University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
01
Cover vol. 14, no. 6, December 2017
0
EN
10.22111/ijfs.2017.3504
http://ijfs.usb.ac.ir/article_3504.html
http://ijfs.usb.ac.ir/article_3504_e75c3dcf8c1fe24b35436246ee473aff.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
F-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM
1
13
EN
Irina
Perfilieva
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
irina.perfilieva@osu.cz
Petra
Stevuliakova
University of Ostrava, Centre of Excellence IT4Innovations,
Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03
Ostrava 1, Czech Republic
Radek
Valasek
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1,
Czech Republic
10.22111/ijfs.2017.3495
We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed method. We show that the F-transform-based approach does not only extend the set of its applications, but has a certain advantage in the solution of ill-posed problems.
F-transform,Differential equation,Boundary value problem,Second order differential equation
http://ijfs.usb.ac.ir/article_3495.html
http://ijfs.usb.ac.ir/article_3495_ccab4ef5ff4c62aba8a2fe33db1a5b8e.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
DIAGNOSIS OF BREAST LESIONS USING THE LOCAL CHAN-VESE MODEL, HIERARCHICAL FUZZY PARTITIONING AND FUZZY DECISION TREE INDUCTION
15
40
EN
Fouzia
Boutaouche
laboraoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
boutaouche-f@netcourrier.com
Nacéra
Benamrane
laboratoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
10.22111/ijfs.2017.3496
Breast cancer is one of the leading causes of death among women. Mammography remains today the best technology to detect breast cancer, early and efficiently, to distinguish between benign and malignant diseases. Several techniques in image processing and analysis have been developed to address this problem. In this paper, we propose a new solution to the problem of computer aided detection and interpretation for breast cancer. In the proposed approach, a Local Chan-Vese (LCV) model is used for the mass lesion segmentation step to isolate a suspected abnormality in a mammogram. In the classification step, we propose a two-step process: firstly, we use the hierarchical fuzzy partitioning (HFP) to construct fuzzy partitions from data, instead of using the only human information, available from expert knowledge, which are not sufficiently accurate and confronted to errors or inconsistencies. Secondly,fuzzy decision tree induction are proposed to extract classification knowledge from a set of feature-based examples. Fuzzy decision trees are first used to determine the class of the abnormality detected (well-defined mass, ill-defined mass, architectural distortion, or speculated masses), then, to identify the Severity of the abnormality, which can be benign or malignant. The proposed system is tested by using the images from Mammographic Image Analysis Society[MIAS] database. Experimental results show the efficiency of the proposed approach, resulting in an accuracy rate of 87, a sensitivity of 82.14%, and good specificity of 91.42
Breast cancer,Mass segmentation,Local Chan-Vese model fuzzy decision tree,Fuzzy partitioning,Computer-aided detection
http://ijfs.usb.ac.ir/article_3496.html
http://ijfs.usb.ac.ir/article_3496_9e3953081f1d3b480e734c66534326f0.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
INFORMATION MEASURES BASED TOPSIS METHOD FOR MULTICRITERIA DECISION MAKING PROBLEM IN INTUITIONISTIC FUZZY ENVIRONMENT
41
63
EN
Arunodaya Raj
Mishra
Department of Mathematics, ITM University, Gwalior-
474001, M. P., India
Pratibha
Rani
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
pratibha138@gmail.com
10.22111/ijfs.2017.3497
In the fuzzy set theory, information measures play a paramount role in several areas such as decision making, pattern recognition etc. In this paper, similarity measure based on cosine function and entropy measures based on logarithmic function for IFSs are proposed. Comparisons of proposed similarity and entropy measures with the existing ones are listed. Numerical results limpidly betoken the efficiency of these measures over others. An intuitionistic fuzzy weighted measures (IFWM) with TOPSIS method for multi-criteria decision making (MCDM) quandary is introduced to grade the alternatives. This approach is predicated on entropy and weighted similarity measures for IFSs. An authentic case study is discussed to rank the four organizations. To compare the different rankings, a portfolio selection problem is considered. Various portfolios have been constructed and analysed for their risk and return. It has been examined that if the portfolios are developed using the ranking obtained with proposed method, the return is increased with slight increment in risk.
Fuzzy set,Intuitionistic fuzzy set,Entropy,Similarity measure,TOPSIS,MCDM
http://ijfs.usb.ac.ir/article_3497.html
http://ijfs.usb.ac.ir/article_3497_b79c7d8a35da236ddbc695172d3305b4.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
MULTIPERIOD CREDIBILITIC MEAN SEMI-ABSOLUTE DEVIATION PORTFOLIO SELECTION
65
86
EN
Peng
Zhang
School of Economics and Management, South China Normal University,
Guangzhou 510006, P. R. China
zhangpeng300478@aliyun.com
10.22111/ijfs.2017.3498
In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- absolute deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with the return rate on a risky asset by its credibilitic expected value and semi- absolute deviation. Since the proposed model is a nonlinear dynamic optimization problem with path dependence, we design a novel forward dynamic programming method to solve it. Finally, we provide a numerical example to demonstrate the performance of the designed algorithm and the application of the proposed model.
Finance,Multiperiod portfolio selection,Mean semi-absolute deviation,Entropy constraints,The forward dynamic programming method
http://ijfs.usb.ac.ir/article_3498.html
http://ijfs.usb.ac.ir/article_3498_174cd4e7a275172b16ebbf632749d7bd.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS
87
102
EN
B. M.
Uzzal Afsan
Department of Mathematics, Sripat Singh College, Jiaganj-742123, Murshidabad, West Bengal, India
10.22111/ijfs.2017.3499
The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which the point-wise limit of a sequence of fuzzy Henstock integrable functions is fuzzy Henstock integrable has been established.
Fuzzy number,Fuzzy number function,Fuzzy Henstock integral,Fuzzy monotone sequence
http://ijfs.usb.ac.ir/article_3499.html
http://ijfs.usb.ac.ir/article_3499_6f4cc2d0c57b2e8308bf4c95c9724bbb.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
CREDIBILITY THEORY ORIENTED PREFERENCE INDEX FOR RANKING FUZZY NUMBERS
103
117
EN
Gholamreza
Hesamian
Department of Statistics, Payame Noor University,, Tehran
19395-3697, Iran
ghesamian@math.iut.ac.ir
Farid
Bahrami
Department of Mathematical Sciences,, Isfahan University of Technology,, Isfahan 84156-83111, Iran
f.ahmadi@math.iut.ac.ir
10.22111/ijfs.2017.3500
This paper suggests a novel approach for ranking the most applicable fuzzy numbers, i.e. $LR$-fuzzy numbers. Applying the $alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed preference criterion are also studied. Moreover, the proposed method is applied for ranking fuzzy numbers using target-rank-based methods. Some numerical examples are used to illustrate the proposed ranking procedure. The proposed preference criterion is also examined in order to compare with some common methods and the feasibility and effectiveness of the proposed ranking method is cleared via some numerical comparisons.
Credibility index,$alpha$-optimistic values,Robustness,Reciprocity,Fuzzy target
http://ijfs.usb.ac.ir/article_3500.html
http://ijfs.usb.ac.ir/article_3500_c8f1b5309e61cf8692e840b8009dfcf8.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES
119
134
EN
Hamed
Ahmadzade
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
ahmadzadeh.h.63@gmail.com
Mohammad
Amini
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad 91775, Iran
mamini48@yahoo.com
Seyed Mahmoud
Taheri
Faculty of Engineering Science, College of Engineering,
University of Tehran, Tehran, Iran
sm_taheri@yahoo.com
Abolghasem
Bozorgnia
Department of Statistics, Khayyam University, Mashhad,
Iran
a.bozorgnia@khayyam.ac.ir
10.22111/ijfs.2017.3501
In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequalities to independent fuzzy random variables.Furthermore, a weak law of large numbers for independent fuzzy random vari-ables is stated and proved.
Fuzzy random variable,Linearly Positive Quadrant Dependence,Independence,Law of Large Numbers
http://ijfs.usb.ac.ir/article_3501.html
http://ijfs.usb.ac.ir/article_3501_4354e3e5670f8d20ba3ab0bb1f95685b.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
ROBUSTNESS OF THE TRIPLE IMPLICATION INFERENCE METHOD BASED ON THE WEIGHTED LOGIC METRIC
135
148
EN
Jun
Li
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
lijun@lut.cn
Chao
Fu
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
fuchao45612@sina.com
10.22111/ijfs.2017.3502
This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple implication method possesses a good behavior of robustness.
Robustness,Triple implication method,Weighted logic metric,Weighted logic similarity degree,Fuzzy reasoning
http://ijfs.usb.ac.ir/article_3502.html
http://ijfs.usb.ac.ir/article_3502_3af181b32a04b615e978e930b50b64b4.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
30
ON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES
149
164
EN
Gunther
Jager
School of Mechanical Engineering, University of Applied Sciences
Stralsund, D-18435 Stralsund, Germany
g.jager@ru.ac.za, gunther.jaeger@fh-stralsund.de
10.22111/ijfs.2017.3503
In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our category to the categories of stratified $L$-topological spaces and of enriched $LM$-fuzzy topological spaces.
Lattice-valued convergence,$LM$-convergence space,Stratified $LMN$-convergence tower space,Stratified $LM$-filter,Stratified $L$-topological space,Enriched $LM$-fuzzy topological space
http://ijfs.usb.ac.ir/article_3503.html
http://ijfs.usb.ac.ir/article_3503_08f77d70db13a2b7b2554e34ebcef52f.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
6
2017
12
01
Persian-translation Vol.14, No.6
167
175
EN
10.22111/ijfs.2017.3505
http://ijfs.usb.ac.ir/article_3505.html
http://ijfs.usb.ac.ir/article_3505_70f72100261fda6aa83bea4e659894cb.pdf