University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
28
Cover vol. 8, no. 2, June 2011
0
EN
10.22111/ijfs.2011.2872
http://ijfs.usb.ac.ir/article_2872.html
http://ijfs.usb.ac.ir/article_2872_9c5871395928c89e9f42cf3a6911447f.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
16
POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY
SET THEORIES
1
46
EN
Sergey A.
Solovyov
Department of Mathematics, University of Latvia, Zellu iela 8,
LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia
sergejs.solovjovs@lu.lv
10.22111/ijfs.2011.259
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, we provide a direct lift of the backward powerset operator using the notion of categorical biproduct. The obtained framework is readily extended to the variable-basis case, justifying the powerset theories currently popular in the fuzzy community. At the end of the paper, our general variety-based setting postulates the requirements, under which a convenient variety-based powerset theory can be developed, suitable for employment in all areas of fuzzy mathematics dealing with fuzzy powersets, including fuzzy algebra, logic and topology.
(Backward,forward) powerset (operator,theory), (Bi,co) product,
(Composite) (variety-based) topological (space,system), (Convenient) variety, Ground category,
(L-) fuzzy set, (Localic) algebra, Monadic (category,logic), Ordered category, Pointed category,
Quantaloid, (Semi-) quantale, (Unital) (quantale,ring) (algebra,module), Zero (morphism,object)
http://ijfs.usb.ac.ir/article_259.html
http://ijfs.usb.ac.ir/article_259_70ec1ad6ec163ed0aae61e0371fe26ac.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
ACCEPTANCE SINGLE SAMPLING PLAN
WITH FUZZY PARAMETER
47
55
EN
Bahram
Sadeghpour Gildeh
Department of Statistics, Faculty of Basic Science,
University of Mazandaran, P.O. Box 311, Babolsar, Iran
sa deg hpour@umz.ac.ir
Ezzatallah
Baloui Jamkhaneh
PhD student, Science and Research Branch, Islamic
Azad University (IAU), Tehran, Iran
e_baloui2008@yahoo.com
Gholamhossein
Yari
Iran University of Science and Technology, Tehran, Iran
yari@iust.ac.ir
10.22111/ijfs.2011.272
The acceptance sampling plan problem is an important topic inquality control and both the theory of probability and theory of fuzzy sets maybe used to solve it. In this paper, we discuss the single acceptance samplingplan, when the proportion of nonconforming products is a fuzzy number. We
show that the operating characteristic (𝑂𝐶) curve of the plan is a band havinghigh and low bounds and that for fixed sample size and acceptance number,the width of the band depends on the ambiguity proportion parameter in thelot. When the acceptance number equals zero, this band is convex and the
convexity increases with 𝑛 Finally, we compare the 𝑂𝐶 bands for a given value of 𝑐.
Statistical quality control,Single sampling plan,Fuzzy number,Fuzzy
probability of acceptance
http://ijfs.usb.ac.ir/article_272.html
http://ijfs.usb.ac.ir/article_272_418a9022650750f9cf0335d218551f21.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
CREDIBILISTIC PARAMETER ESTIMATION AND ITS
APPLICATION IN FUZZY PORTFOLIO SELECTION
57
65
EN
Xiang
Li
The State Key Laboratory of Rail Traffic Control and Safety, Beijing
Jiaotong University, Beijing 100044, China
xiang-li04@mail.tsinghua.edu.cn
Zhongfeng
Qin
School of Economics and Management, Beihang University, Beijing
100191, China
qin@buaa.edu.cn
Dan
Ralescu
Department of Mathematical Sciences, University of Cincinnati, Cincin-
nati, Ohio 45221, USA
ralescd@uc.edu
10.22111/ijfs.2011.276
In this paper, a maximum likelihood estimation and a minimum entropy estimation for the expected value and variance of normal fuzzy variable are discussed within the framework of credibility theory. As an application, a credibilistic portfolio selection model is proposed, which is an improvement over the traditional models as it only needs the predicted values on the security returns instead of their membership functions.
Normal fuzzy variable,Credibility theory,Condence interval,Point
estimation,Portfolio selection
http://ijfs.usb.ac.ir/article_276.html
http://ijfs.usb.ac.ir/article_276_d8874dd3f7ef8e982def5dc5a05f1138.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
LATTICE-VALUED CATEGORIES OF LATTICE-VALUED
CONVERGENCE SPACES
67
89
EN
Gunther
Jager
Department of Statistics, Rhodes University, 6140 Grahamstown,
South Africa
g.jager@ru.ac.za
10.22111/ijfs.2011.277
We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topological spaces.
L-fuzzy convergence,L-topology,L-lter,L-limit space,L-category,Fuzzy category
http://ijfs.usb.ac.ir/article_277.html
http://ijfs.usb.ac.ir/article_277_79566496e14adbdda02f6a7a00901123.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
$(A)_ {Delta}$ - double Sequence Spaces of fuzzy numbers via Orlicz Function
91
103
EN
E.
Savas
Istanbul Ticaret University, Department of Mathematics, Uskudar-Istanbul,
Turkey
ekremsavas@yahoo.com
10.22111/ijfs.2011.278
The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$-convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy numbers areexamined. In addition, we define the double$(A,Delta)$-statistical convergence of fuzzy numbers andestablish some connections between the spaces of strong double$(A)_ {Delta}$-convergent sequence and double $(A,Delta)$-statistical convergent sequence.
Orlicz function,Double statistical convergence,Fuzzy
number
http://ijfs.usb.ac.ir/article_278.html
http://ijfs.usb.ac.ir/article_278_ef2ae7f0cde58ba40cbfd7dc90d5c603.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
BIPOLAR FUZZY HYPER BCK-IDEALS IN HYPER
BCK-ALGEBRAS
105
120
EN
Young Bae
Jun
Department of Mathematics Education (and RINS), Gyeongsang National
University, Chinju 660-701, Korea
skywine@gmail.com
Min Su
Kang
Department of Mathematics, Hanyang University, Seoul 133-791, Korea
sinchangmyun@hanmail.net
Hee Sik
Kim
Department of Mathematics, Hanyang University, Seoul 133-791, Korea
heekim@hanyang.ac.kr
10.22111/ijfs.2011.279
Using the notion of bipolar-valued fuzzy sets, the concepts of bipolarfuzzy (weak, 𝑠-weak, strong) hyper BCK-ideals are introduced, and theirrelations are discussed. Moreover, several related properties are investigated.
(Strong,weak,s-weak) hyper BCK-ideal,Bipolar fuzzy hyper BCKideal,Bipolar fuzzy strong hyper BCK-ideal,Bipolar fuzzy weak hyper BCK-ideal,Bipolar fuzzy
s-weak hyper BCK-ideal,inf-sup property
http://ijfs.usb.ac.ir/article_279.html
http://ijfs.usb.ac.ir/article_279_f6c72ec3d3126db90f5abc49dbb8e610.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
NET-THEORETICAL L-GENERALIZED
CONVERGENCE SPACES
121
131
EN
Wei
Yao
Department of Mathematics, Hebei University of Science and Technology,
Shijiazhuang 050018, P.R. China
yaowei0516@163.com
10.22111/ijfs.2011.280
In this paper, the denition of net-theoretical L-generalized convergencespaces is proposed. It is shown that, for L a frame, the category ofenriched L-fuzzy topological spaces can be embedded in that of L-generalizedconvergence spaces as a reective subcategory and the latter is a cartesianclosedtopological category.
Net,(Net-theoretical) L-generalized convergence space,(Enriched)
L-fuzzy topological space,Cartesian-closed category
http://ijfs.usb.ac.ir/article_280.html
http://ijfs.usb.ac.ir/article_280_9316551223b467dab2248c0332fe0d3d.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
GENERALIZED REGULAR FUZZY MATRICES
133
141
EN
A. R.
Meenakshi
Department of Mathematics, Karpagam college of Engineering,
Coimbatore 641 032, India
arm meenakshi@yahoo.co.in
P.
Jenita
Department of Mathematics, Karpagam college of Engineering, Coimbat-
ore 641 032, India
sureshjenita@yahoo.co.in
10.22111/ijfs.2011.281
In this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.
Fuzzy matrices,K-regular fuzzy matrices,Index,period
http://ijfs.usb.ac.ir/article_281.html
http://ijfs.usb.ac.ir/article_281_419deaac4d3074913d6a23fcc112230c.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
17
GRADATION OF CONTINUITY IN FUZZY TOPOLOGICAL
SPACES
143
159
EN
Ramkrishna
Thakur
Department of Mathematics, Visva-Bharati, Santiniketan-731235,
West Bengal, India
thakurram06@gmail.com
S. K.
Samanta
Department of Mathematics, Visva-Bharati, Santiniketan-731235,
West Bengal, India
syamal 123@yahoo.co.in
K. K.
Mondal
Department of Mathematics, Kurseong College, Kurseong-734203,
West Bengal, India
krishnakmondal@yahoo.co.in
10.22111/ijfs.2011.282
In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the N-compactnessgrade is examined. Concept of gradation is also introduced in openness, closed-ness, homeomorphic properties of mappings and T2 separation axiom. Effectof the grades interrelated with N-compactness, closedness, T2 separation andhomeomorphism of mappings are studied.
Fuzzy belongingness,Fuzzy quasi-coincidence,Gradation of openness,Gradation of neighborhoodness,Fuzzy topological spaces,Fuzzy filters,Graded continuity
http://ijfs.usb.ac.ir/article_282.html
http://ijfs.usb.ac.ir/article_282_d0a6af44b663cec5b8dab7fa087edf53.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
2
2011
06
28
Persian-translation vol. 8, no. 2, June 2011
163
171
EN
10.22111/ijfs.2011.2873
http://ijfs.usb.ac.ir/article_2873.html
http://ijfs.usb.ac.ir/article_2873_40e3f20f6eb514fd5ac11e3db5c126b9.pdf