2011
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FUZZY LOGISTIC REGRESSION: A NEW POSSIBILISTIC
MODEL AND ITS APPLICATION IN
CLINICAL VAGUE STATUS
FUZZY LOGISTIC REGRESSION: A NEW POSSIBILISTIC
MODEL AND ITS APPLICATION IN
CLINICAL VAGUE STATUS
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2
Logistic regression models are frequently used in clinicalresearch and particularly for modeling disease status and patientsurvival. In practice, clinical studies have several limitationsFor instance, in the study of rare diseases or due ethical considerations, we can only have small sample sizes. In addition, the lack of suitable andadvanced measuring instruments lead to nonprecise observations and disagreements among scientists in defining diseasecriteria have led to vague diagnosis. Also,specialists oftenreport their opinion in linguistic terms rather than numerically. Usually, because of these limitations, the assumptions of the statistical model do not hold and hence their use is questionable. We therefore need to develop new methods formodeling and analyzing the problem. In this study, a model called the `` fuzzy logistic model '' isproposed for the case when the explanatory variables arecrisp and the value of the binary response variable is reportedas a number between zero and one (indicating the possibility ofhaving the property). In this regard, the concept of `` possibilistic odds '' is alsointroduced. Then, the methodology and formulationof this model is explained in detail and a linear programming approach is use to estimate the model parameters. Some goodnessoffit criteria are proposed and a numerical example is given as an example.
1
Logistic regression models are frequently used in clinicalresearch and particularly for modeling disease status and patientsurvival. In practice, clinical studies have several limitationsFor instance, in the study of rare diseases or due ethical considerations, we can only have small sample sizes. In addition, the lack of suitable andadvanced measuring instruments lead to nonprecise observations and disagreements among scientists in defining diseasecriteria have led to vague diagnosis. Also,specialists oftenreport their opinion in linguistic terms rather than numerically. Usually, because of these limitations, the assumptions of the statistical model do not hold and hence their use is questionable. We therefore need to develop new methods formodeling and analyzing the problem. In this study, a model called the `` fuzzy logistic model '' isproposed for the case when the explanatory variables arecrisp and the value of the binary response variable is reportedas a number between zero and one (indicating the possibility ofhaving the property). In this regard, the concept of `` possibilistic odds '' is alsointroduced. Then, the methodology and formulationof this model is explained in detail and a linear programming approach is use to estimate the model parameters. Some goodnessoffit criteria are proposed and a numerical example is given as an example.
1
17
Saeedeh
Pourahmad
Saeedeh
Pourahmad
Department of Biostatistics, School of Medicine, Shiraz University
of Medical Sciences, Shiraz, 713451874, Iran
Department of Biostatistics, School of Medicine,
Iran
pourahmad@sums.ac.ir
S. Mohammad
Taghi Ayatollahi
S. Mohammad
Taghi Ayatollahi
Department of Biostatistics, School of Medicine,
Shiraz University of Medical Sciences, Shiraz, 713451874, Iran
Department of Biostatistics, School of Medicine,
Iran
ayatolahim@sums.ac.ir
S. Mahmoud
Taheri
S. Mahmoud
Taheri
Department of Mathematical Sciences, Isfahan University of
Technology, Isfahan, 8415683111, Iran
Department of Mathematical Sciences, Isfahan
Iran
sm_taheri@yahoo.com
Logistic Regression
Clinical research
Fuzzy logistic regression
Possibilistic odds
[bibitem{Ag:cda}##A. Agresti, {it Categorical data analysis}, Wiley, New york,##bibitem{ArTa:Epflrm}##A. R. Arabpour and M. Tata, {it Estimating the parameters of a##fuzzy linear regression model}, Iranian Journal of Fuzzy Systems,##{bf 5} (2008), 119. ##bibitem{BaWhGo:Lrmlsur}##S. C. Bagley, H. White and B. A. Golomb, {it Logistic regression##in the medical literature: standards for use and reporting with##particular attention to one medical domain}, Journal of Clinical##Epidemiology, {bf 54} (2001), 979985. ##bibitem{Cel:Lsmffvd}##A. Celmins, {it Least squares model fitting to fuzzy vector##data}, Fuzzy Sets and Systems, {bf 22} (1987), 260269. ##bibitem{CoDuGiSa:Lselrmfr}##R. Coppi, P. D'Urso, P. Giordani and A. Santoro, {it Least##squares estimation of a linear regression model with LR fuzzy##response}, Computational Statistics and Data Analysis, {bf##51} (2006), 267286. ##bibitem{Di:Lsfsfv}##P. Diamond, {it Least squares fitting of several fuzzy##variables}, Proc. of the Second IFSA Congress, Tokyo, (1987),##bibitem{DuKeMePr:Fia}##D. Dubois, E. Kerre, R. Mesiar and H. Prade, {it Fuzzy interval##analysis, In: D. Dubois, H. Prade, eds.}, Fundamentals of Fuzzy##Sets, Kluwer, 2000. ##bibitem{FaBrKaHa:Haprinme}##A. S. Fauci, E. Braunwald, D. L. Kasper, S. L. Hauser, D. L.##Longo, J. L. Jameson and J. Loscalzo, {it Harrison's principals##of internal medicine}, Wiley, New York, {bf II} (2008), 22752279. ##bibitem{GAMs:G}##GAMS (General Algebraic Modeling System), {it A highlevel modeling##system for mathematical programming and optimization}, GAMS##Development Corporation, Washington, DC, USA, 2007. ##bibitem{HaMaYa:Aeflr}##H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A note on##evaluation of fuzzy linear regression models by comparing##membership functions}, Iranian Journal of Fuzzy Systems, {bf##6} (2009), 16. ##bibitem{HoSoDo:Fulelireanus}##D. H. Hong, J. Song and H. Y. Do, {it Fuzzy leastsquares linear##regression analysis using shape preserving operation}, Information##Sciences, {bf 138} (2001), 185193. ##bibitem{Lingo:A}##LINGO 8.0, {it A linear programming, integer programming, nonlinear##programming and global optimization solver}, Lindo System##Inc, 1415 North Dayton Str., Chicago, 2003. ##bibitem{MATLAB:A}##MATLAB R., {it A technical computing environment for highperformance##numeric computation and Visualization}, The Math Works Inc.,##bibitem{MiTa:Plrlpa}##S. Mirzaei Yeganeh and S. M. Taheri, {it Possibilistic logistic##regression by linear programming approach}, Proc. of the 7th##Seminar on Probability and Stochastic Processes, Isfahan##University of Technology, Isfahan, Iran, (2009), 139143. ##bibitem{MoTa:Pedomodel}##J. Mohammadi and S. M. Taheri, {it Pedomodels fitting with fuzzy##least squares regression}, Iranian Journal of Fuzzy Systems, {bf##1} (2004), 4561. ##bibitem{Pe:Alfm}##G. Peters, {it A linear forecasting model and its application in##economic data}, Journal of Forecasting, {bf 20} (2001), 315328. ##bibitem{RoPe:Mtfgrfr}##S. Roychowdhury and W. Pedrycz, {it Modeling temporal functions##with granular regression and fuzzy rule}, Fuzzy Sets and Systems,##{bf 126} (2002), 377387. ##bibitem{SaGi:A}##B. Sadeghpour and D. Gien, {it A goodness of fit index to##reliability analysis in fuzzy model, In: A. Grmela, ed.,##Advances in Intelligent Systems, Fuzzy Systems, Evolutionary##Computation}, WSEAS Press, Greece, (2002), 7883. ##bibitem{Sh:Frm}##A. F. Shapiro, {it Fuzzy regression models}, ARC, 2005. ##bibitem{TaHe:Amu}##B. D. Tabaei, and W. H. Herman, {it A multivariate logistic##regression equation to screen for Diabetes}, Diabetes Care, {bf##25} (2002), 19992003. ##bibitem{Ta:Trends}##S. M. Taheri, {it Trends in fuzzy statistics}, Austrian Journal##of Statistics, {bf 32} (2003), 239257. ##bibitem{TaKe:Flar}##S. M. Taheri and M. Kelkinnama, {it Fuzzy least absolutes##regression}, Proc. of 4th International IEEE Conference on##Intelligent Systems, Varna, Bulgaria, {bf 11} (2008), 5558. ##bibitem{TaUeAs:Lraw}##H. Tanaka, S. Uejima, K. Asai, {it Linear regression analysis##with fuzzy model}, IEEE Trans. Systems Man Cybernet., {bf##12} (1982), 903907. ##bibitem{VaBa:Fast}##E. Van Broekhoven and B. D. Baets, {it Fast and accurate of##gravity defuzzification of fuzzy systems outputs defined on##trapezoidsal fuzzy partitions}, Fuzzy Sets and Systems, {bf##157} (2006), 904918. ##bibitem{Za:Fs}##L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf##8} (1965), 338353. ##bibitem{Zimm:Fu}##H. J. Zimmermann, {it Fuzzy set theory and its applications}, 3rd##ed., Kluwer, Dodrecht, 1996.##]
TOWARDS THE THEORY OF LBORNOLOGICAL SPACES
TOWARDS THE THEORY OF LBORNOLOGICAL SPACES
2
2
The concept of an $L$bornology is introduced and the theory of $L$bornological spacesis being developed. In particular the lattice of all $L$bornologies on a given set is studied and basic properties ofthe category of $L$bornological spaces and bounded mappings are investigated.
1
The concept of an $L$bornology is introduced and the theory of $L$bornological spacesis being developed. In particular the lattice of all $L$bornologies on a given set is studied and basic properties ofthe category of $L$bornological spaces and bounded mappings are investigated.
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28
mati
Abel
mati
Abel
Institute of Pure Mathematics, University of Tartu, J.Liivi street 2,
EE50409 Tartu, Estonia
Institute of Pure Mathematics, University
Estonia
mati.abel@ut.ee
aleksandrs
ˇSostaks
aleksandrs
ˇSostaks
Department of Mathematics, University of Latvia, Zellu street
8, LV1002, Riga, Latvia and Institute of Mathematics and CS, University of Latvia,
Raina bulv. 29, LV1586, Riga, Latvia
Department of Mathematics, University of
Latvia
Bornology
$L$set
$L$bornology
Fuzzy set
Fuzzy topology
[bibitem{AHS}J. Ad'amek, H. Herrlich and G. E. Strecker, {it Abstract and##concrete categories}, John Wiley & Sons, New York, 1990. ##bibitem{Beer} G. Beer, {it Metric bornologies and KuratowskaPainleve convergence to the empty set},##{Journal of Convex Analysis}, {bf 8} (2001), 273289.##%bibitem{Beer_Levi} Gerald Beer, Levi ##bibitem{Bir} G. Birkhoff, {it Lattice theory}, AMS Providence, RI,##bibitem{Ch68} C. L. Chang, {it Fuzzy topological spaces}, {J. Math. Anal.##Appl.}, {bf 24} (1968), 182190. ##bibitem{Gierz} G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, {it Continuous lattices and domains},##Cambridge University Press, Cambridge, 2003. ##bibitem{Go67} J. A. Goguen, {it $L$fuzzy sets}, {J. Math. Anal. Appl.}, {bf 18} (1967) 145174. ##bibitem{Go73} J. A. Goguen, {it The fuzzy Tychonoff theorem}, { J. Math. Anal. Appl.}, {bf 18} (1973), 734742. ##bibitem{HS} H. Herrlich and G. E. Strecker, { it Category theory}, Heldermann Verlag, Berlin, 1987. ##bibitem{HN} H. HogbeNlend, {it Bornology and functional analysis}, Math. Studies, NorthHolland, Amsterdam, {bf 26} (1977). ##bibitem{HoSo99} U. H"ohle and A. v{S}ostak, {it Axiomatics for fixedbased fuzzy topologies}, Chapter 3 in [8]. ##bibitem{HuS1} S. T. Hu, {it Boundedness in a topological space}, {it J. Math. Pures Appl.}, {bf 28} (1949), 287320. ##bibitem{HuS2} S. T. Hu, {it Introduction to general topology}, HoldenDay, SanFrancisko, 1966. ##bibitem{Hut} B. Hutton, {it Normality in fuzzy topologicl spaces}, {J. Math. Anal. Appl.}, {bf 50} (1975), 7479.##bibitem{JiangYan} S. Q. Jiang and C. H. Yan, { it Fuzzy bounded sets and totally fuzzy bounded sets in Itopological vector spaces},##{ Iranian Journal of Fuzzy Systems}, {bf 6(3)} (2009), 7390. ##bibitem{MFS} U. H"ohle and S. E. Rodabaugh, eds., {it Mathematics of fuzzy sets: logic, topology and##measure theory}, Handbook Series, Kluwer Acad. Publ., {bf3} (1999). ##bibitem{NVT} A. Narayaanan, S. Vijayabalaji and N. Thillaigovitidan, {it Intuitionistic fuzzy linear bounded operators},##{Iranian Journal of Fuzzy Systems}, {bf 4(1)} (2007), 8993. ##bibitem{NR} C. V. Negoita and D. A. Ralescu, { it Application of fuzzy sets to system analysis}, John Wiley & Sons,##New York, 1975.##bibitem{Ro99} S. E. Rodabaugh, {it Powerset operator foundations for poslat fuzzy set theories and topologies},##Chapter 2 in##cite{MFS}.##bibitem{Za} L. Zadeh, {it Fuzzy sets}, {Information and Control}, {bf 8} (1965), 338353.##]
ORDERED INTUITIONISTIC FUZZY SOFT
MODEL OF FLOOD ALARM
ORDERED INTUITIONISTIC FUZZY SOFT
MODEL OF FLOOD ALARM
2
2
A flood warning system is a nonstructural measure for flood mitigation. Several parameters are responsible for flood related disasters. This work illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. In this paper, we first define ordered intuitionistic fuzzy soft sets and establish some results on them. Then, we define similarity measures between ordered intuitionistic fuzzy soft (OIFS) sets and apply these similarity measures to five selected sites of Kerala, India to predict potential flood.
1
A flood warning system is a nonstructural measure for flood mitigation. Several parameters are responsible for flood related disasters. This work illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. In this paper, we first define ordered intuitionistic fuzzy soft sets and establish some results on them. Then, we define similarity measures between ordered intuitionistic fuzzy soft (OIFS) sets and apply these similarity measures to five selected sites of Kerala, India to predict potential flood.
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39
Sunny Joseph
Kalayathankal
Sunny Joseph
Kalayathankal
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
Department of Mathematics, K.E.College, Mannanam,
India
sunnyjose2000@yahoo.com
G. Suresh
Singh
G. Suresh
Singh
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
Department of Mathematics, University of
India
P. B.
Vinodkumar
P. B.
Vinodkumar
Department of Mathematics, Rajagiri School of Engineering &
Technology, Cochin, Kerala, India
Department of Mathematics, Rajagiri School
India
Sabu
Joseph
Sabu
Joseph
Department of Environmental Science, University of Kerala, Trivan
drum, Kerala, India
Department of Environmental Science, University
India
Jobin
Thomas
Jobin
Thomas
Department of Environmental Science, University of Kerala, Trivan
drum, Kerala, India
Department of Environmental Science, University
India
rainfall
Intuitionistic fuzzy soft set
Flood
Simulation
[bibitem{at} K. Atanassov, emph{Intuitionistic fuzzy sets}, Fuzzy sets and Systems, {bf20} (1986), 8796.##bibitem{bu} J. J. Buckley, K. D. Reilly and L. J. Jowers, emph{Simulating continuous fuzzy systems}, Iranian Journal of fuzzy systems, {bf 2(1)} (2005), 118.##bibitem{ca}J. M. Cadenas and J. L. Verdegay, emph{A primer on fuzzy optimization models and methods}, Iranian Journal of fuzzy systems, {bf 3(1)} (2006), 121. ##bibitem{shu}S. L. Chen, emph{The application of comprehensive fuzzy judgement in the interpretation of waterflooded reservoirs}, The Journal of Fuzzy Mathematics, {bf9(3)} (2001), 739743.##bibitem{ch} S. M. Chen, S. M. Yeh and P. H. Hasiao, emph{A comparison of similarity measures of fuzzy values}, Fuzzy sets and Systems, {bf72} (1995), 7989. ##bibitem{su} S. Joseph Kalayathankal and S. Singh, emph{Need and significance of fuzzy modeling of rainfall}, In: Proceedings of the National Seminar on Mathematical Modeling and Simulation, Department of Mathematics, K. E. College, Mannanam, Kerala, India, (2007), 2735.##bibitem{sun}S. Joseph Kalayathankal, G. Suresh Singh and P. B. Vinodkumar, emph{OIIF model of flood alarm}, Global Journal of Mathematical Sciences: Theory and Practical, {bf1(1)} (2009), 18.##bibitem{sunn}S. Joseph Kalayathankal and G. Suresh Singh, emph{IFS model of flood alarm}, Global Journal of Pure and Applied Mathematics, {bf9} (2009), 1522.##bibitem{suy} S. Joseph Kalayathankal and G. Suresh Singh, emph{A fuzzy soft flood alarm model}, Mathematics and Computers in Simulation, {bf80} (2010), 887893.##bibitem{sunm}S. Joseph Kalayathankal, G. Suresh Singh and P. B. Vinodkumar, emph{MADM models using ordered ideal intuitionistic fuzzy sets}, Advances in Fuzzy Mathematics, {bf4(2)} (2009), 101106. ##bibitem{pa}P. Kumar Maji, R. Biswas and A. Ranjan Roy, emph{Intuitionistic fuzzy soft sets}, The Journal of Fuzzy Mathematics, {bf9(3)} (2001) 677692.##bibitem{pab}P. Kumar Maji, R. Biswas and A. Ranjan Roy, emph{Fuzzy soft sets}, The Journal of Fuzzy Mathematics, {bf9(3)} (2001), 589602. ##bibitem{mo} D. Molodtsov, emph{Soft set theoryfirst results}, Computers and Mathematics with Applications, {bf37} (1999), 1931.##bibitem{pc} P. C. Nayak, K. P. Sudheer and K. S. Ramasastri, emph{Fuzzy computing based rainfallrunoff model for real time flood forecasting}, Hydrological Processes, {bf19} (2005), 955968. ##bibitem{ped} W. Pedrycz, emph{Distributed and collaborative fuzzy modeling}, Iranian Journal of fuzzy systems, {bf 4(1)} (2007), 119. ##bibitem{to}E. Toth, A. Brath and A. Montanari, emph{Comparison of shortterm rainfall prediction models for realtime flood forecasting}, Journal of Hydrology, {bf239} (2000), 132147.##bibitem{xu} Z. S. Xu and J. Chen, emph{An overview of distance and similarity measures of intuitionistic fuzzy sets}, International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems, {bf16(4)} (2008), 529555.##bibitem{zes}Z. Xu, emph{Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making}, Fuzzy Optim. Decis. Making, {bf6} (2007), 109121.##]
DISCRETE TOMOGRAPHY AND FUZZY INTEGER
PROGRAMMING
DISCRETE TOMOGRAPHY AND FUZZY INTEGER
PROGRAMMING
2
2
We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.
1
We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.
41
48
Fethi
Jarray
Fethi
Jarray
Laboratoire CEDRICCNAM, 292 rue StMartin, 75003 Paris, France,
Gabes University of Sciences, 6072 Gabes, Tunisia
Laboratoire CEDRICCNAM, 292 rue StMartin,
Tunisia
fethi.jarray@cnam.fr
Discrete tomography
F uzzy integer programming
Image reconstruction
[[1] T. Allahviranloo,K. Shamsolkotabi, N. A. Kiani and L. Alizadeh, Fuzzy integer linear programming##problems,In t. J. Contemp. Math. Sciences, 2(4) (2007),167 181.##[2] M. G. Bailey and B. E. Gillett, Parametric integer programming analysis: A contraction##approach,Jour nal of the Operational Research Society, 31 (1980),253 262.##[3] K. J. Batenburg, Network flow algorithms for discrete tomography,A dvances in Discrete##Tomography and its Applications,Bi rkh¨auser,Bos ton, (2007), 175205.##[4] J. J. Buckley and L. J. Jowers, Monte carlo methods in fuzzy optimization,Studi es in Fuzziness##and Soft Computig, 222 (2008),223 226.##[5] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,##Iranian Journal of Fuzzy Systems, 3(1) (2006),1 21.##[6] R. J. Gardner,P . Gritzmann and D. Prangenberg, The computational complexity of reconstructing##lattice sets from their Xrays,D iscrete Math., 202 (1999),45 71.##[7] F. Herrera and J. L. Verdegay, Three models of fuzzy integer linear programming,Eur opean##Journal of Operational Research, 83 (1995),581 593.##[8] F. Jarray, Solving problems of discrete tomography: applications in workforce scheduling,##Ph.D. Thesis,U niversity of CNAM,P aris, 2004.##[9] F. Jarray,M . C. Costa and C. Picouleau, Complexity results for the horizontal bar packing##problem,I nformation Processing Letters, 108(6) (2008),356 359.##[10] N. Javadian,Y . Maali and N. MahdaviAmiri, Fuzzy linear programming with grades of##satisfaction in constraints,Ir anian Journal of Fuzzy Systems, 6(3) (2009),17 35.##[11] A. Mitsos and P. I. Barton, Parametric mixedinteger 01 linear programming: the general##case for a single parameter,Eur opean Journal of Operational Research, 194 (2009),663 686.##[12] S. A. Orlovski, On programming with fuzzy constraint sets,K ybernetes, 6 (1977),197 201.##[13] M. S. Osman,O . M. Saad and A. G. Hasan, Solving a special class of LargeScale fuzzy##multiobjective integer linear programming problems,F uzzy sets and systems, 107 (1999),##[14] H. J. Ryser, Combinatorial properties of matrices of zeros and ones,Canad. J. Math, 9##(1957),371 377.##[15] E. Shivantian,E. Khorram and A. Ghodousian, Optimization of linear objective function subject##to fuzzy relation inequalities constraints with maxaverage composition,Ir anian Journal##of Fuzzy Systems, 4(2) (2007),15 29.##[16] J. L. Verdegay, Fuzzy mathematical programming,In M. M. Gupta and E. Sanchez,Eds .,##Fuzzy Information and Decision Processes,N orthHolland,(1982), 231236.##[17] S. Weber,T. Schule,J. Hornegger and C. Schnorr, Binary tomography by iterating linear##programs from noisy projections,LNCS, 233 (2004),38 51.##[18] H. J. Zimmermann, Description and optimization of fuzzy systems,In ternational Journal##General Systems, 2 (1976),209 215.##[19] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions,##F uzzy Sets and Systems, 1 (1978),45 55.##]
MODIFIED KSTEP METHOD FOR SOLVING FUZZY INITIAL
VALUE PROBLEMS
MODIFIED KSTEP METHOD FOR SOLVING FUZZY INITIAL
VALUE PROBLEMS
2
2
We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.
1
We are concerned with the development of a K− step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.
49
63
Omid
Solaymani Fard
Omid
Solaymani Fard
School of Mathematics and Computer Science, Damghan
University, Damghan, Iran
School of Mathematics and Computer Science,
Iran
osfard@du.ac.ir, omidsfard@gmail.com
Ali
Vahidian Kamyad
Ali
Vahidian Kamyad
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Mathematics, Ferdowsi University
Iran
avkamyad@math.um.ac.ir
Fuzzy numbers
Fuzzy differential equations
Modified kstep method
[bibitem{abb1} S. Abbasbandy, J. J. Nieto and M. Alavi, {it Tuning of reachable set in one dimensional fuzzy differential inclusions}, Chaos, Solitons Fractals, {bf 26} (2005), 13371341. ##bibitem{abb2} S. Abbasbandy, T. Allahviranloo, O. LópezPouso and J. J. Nieto, {it Numerical methods for fuzzy differential inclusions}, Comput. Math. Appl., {bf 48} (2004), 16331641. ##bibitem{abb3} S. Abbasbandy and T. Allahviranloo, {it Numerical solutions of fuzzy differential equations by Taylor method}, , Journal of Computational Methods in Applied Mathematics, {bf 2} (2002), 113124. ##bibitem{alh1} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Numerical solution of fuzzy differential equations by predictor–corrector method}, Information Sciences, {bf 177} (2007), 16331647. ##bibitem{alh2} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Improved predictor–corrector method for solving fuzzy initial##value problems}, Information Sciences, {bf 179} (2009), 945955. ##bibitem{bede1} B. Bede, {it Note on "Numerical solutions of fuzzy differential equations by predictor–corrector method"}, Information Sciences, {bf 178} (2008), 19171922.##bibitem{bede2} B. Bede and S. G. Gal, {it Generalizations of the differentiability of fuzzy umber valued functions with applications to fuzzy differential equation}, Fuzzy Sets and Systems, {bf 151} (2005), 581599. ##bibitem{bede3} B. Bede, J. Imre, C. Rudas and L. Attila, {it First order linear fuzzy differential equations under generalized differentiability}, Information Sciences, {bf 177} (2007), 36273635. ##bibitem{buk1} J. J. Buckley and T. Feuring, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 110} (2000), 4354. ##bibitem{can1} Y. ChalcoCano and H. RomanFlores, {it On new solutions of fuzzy differential equations}, Chaos, Solitons and Fractals, {bf 38} (2008), 112119. ##bibitem{can2} Y. ChalcoCano, H. RomanFlores, M. A. RojasMedar, O. Saavedra and M. JiménezGamero, {it The extension principle and a decomposition of##fuzzy sets}, Information Sciences, {bf 177} (2007), 53945403. ##bibitem{chen1} C. K. Chen and S. H. Ho, {it Solving partial differential equations by twodimensional differential transform method}, Applied Mathematics and Computation, {bf 106} (1999), 171179. ##bibitem{cho} Y. J. Cho and H. Y. Lan, {it The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions}, Dynamics Continuous Discrete Inpulsive Systems Ser. AMath. Anal., {bf 14} (2007), 873884. ##bibitem{con} W. Congxin and S. Shiji, {it Exitance theorem to the Cauchy problem of fuzzy differential equations under compactancetype conditions}, Information Sciences, {bf 108} (1993), 123134. ##bibitem{dia1} P. Diamond, {it Timedependent differential inclusions, cocycle attractors and fuzzy differential equations}, IEEE Trans. Fuzzy Systems, {bf 7} (1999), 734740. ##bibitem{dia2} P. Diamond, {it Brief note on the variation of constants formula for fuzzy differential equations}, Fuzzy Sets and Systems, {bf 129} (2002), 6571. ##bibitem{ding} Z. Ding, M. Ma and A. Kandel, {it Existence of solutions of fuzzy differential equations with parameters}, Information Sciences, {bf 99} (1997), 205217.##bibitem{dub} D. Dubois and H. Prade, {it Towards fuzzy differential calculus: part 3, differentiation}, Fuzzy Sets and Systems, {bf 8} (1982), 225233. ##bibitem{fei} W. Fei, {it Existence and uniqueness of solution for fuzzy random differential equations with nonLipschitz coefficients}, Information Sciences, {bf 177} (2007), 3294337. ##bibitem{geo1} R. Goetschel and W. Voxman, {it Topological properties of fuzzy number}, Fuzzy Sets and Systems, {bf 10} (1983), 8799. ##bibitem{geo2} R. Goetschel and W. Voxman, {it Elementary fuzzy calculus}, Fuzzy sets and Systems, {bf 18} (1986), 3143. ##bibitem{ijfs1} M. S. Hashemi, M. K. Mirnia and S. Shahmorad, {it Solving fuzzy linear systems by using the Schur complement when coefficient matrix is an Mmatrix}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(3)} (2008), 1530. ##bibitem{ijfs2}H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A note on evaluation of fuzzy linear regression models by comparing membership functions}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(2)} (2009), 18. ##bibitem{hen} P. Henrici, {it Discrete vatiablr methods in ordinary differential equations}, Wiley, New York, 1962. ##bibitem{jang} M. J. Jang, C. L. Chen and Y. C. Liy, {it On solving the initialvalue problems using the differential transformation method}, Applied Mathematics and Computation, {bf 115} (2000), 145160. ##bibitem{kal1} O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 24} (1987), 301317. ##bibitem{kal2} O. Kaleva, {it The Cauchy problem for fuzzy differential equations}, Fuzzy Sets and Systems, {bf 35} (1990), 389396. ##bibitem{kal3} O. 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Zaeimazad, {it A note on Zimmermann method for solving fuzzy linear programming problems}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(2)} (2007), 3146. ##bibitem{sei} S. Seikkala, {it On the fuzzy initial value problem}, Fuzzy Sets and Systems, {bf 24} (1987), 319330. ##bibitem{ijfs5} A. K. Shaymal and M. Pal, {it Triangular fuzzy matrices}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(1)} (2007), 7587. ##bibitem{song} S. Song, L. Guo and C. Feng, {it Global existence of solutions to fuzzy differential equations}, Fuzzy Sets and Systems, {bf 115} (2000), 371376.##]
On $n$ary Hypergroups and Fuzzy $n$ary Homomorphism
On $n$ary Hypergroups and Fuzzy $n$ary Homomorphism
2
2
1
The aim of this paper is to introduce the notion of fuzzy homomorphismand fuzzy isomorphism between two 𝑛ary hypergroups and to extendthe fuzzy results of fundamental equivalence relations to 𝑛ary hypergroups.We study some of their properties and prove the decomposition theorems forfuzzy homomorphism and fuzzy isomorphism.
65
76
O.
Kazancı
O.
Kazancı
Department of Mathematics, Karadeniz Technical University,61080,
Trabzon, Turkey
Department of Mathematics, Karadeniz Technical
Turkey
kazancio@yahoo.com
S.
Yamak
S.
Yamak
Department of Mathematics, Karadeniz Technical University,61080, Trabzon,
Turkey
Department of Mathematics, Karadeniz Technical
Turkey
syamak@ktu.edu.tr
B.
Davvaz
B.
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
Iran
davvaz@yazduni.ac.ir
Hypergroup
$n$ary hypergroup
Fuzzy set
$n$ary subhypergroup
Fuzzy $n$ary subhypergroup $n$ary homomorphism
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Leoreanu, {it Applications of hyperstructures theory}, Advanced##in Mathematics, Kluwer Academic Publisher, 2003. ##bibitem{8} P. Corsini and I. Tofan, {it On fuzzy hypergroups}, Pure Math. Appl., {bf 8} (1997), 2937. ##bibitem{9} P. S. Das, {it Fuzzy groups and level subgroups}, J. Math. Anal. Apple., {bf 85} (1981), 264269. ##bibitem{10} B. Davvaz, {it Fuzzy $H_v$groups}, Fuzzy Sets and##Systems, {bf 101} (1999), 191195. ##bibitem{11} B. Davvaz, {it On connection between uncertainty algebraic hypersystems and probability##spaces}, Internat. J. Uncertain. Fuzziness KnowledgeBased Systems, {bf 13(3)} (2005), 337345. ##bibitem{12} B. Davvaz, {it Approximations in $n$ary algebraic systems}, Soft Computing, {bf 12} (2008), 409418. ##bibitem{13} B. Davvaz, {it On $H_v$groups and fuzzy homomorphism}, The Journal of Fuzzy Mathematics## {bf 9(2)} (2001), 271278. ##bibitem{14} B. Davvaz, {it A brief survey of the theory of $H_v$structures},##Proc. 8th INT. Congress on AHA, Greece, 2002, Spanidis Press, (2003), 3970. ## bibitem{15} B. Davvaz and T. Vougiouklis, {it $n$ary hypergroups},##Iranian Journal of Science and Technology, Transaction A, {bf 30(A2)} (2006), 165174. ##bibitem{16} B. Davvaz and P. Corsini, {it Fuzzy $n$ary hypergroups}, Journal of Intelligent and Fuzzy## Systems, {bf 18(4)} (2007), 377382. ## bibitem{17} B. Davvaz and W. A. Dudek, {it Fuzzy $n$ary groups as a generalization of Rosenfeld's fuzzy groups},## Journal of MultipleValued Logic and Soft Computing, {bf 15(56)} (2009), 451469. ##bibitem{18} W. D{"o}rnte, {it Unterschungen uber einen verallgemeinerten gruppenbegriff}, Math.Z.,##{bf 6} (1929), 119. ##bibitem{19} W. A. Dudek, {it Fuzzification of $n$ary groupoids},##Quasigroups and Related Systems, {bf 7} (2000), 4566. ##bibitem{20} W. A. Dudek, {it Idempotents in $n$ary semigroups}, Southeast Asian Bull. Math.,## {bf 25} (2001), 97104. ##bibitem{21} F. JinXuan, {it Fuzzy homomorphism and fuzzy isomorphism}, Fuzzy Sets##and Systems, {bf 63} (1994), 237242. ##bibitem{22} E. Kasner, {it An extension of the group concept}##(reported by L. G. Weld), Bull. Amer. Math. Soc., {bf 10 }(1904), 290291. ##bibitem{23} M. Koskas, {it Groupoides, Demihypergroupes et hypergroupes}, J. Math. Pures et Appl., {bf 49} (1970),## 155192. ##bibitem{24} V. Leoreanu, {it About hyperstructures associated with fuzzy sets of type 2},## Italian J. Pure Appl. Math., {bf 17} (2005), 127136. ##bibitem{25} V. LeoreanuFotea and B. Davvaz, {it $n$hypergroups and##binary relations}, European Journal of Combinatorics, {bf 29} (2008), 12071218. ##bibitem{26} S. Y. Li, D. G. Chen, W. X. Gu and H. Wang, {it Fuzzy homomorphisms},## Fuzzy Sets and Systems, {bf 79} (1996), 235238. ##bibitem{27} F. Marty, {it Sur une generalization de la notion de group}, 8th Congress Math.##Scandenaves, Stockholm, (1934), 4549. ##bibitem{28} P. P. Ming and Y. M. Ming, {it Fuzzy topology I, neighborhood structure of a fuzzy point and MoorsSmith## convergence}, J. Math. Anal., {bf 76} (1980), 571599. ##bibitem{29} A. Rosenfeld, {it Fuzzy groups}, J. Math. Anal. Appl., {bf 35} (1971), 512517. ##bibitem{30} B. K. Sarma and T. Ali, {it Weak and strong fuzzy homomorphisms of groups},## J. Fuzzy Math., {bf 12} (2004), 357368. ##bibitem{31} S. Sebastian and S. Babu Sunder, {it Fuzzy groups and group homomorphisms},##Fuzzy Sets and Systems, {bf 81} (1996), 397401. ##bibitem{32} T. Vougiouklis, {it Hyperstructures and their representations}, Hadronic Press, Inc,##115, Palm Harber, USA, 1994. ##bibitem{33} T. Vougiouklis, {it The fundamental relation in hyperrings. The##general hyperfield}, Proc. Fourth Int. Congress on Algebraic Hyperstructures##and Applications (AHA 1990), World Scientific, (1991), 203211. ##bibitem{34} L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf 8} (1965), 338353. ##bibitem{35} M. Mashinchi and M. M. Zahedi, {it A counterexample of P. S. Das's paper},## Journal of Mathematical Analysis and Applications, {bf 153(2)} (1990), 591592. ##bibitem{36} M. M. Zahedi, M. Bolurian and A. Hasankhani, {it On## polygroups and fuzzy subpolygroups}, J. Fuzzy Math., {bf 3} (1995), 115.##]
FUZZIFYING CLOSURE SYSTEMS AND CLOSURE
OPERATORS
FUZZIFYING CLOSURE SYSTEMS AND CLOSURE
OPERATORS
2
2
In this paper, we propose the concepts of fuzzifying closure systems and Birkhoff fuzzifying closure operators. In the framework of fuzzifying mathematics, we find that there still exists a one to one correspondence between fuzzifying closure systems and Birkhoff fuzzifying closure operators as in the case of classical mathematics. In the aspect of category theory, we prove that the category of fuzzifying closure system spaces is isomorphic to the category of Birkhoff fuzzifying closure spaces. In addition, we obtain an important result that the category of fuzzifying closure spaces and that of fuzzifying closure system spaces can be both embedded in the category of Birkhoff 𝐼 closure spaces. Finally, using fuzzifying closure systems of the paper, we introduce a set of separation axioms in fuzzifying closure system spaces, which offer a try how to research the properties of spaces by fuzzifying closure systems.
1
In this paper, we propose the concepts of fuzzifying closure systems and Birkhoff fuzzifying closure operators. In the framework of fuzzifying mathematics, we find that there still exists a one to one correspondence between fuzzifying closure systems and Birkhoff fuzzifying closure operators as in the case of classical mathematics. In the aspect of category theory, we prove that the category of fuzzifying closure system spaces is isomorphic to the category of Birkhoff fuzzifying closure spaces. In addition, we obtain an important result that the category of fuzzifying closure spaces and that of fuzzifying closure system spaces can be both embedded in the category of Birkhoff 𝐼 closure spaces. Finally, using fuzzifying closure systems of the paper, we introduce a set of separation axioms in fuzzifying closure system spaces, which offer a try how to research the properties of spaces by fuzzifying closure systems.
77
94
Xiaoli
Luo
Xiaoli
Luo
Department of Mathematics, Ocean University of China, Qingdao 266071,
People’s Republic of China
Department of Mathematics, Ocean University
China
luosixi@yahoo.cn
Jinming
Fang
Jinming
Fang
Department of Mathematics, Ocean University of China, Qingdao
266071, People’s Republic of China
Department of Mathematics, Ocean University
China
jinmingfang@163.com
Fuzzifying closure operator
Fuzzifying closure system
Isomorphism of categories
Embedding of categories
Fuzzifying remote neighborhood system
Separation axioms
[[1] J. Ad´𝑎mek, H. Herrlich and G. E. Srreker, Abstract and concrete categories, Wiley, New York,##[2] R. Bˇelohl´avek, Fuzzy closure operators, J. Math. Anal. Appl., 262 (2001), 473489.##[3] M. ´Ciri´c, J. Ignjatovi´c and S. Bogdanovi´c, Fuzzy equivalence relations and their equivalence##classes, Fuzzy Sets and Systems, 158 (2007), 12591313.##[4] J. Fang, 𝐼fuzzy Alexandrov topologies and specialization orders, Fuzzy Sets and Systems, 158##(2007), 23592374.##[5] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous##lattices and domains, Cambridge University Press, 2003.##[6] B. Hutton and I. Reilly, Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems,##3 (1980), 93104.##[7] F. H. Khedr, F. M. Zeyada and O. R. Sayed, On separation axioms in fuzzifying topology,##Fuzzy Sets and Systems, 119 (2001), 439458.##[8] R. Lowen and L. Xu, Alternative characterizations of FNCS, Fuzzy Sets and Systems, 104##(1999), 381391.##[9] A. S. Mashhour and M. H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl., 106 (1985),##[10] J. Shen, Separation axioms in fuzzifying topology, Fuzzy Sets and Systems, 57 (1993), 111##[11] S. P. Sinha, Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems, 45 (1992),##[12] R. Srivastava, A. K. Srivastava and A. Choubey, Fuzzy closure spaces, J. Fuzzy Math., 2##(1994), 525534. ##[13] R. Srivastava and M. Srivastava, On 𝑇0 and 𝑇1fuzzy closure spaces, Fuzzy Sets and Systems,##109 (2000), 263269.##[14] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303321.##[15] Y. Yue and J. Fang, On separation axioms in 𝐼fuzzy topological spaces, Fuzzy Sets and##Systems, 157 (2006), 780793.##[16] W. Zhou, Generalization of 𝐿closure spaces, Fuzzy Sets and Systems, 149 (2005), 415432.##]
SEMISIMPLE SEMIHYPERGROUPS IN TERMS OF
HYPERIDEALS AND FUZZY HYPERIDEALS
SEMISIMPLE SEMIHYPERGROUPS IN TERMS OF
HYPERIDEALS AND FUZZY HYPERIDEALS
2
2
In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.
1
In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.
95
111
Piergiulio
Corsini
Piergiulio
Corsini
Department of Civil Engineering and Architecture, Via delle
Scienze 206, 33100 Udine, Italy
Department of Civil Engineering and Architecture,
Italy
piergiulio.corsini@uniud.it, corsini2002@yahoo.com
Muhammad
Shabir
Muhammad
Shabir
Department of Mathematics, QuaidiAzam University, Islamabad
45320, Pakistan
Department of Mathematics, QuaidiAzam University
Pakistan
mshabirbhatti@yahoo.co.uk
Tariq
Mahmood
Tariq
Mahmood
Department of Mathematics, QuaidiAzam University, Islamabad
45320, Pakistan
Department of Mathematics, QuaidiAzam University
Pakistan
tmhn3367@gmail.com
Semihypergroups
Prime (semiprime) hyperideals of semihypergroups
Prime (semiprime) fuzzy hyperideals of semihypergroups
Semisimple semihypergroups
[[1] J. Ahsan, K. Saifullah and M. F. Khan, Semigroups characterized by thier fuzzy ideals, Fuzzy##systems and Math., 9 (1995) 2932.##[2] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, AMS, Math., Surveys,##Providence, R. I., 1&2(7) (1961/67).##[3] P. Corsini, Join spaces, power sets, fuzzy sets, Proceedings of the 5th International Congress##on Aigebraic Hyperstructures and Applications 1993, Isai, Romania, Hadronic Press, 1994.##[4] P. Corsini, New themes of research on hyperstructures associated with fuzzy sets., J. of Basic##Science, Mazandaran, Iran, 2(2) (2003), 2536.##[5] P. Corsini, A new connection between hypergroups and fuzzy sets., Southeast Bul. of Math.,##27 (2003), 221229.##[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,##Dordrecht, Hardbound, 2003.##[7] I. Cristea, Hyperstructures and fuzzy sets endowed with two membership functions, Fuzzy##Sets and Systems, 160 (2009), 11141124.##[8] I. Cristea, About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal##of FuzzySy stems, 7(2) (2010), 95108.##[9] B. Davvaz, Fuzzy hyperideals in semihypergroups, Italian J. Pure and Appl. Math., 8 (2000),##[10] B. Davvaz, Strong regularity and fuzzy strong regularity in semihypergroups., Korean J. Comput.##& Appl. Math., 7(1) (2000), 205213. ##[11] A. Hasankhani, Ideals in a semihypergroup and Green’s relations., Ratio Mathematica, 13##(1999), 2936.##[12] A. Kehagias, Latticefuzzy meet and join hyperoperations, Proceedings of the 8th International##Congress on AHA and Appl., Samothraki, Greece, (2003), 171182.##[13] N. Kuroki, Fuzzy biideals in semigroups, Comment. Math. Univ. St. Paul., 28 (1979) 1721.##[14] V. Leoreanu, About hyperstructures associated with fuzzy sets of type 2., Italian J. of Pure##and Appl. Math., 17 (2005), 127136.##[15] F. Marty, Sur une generalization de la notion de groupe, 8𝑖𝑒𝑚 Congress Math. Scandinaves,##Stockholm, (1934), 4549.##[16] J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy semigroups, Springer, 2003.##[17] M. Stefanescu and I. Cristea, On the fuzzy grade of hypergroups, FuzzySets and Systems,##159(9) (2008), 10971106##[18] I. Tofan and A. C. Volf, On some connections between hyperstructures and fuzzy sets, Italian##J. of Pure and Appl. Math., 7 (2000), 6368.##[19] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
SOME HYPER KALGEBRAIC STRUCTURES INDUCED BY
MAXMIN GENERAL FUZZY AUTOMATA
SOME HYPER KALGEBRAIC STRUCTURES INDUCED BY
MAXMIN GENERAL FUZZY AUTOMATA
2
2
We present some connections between the maxmin general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCKalgebra induced by a maxmin general fuzzy automaton. Then, we study the properties of this hyper BCKalgebra. Particularly, some theorems and results for hyper BCKalgebra are proved. For example, it is shown that this structure consists of different types of (positive implicative) commutative hyper Kideals. As a generalization, we extend the definition of this hyper BCKalgebra to a bounded hyper Kalgebra and obtain relative results.
1
We present some connections between the maxmin general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCKalgebra induced by a maxmin general fuzzy automaton. Then, we study the properties of this hyper BCKalgebra. Particularly, some theorems and results for hyper BCKalgebra are proved. For example, it is shown that this structure consists of different types of (positive implicative) commutative hyper Kideals. As a generalization, we extend the definition of this hyper BCKalgebra to a bounded hyper Kalgebra and obtain relative results.
113
134
khadijeh
Abolpour
khadijeh
Abolpour
Department of Mathematics, Islamic Azad University, Kerman
Branch, Kerman, Iran
Department of Mathematics, Islamic Azad University
Iran
abolpor kh@yahoo.com
Mohammad Mehdi
Zahedi
Mohammad Mehdi
Zahedi
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
Department of Mathematics, Tarbiat Modares
Iran
zahedi mm@modares.ac.ir
Masoome
Golmohamadian
Masoome
Golmohamadian
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
Department of Mathematics, Tarbiat Modares
Iran
(Positive implicative) Commutative hyper Kideal
(Bounded) Hyper BCKalgebra
Hyper BCKideal
Maxmin general fuzzy automata
[[1] M. A. Arbib, From automata theory to brain theory, Int. J. ManMachine Stud., 7(3) (1975),##[2] W. R. Ashby, Design for a brain, Chapman and Hall, London, 1954.##[3] R. A. Borzooei, Hyper BCK and Kalgebras, Ph.D. Thesis, Department of Mathematics,##Shahid Bahonar University of Kerman, Iran, 2000.##[4] R. A. Borzooei, A. Hasankhani, M. M. Zahedi and Y. B. Jun, On hyper Kalgebras, Scientiae##Mathematicae Japonica, 52(1) (2000), 113121.##[5] A. W. Burks, Logic, biology and automatasome historical reflections, Int. J. ManMachine##Stud., 7(3) (1975), 297312.##[6] P. Corsini, Prolegomena of hyper group theory, Avian Editor, Italy, 1993.##[7] P. Corsini and V. Leoreanu, Applications of hyper structure theory, Advances in Mathematics,##Kluwer Academic Publishers, 5 (2003).##[8] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal##of Approximate Reasoning, 38 (2005), 175214.##[9] J. E. Hopcroft, R. Motwani and J. D. Ullman, Introduction to automata theory, languages##and computation, seconded, AddisonWesley, Reading, MA, 2001.##[10] M. Horry and M. M. Zahedi, Uniform and semiuniform topology on general fuzzy automata,##Iranian Journal of Fuzzy Systems, 6(2) (2009), 1929.##[11] M. Horry and M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of##Fuzzy Systems, 6(2) (2009), 6174.##[12] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV Proc. Japan Academy,##42 (1966), 1922.##[13] D. S. Malik and J. N. Mordeson, Fuzzy discrete structures, PhysicaVerlag, NewY ork, 2000.##[14] F. Marty, Sur une generalization de la notion de groups, 8th Congress Math. Scand naves,##Stockholm, (1934), 4549.##[15] W. S. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity,##Bull. Math. Biophysics., 5 (1943), 115133.##[16] J. Meng and Y. B. Jun, BCKalgebra, Kyung Moons, Co., Seoul, 1994.##[17] M. L. Minsky, Computation: finite and infinite machines, PrenticeHall, Englewood Cliffs,##NJ, Chapter 3, (1967), 3266.##[18] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,##Chapman and Hall/CRC, London/Boca Raton, FL, 2002.##[19] M. A. Nasr Azadani and M. M. Zahedi, Sabsorbing set and (P)decomposition in hyper##Kalgebras, Italian Journal of Pure and Applied Mathematics, to appear.##[20] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: automata,##runs, and dynamicfuzzy systems, Proc. IEEE, 87(9) (1999), 16231640.##[21] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy finitestate automata can be deterministically##encoded into recurrent neural networks, IEEE Trans. Fuzzy Systems, 5(1) (1998),##[22] T. Roodbari, Positive implicative and commutative hyper Kideals, Ph.D. Thesis, Department##of Mathematics, Shahid Bahonar University of Kerman, Iran, 2008.##[23] T. Roodbari, L. Torkzadeh and M. M. Zahedi, Normal hyper Kalgebras, Sciatica Mathematical##Japonica, 68(2) (2008), 265278.##[24] T. Roodbari and M. M. Zahedi, Positive implicative hyper Kideals II, Scientiae Mathematicae##Japonica, 66(3) (2007), 391404.##[25] L. Torkzadeh, Dual positive implicative and commutative hyper Kideals, Ph.D. Thesis, Department##of Mathematics, Shahid Bahonar University of Kerman, Iran, 2005.##[26] L. Torkzadeh, T. Roodbari and M. M. Zahedi, Hyper stabilizers and normal hyper BCKalgebras,##SetValued Mathematics and Applications, to appear.##[27] A. Turing, On computable numbers, with an application to the entscheidungs problem, Proc.##London Math. Soc., 42 (193637), 220265. ##[28] J. Von Neumann, Theory of selfreproducing automata, University of Illinois Press, Urbana,##[29] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept##to pattern classification, Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.##[30] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##[31] M. M. Zahedi, R. A. Borzooei and H. Rezaei, Some classifications of hyper Kalgebra of order##3, Math. Japon., (2001), 133142.##[32] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (general) topology on maxmin general##fuzzy automata , Advances in Fuzzy Mathematics, 3(1) (2008), 5168.##]
NORM AND INNER PRODUCT ON FUZZY LINEAR SPACES
OVER FUZZY FIELDS
NORM AND INNER PRODUCT ON FUZZY LINEAR SPACES
OVER FUZZY FIELDS
2
2
In this paper, we introduce the concepts of norm and inner prod uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.
1
In this paper, we introduce the concepts of norm and inner prod uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.
135
144
C. P.
Santhosh
C. P.
Santhosh
Department of Mathematical Sciences, Kannur University, Man
gattuparamba, Kannur, Kerala, 670 567, India.
Department of Mathematical Sciences, Kannur
India
santhoshcpchu@yahoo.co.in
T. V.
Ramakrishnan
T. V.
Ramakrishnan
Department of Mathematical Sciences, Kannur University, Man
gattuparamba, Kannur, Kerala, 670 567, India.
Department of Mathematical Sciences, Kannur
India
ramakrishnantv@rediffmail.com
Fuzzy fields
Fuzzy linear spaces
Norm on fuzzy linear spaces
Inner product on fuzzy linear spaces
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VAGUE RINGS AND VAGUE IDEALS
VAGUE RINGS AND VAGUE IDEALS
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In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.
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In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.
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Sevda
Sezer
Sevda
Sezer
Faculty of Education, Akdeniz University, 07058, Antalya, Turkey
Faculty of Education, Akdeniz University,
Turkey
sevdasezer@yahoo.com , sevdasezer@akdeniz.edu.tr
Vague group
Generalized vague subgroup
Vague ring
Vague subring
Vague ideal
Vague prime ideal
Vague maximal ideal
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