A fuzzy subset A of an Hv-ring R is an ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideal if and only if an At, level cut of A, is an Hv-ideal of R, for all t$epsilon$(0, 0.5]. This shows that an($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideal is a generalization of the existing concept of fuzzy Hv-ideal. Finally, we extend the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy H_{v}-ideal with thresholds.

Hyperstructure H_{v}-ring Fuzzy set Fuzzy H_{v}-ideal
 S. K. Bhakat, ($epsilon$ $vee$ q)-fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and Systems,112 (2000), 299-312.  S. K. Bhakat and P. Das,Fuzzy subrings and ideals, Fuzzy Sets and Systems, 81 (1996),383-393.  S. K. Bhakat and P. Das, ($epsilon$ $vee$ q)-fuzzy subgroup, Fuzzy Sets and Systems, 80 (1996),  P. Corsini,Prolegomena of hypergroup theory, Second Edition, Aviani Editor, 1993.  P. Corsini and V. Leoreanu,Applications of hyperstructures theory, Advanced in Mathematics, Kluwer Academic Publishers, 2003.  B. Davvaz, ($epsilon$ $vee$ q)-fuzzy subnear-rings and ideals, Soft Computing 10 (2006), 206-211.  B. Davvaz,A brief survey of the theory of H_{v}-structures, in: Proc. 8th International Congress on Algebraic Hyperstructures and Applications, 1-9 Sep., 2002, Samothraki, Greece, Spanidis Press, 2003, 39-70.  B. Davvaz,Fuzzy H_{v}-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.  B. Davvaz,Fuzzy H_{v}-submodules, Fuzzy Sets and Systems, 117 (2001), 477-484.  B. Davvaz,T-fuzzy H_{v}-subrings of an H_{v}-ring, J. Fuzzy Math., 11 (2003), 215-224.  B. Davvaz,On Hv-rings and fuzzy H_{v}-ideals, J. Fuzzy Math., 6 (1998), 33-42.  B. Davvaz,Product of fuzzy H_{v}-ideals in Hv-rings, Korean J. Compu. Appl. Math., 8 (2001),  Y. B. Jun,On ( $alpha, beta$ )-fuzzy subalgebra of BCK/BCI-algebras, Bull. Korean Math. Soc., 42 (2005), 703-711.  W. J. Liu,Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),  F. Marty,Sur une generalization de la notion de group, 8th Congress Math. Scandenaves, Stockholm, 1934, 45-49.  P. M. Pu and Y. M. Liu,Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.  A. Rosenfeld,Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.  T. Vougiouklis,Hyperstructures and their representations, Hadronic Press, Inc, 115, Palm Harber, USA, 1994.  T. Vougiouklis,The fundamental relation in hyperrings. The general hyperfield, in: Proc. 4th International Congress on Algebraic Hyperstructures and Applications, Xanthi, 1990, World Sci. Publishing, Teaneck, NJ, (1991), 203-211.  X. Yuan, C. Zhang and Y. Ren,Generalized fuzzy groups and many-valued implications, Fuzzy Sets and Systems,138 (2003), 205-211.  L. A. Zadeh,Fuzzy sets, Inform. Control, 8 (1965), 338-353.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.333 Research Paper A COMMON FIXED POINT THEOREM FOR SIX WEAKLY COMPATIBLE MAPPINGS IN M-FUZZY METRIC SPACES A COMMON FIXED POINT THEOREM FOR SIX WEAKLY COMPATIBLE MAPPINGS IN M-FUZZY METRIC SPACES Sedghi Shaban Department of Mathematics, Islamic Azad University-Ghaemshahr Branch, Ghaemshahr P.O.Box 163, Iran Rao K. P. R. Department of Applied Mathematics, Acharya Nagarjuna University- Nuzvid Campus, Nuzvid-521201, A.P., India Shobe Nabi Department of Mathematics, Islamic Azad University-Babol Branch, Iran 08 06 2008 5 2 49 62 08 04 2007 08 11 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_333.html

In this paper, we give some new definitions of M-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete M-fuzzy metric spaces.

M-fuzzy metric spaces Weakly compatible maps Hadzic-type t-norm Common fixed point theorem
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.334 Research Paper REDEFINED FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS REDEFINED FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS Borumand Saeid Arsham Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran Jun Y. B. Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Korea 08 06 2008 5 2 63 70 08 09 2006 08 02 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_334.html

Using the notion of anti fuzzy points and its besideness to and nonquasi-coincidence with a fuzzy set, new concepts in anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their properties and relationships are investigated.

Besides to Non-quasi coincident with ($\alpha \beta$)^{*}-fuzzy subalgebra
 S. A. Bhatti, M. A. Chaudhry and B. Ahmad,On classification of BCI-algebras, Math. Jpn., 34(6)(1989), 865-876.  S. K. Bhakat and P. Das, ($epsilon$, $epsilon$ $vee$ q)-fuzzy subgroup, Fuzzy Sets and Systems, 80 (1996),359-368.  Y. B. Jun,On ($alpha, beta$)-fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc., 42(4) (2005), 703-711.  J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Korea (1994).  L. A. Zadeh,Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.335 Research Paper MODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS OF A RING MODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS OF A RING JAHAN IFFAT DEPARTMENT OF MATHEMATICS, RAMJAS COLLEGE, UNIVERSITY OF DELHI, NEW DELHI , INDIA 08 06 2008 5 2 71 78 08 12 2006 08 06 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_335.html

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set theoretic proof of the fact that the lattice  $vartheta$(R) of all fuzzy ideals of a ring R is modular.

Algebra Lattice Modularity Ideal of a ring Morphism
N. Ajmal, The lattice of fuzzy normal subgroups is modular, Inform. Sci., 83 (1995) 199-209. N. Ajmal, Fuzzy groups with sup property, Inform. Sci., 93 (1996), 247-264. N. Ajmal and K. V. Thomas, The lattice of fuzzy subgroups and fuzzy normal subgroups Inform. Sci.,76 (1994), 1-11. N. Ajmal and K.V. Thomas, The lattice of fuzzy ideals of a ring R, Fuzzy Sets and Systems,74 (1995), 371-379. N. Ajmal and K. V. Thomas, A complete study of the lattices of fuzzy congruences and fuzzy normal subgroups, Inform. Sci., 82 (1995), 198-218. P. S. Das, Fuzzy subgroups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264-269. T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and Systems,73 (1995), 349-358. R. Kumar, Non distributivity of the lattice of fuzzy ideals of a ring R, Fuzzy Sets and Systems,97 ( 1998), 393-394. Majumdar and Sultana, The lattice of fuzzy ideals of a ring R, Fuzzy Setsand Systems, 81 (1996), 271-273. A. Rosenfeld, Fuzzy subgroups, J. Math. Anal. Appl., 35(1971), 512-517. Q. Zhang and Meng , On the lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 112(2000), 349-353. Q. Zhang, The lattice of fuzzy (left, right) ideals of a ring is modular, Fuzzy Sets and Systems, 125 (2002), 209-214.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.336 Research Paper A NEW NOTION OF FUZZY PS-COMPACTNESS A NEW NOTION OF FUZZY PS-COMPACTNESS Bai Shi-Zhong Department of Mathematics, Wuyi University, Guangdong 529020, P.R.China 08 06 2008 5 2 79 86 08 07 2006 08 02 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_336.html

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

L-topology Pre-semi-open L-set Compactness PS-compactness
 S. Z. Bai,Pre-semiclosed sets and PS-convergence in L-fuzzy topological spaces, J. Fuzzy Math.,9 (2001), 497-509.  S. Z. Bai,L-fuzzy PS-compactness, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,10 (2002), 201-209.  S. Z. Bai,Near PS-compact L-subsets, Information Sciences, 115 (2003), 111-118.  C. L. Chang,Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.  P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive complete lattice, I, Nederl. Akad. Wetensch. Indag. Math., 44 (1982), 403-414.  G. Gierz and et al.,A Compendium of Continuous Lattices, Springer Verlag, Berlin, 1980.  Y. M. Liu and M. K. Luo,Fuzzy topology, World Scientific Publishing, Singapore, 1998.  F. G. Shi,Countable compactness and the Lindel¨of propeerty of L-fuzzy sets, Iranian Journal of Fuzzy Systems,1 (2004), 79-88.  F. G. Shi,Semicompactness in L-topological spaces, International Journal of Mathematics Mathematical Sciences,12 (2005), 1869-1878.  F. G. Shi,A new definition of fuzzy compactness, Fuzzy Sets and Systems, 158 (2007), 1486-1495.  G. J. Wang,Theory of L-fuzzy topological spaces, Shaanxi Normal University, Xian, 1988.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.337 Research Paper FUZZY SEMI-IDEAL AND GENERALIZED FUZZY QUOTIENT RING FUZZY SEMI-IDEAL AND GENERALIZED FUZZY QUOTIENT RING BINGXUE YAO DEPARTMENT OF MATHEMATICS, HAINAN NORMAL UNIVERSITY, HAIKOU, HAINAN 571158, CHINA AND SCHOOL OF MATHEMATICS SCIENCE, LIAOCHENG UNIVERSITY, LIAOCHENG, SHANDONG 252059, CHINA 08 06 2008 5 2 87 92 08 05 2006 08 09 2006 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_337.html

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

Fuzzy Semi-ideal Generalized Fuzzy Quotient Ring homomorphism Isomorphism
Y. Bingxue, Homomorphism and isomorphism of regular power ring, Chinese Quarterly Journal of Mathematics,2 (2000), 23-28. Y. Bingxue, The structure of fuzzy power ring, The Journal of Fuzzy Mathematics, 4 (2000),953-961. H. V. Kumbhojkar and M. S. Bapat, Correspondence theorem for fuzzy ideals, Fuzzy Sets and Systems,11 (1983), 213-219. W. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),133-139. T. K. Mukherje and M. K. Sen, On fuzzy ideals of rings, Fuzzy Sets and Systems, 21 (1987),99-104. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517. Y. Zhang, Prime L-fuzzy ideals and primary Prime L-fuzzy ideals, Fuzzy Sets and Systems,27(1988), 345-350.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.338 Research Paper t-BEST APPROXIMATION IN FUZZY NORMED SPACES t-BEST APPROXIMATION IN FUZZY NORMED SPACES Vaezpour S. M. Department of Mathematics, Amirkabir University, Tehran, Iran Karimi F. Department of Mathematics, University of Yazd, Yazd, Iran 08 06 2008 5 2 93 99 08 03 2006 08 06 2007 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_338.html

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.

Fuzzy normed space t-best approximation t-proximinal set
 T. Bag and S. K. Samanta,Finite dimentional fuzzy normed linear spaces, J. Fuzzy Math., 11(3)(2003), 678-705.  S. C. Cheng and J. N. Mordeson,Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc.,86 (1994), 429-436.  F. Deutsch,Best approximation in inner product spaces, Springer-Verlag, 2001.  A. George and P. Veeramani,On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(1994), 395-399.  A. George and P. Veeramani,On Some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems,90 (1997), 365-368.  R. Saadati and S. M. Vaezpour,Some results on fuzzy Banach spaces, J. Appl. Math. & Computing,17(1-2) (2005), 475-484.  I. Singer,Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, 1970.  P. Veeramani,Best approximation in fuzzy metric spaces, J. Fuzzy Math., 9(1) (2001), 75-80.  L. A. Zadeh,Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2008.2904 unavailable Persian-translation Vol.5, No.2, June 2008 30 06 2008 5 2 103 111 02 01 2017 02 01 2017 Copyright © 2008, University of Sistan and Baluchestan. 2008 http://ijfs.usb.ac.ir/article_2904.html

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