eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-01
15
2
0
10.22111/ijfs.2018.3756
3756
Cover vol. 15, no. 2, April 2018
http://ijfs.usb.ac.ir/article_3756_a827a8e2afdf2fe8eb4bb7c5a5bd0217.pdf
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
1
21
10.22111/ijfs.2018.3753
3753
مقاله پژوهشی
POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS
D. R. Jardon
1
M. Sanchis
2
Academia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa s/n, Col. Lomas de Zaragoza 09620, Ciudad de Mexico , Mexico
Institut de Matematiques i Aplicacions de Castello (IMAC), Universitat Jaume I, Campus Riu Sec, 12071-Castello, Spain
We study the space of all continuous fuzzy-valued functions from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$ endowed with the pointwise convergence topology. Our results generalize the classical ones for continuous real-valued functions. The field of applications of this approach seems to be large, since the classical case allows many known devices to be fitted to general topology, functional analysis, coding theory, Boolean rings, etc.
http://ijfs.usb.ac.ir/article_3753_2b8058838050761d26d4f9d8d6a43cfd.pdf
Fuzzy-number
Fuzzy analysis
Function space
Pointwise convergence
Dual map
Evaluation map
Fr'echet space
Grothendieck's theorem
Cardinal function
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
23
40
10.22111/ijfs.2018.3754
3754
مقاله پژوهشی
L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS
Chong Shen
shenchong0520@163.com
1
Fu-Gui Shi
fuguishi@bit.edc.cn
2
School of Mathematics and statistics, Beijing Institute of Technology, Beijing 100081, P.R. China
School of Mathematics and statistics, Beijing Institute of Technology, Beijing 100081, P.R. China
The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.
http://ijfs.usb.ac.ir/article_3754_de43053a691df5ee38c5df21e874a1b9.pdf
$L$-convex system
Scott-hull space
Induced $L$-convex structure
Quotient system
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
41
52
10.22111/ijfs.2018.3755
3755
مقاله پژوهشی
BASES AND CIRCUITS OF FUZZIFYING MATROIDS
Shao-Jun Yang
shaojunyang@outlook.com
1
Fu-Gui Shi
fuguishi@bit.edc.cn
2
The Fujian Provincial Key Laboratory of Network Security and Cryptology, School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, P.R. China
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, P.R. China; Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 102488, P.R. China
In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis axioms or circuit axioms.
http://ijfs.usb.ac.ir/article_3755_3eb0a96d3cd8eee16ffe525dc4b0db85.pdf
Fuzzifying matroid
Fuzzifying base-map
Fuzzifying basis axiom
Fuzzifying circuit-map
Fuzzifying circuit axiom
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
53
73
10.22111/ijfs.2018.3759
3759
مقاله پژوهشی
QUANTALE-VALUED SUP-ALGEBRAS
Radek Slesinger
1
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic
Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following cite{solovyov-qa}, we show that the category of $Q$-sup-algebras is isomorphic to a certain subcategory of a category of $Q$-modules.
http://ijfs.usb.ac.ir/article_3759_15a2e675b28ad7601164f7c1adefa982.pdf
$Q$-order
$Q$-sup-lattice
$Q$-ordered algebra
$Q$-sup-algebra
Quotient
subalgebra
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
75
87
10.22111/ijfs.2018.3760
3760
مقاله پژوهشی
BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES
Zhen-Yu Xiu
xyz198202@163.com
1
Bin Pang
pangbin1205@163.com
2
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P.R.China
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbases can be used to characterize CP mappings and CC mappings between $M$-fuzzifying convex spaces.
http://ijfs.usb.ac.ir/article_3760_b615cc331d0d71e72929cb7e6d511ca6.pdf
$M$-fuzzifying convex structure
Base axiom
Subbase axiom
CP mapping
CC mapping
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
89
108
10.22111/ijfs.2018.3761
3761
مقاله پژوهشی
ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
Hui Li
ximuhuizi@163.com
1
Bo Zhang
bzhang3@masonlive.gmu.edu
2
Jin Peng
pengjin01@tsinghua.org.cn)
3
School of Information and Engineering, Wuchang University of Technology, Wuhan, 430223, China
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China
Institute of Uncertain Systems, Huanggang Normal University, Huang- gang, 438000, China
Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain variable.Different from that in a deterministic graph, it is more meaningful to investigate the uncertain measure that an uncertain graph is $k$-edge matching (i.e., the matching number is greater than or equal to $k$).We first study the properties of the matching number of an uncertain graph, and then give a fundamental formula for calculating the uncertain measure. We further prove that the fundamental formula can be transformedinto a simplified form. What is more, a polynomial time algorithm to numerically calculate the uncertain measure is derived from the simplified form.Finally, some numerical examples are illustrated to show the application and efficiency of the algorithm.
http://ijfs.usb.ac.ir/article_3761_843af24ca521b1d9f207a6a79751dcc4.pdf
Uncertainty theory
Uncertain measure
Maximum matching
Matching number
Uncertain graph
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
109
131
10.22111/ijfs.2018.3762
3762
مقاله پژوهشی
RESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION EQUATION CONSTRAINTS USING GENETIC ALGORITHM
Hassan Dana Mazraeh
1
Ali Abbasi Molai
a abbasimolai@du.ac.ir
2
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses the structure of the feasible domain of the problems and lower and upper bound of the feasible solution set to choose the initial population. The GA employs two different crossover operations: 1- N-points crossover and 2- Arithmetic crossover. We run the GA with two crossover operations for some test problems and compare their results and performance to each other. Also, their results are compared with the results of other authors' works.
http://ijfs.usb.ac.ir/article_3762_2154eb21dc0b0710dca0c101b1419ad8.pdf
Bipolar fuzzy relation equations
Max-min composition
Nonlinear optimization
Genetic Algorithm
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
133
142
10.22111/ijfs.2018.3764
3764
مقاله پژوهشی
SOME PROPERTIES OF UNCERTAIN INTEGRAL
Cuilian You
yycclian@163.com
1
Na Xiang
xiangnahbu@126.com
2
College of Mathematics and Information Science, Hebei University, Baoding 071002, China
College of Mathematics and Information Science, Hebei University, Baoding 071002, China
Uncertainty theory is a mathematical methodology for dealing withnon-determinate phenomena in nature. As we all know, uncertainprocess and uncertain integral are important contents of uncertaintytheory, so it is necessary to have deep research. This paperpresents the definition and discusses some properties of strongcomonotonic uncertain process. Besides, some useful formulas ofuncertain integral such as nonnegativity, monotonicity, intermediateresults are studied.
http://ijfs.usb.ac.ir/article_3764_a8b8715f896bcb2aeaba59a2dcf9c552.pdf
Uncertain variable
Uncertain process
Uncertain integral
Monotonicity
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
143
163
10.22111/ijfs.2018.3765
3765
مقاله پژوهشی
POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS
J. Mockor
1
University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theory there exists a strong relation, which can be represented as a homomorphism. Analogical results are also proved for new powerset theories of extensional fuzzy sets.
http://ijfs.usb.ac.ir/article_3765_d621b021f19eac714bf7d16a69c7da75.pdf
Extensional fuzzy sets
Powerset operators
Monads in categories
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-29
15
2
165
182
10.22111/ijfs.2018.3766
3766
مقاله پژوهشی
GENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM
S. P. Tiwari
1
I. Perfilieva
irina.perﬁlieva@osu.cz
2
A. P. Singh
3
Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad-826004, Jharkhand, India
University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad-826004, Jharkhand, India
The aim of the present work is to study the $F$-transform over a generalized residuated lattice. We discuss the properties that are common with the $F$-transform over a residuated lattice. We show that the $F^{uparrow}$-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.
http://ijfs.usb.ac.ir/article_3766_2e1aae518019f70a853a251e8e71e464.pdf
Generalized residuated lattice
Fuzzy partition
Direct $F$-transform
Inverse $F$-transform
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2018-04-01
15
2
185
194
10.22111/ijfs.2018.3767
3767
مقاله پژوهشی
Persian-translation Vol.15, No.2 April 2018
http://ijfs.usb.ac.ir/article_3767_5165ec122a668e255726ff4271fa0e61.pdf