University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
01
Cover vol. 15, no. 2, April 2018
0
EN
10.22111/ijfs.2018.3756
http://ijfs.usb.ac.ir/article_3756.html
http://ijfs.usb.ac.ir/article_3756_a827a8e2afdf2fe8eb4bb7c5a5bd0217.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS
1
21
EN
D. R.
Jardon
Academia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa s/n, Col. Lomas de Zaragoza 09620, Ciudad de Mexico ,
Mexico
M.
Sanchis
Institut de Matematiques i Aplicacions de Castello (IMAC), Universitat
Jaume I, Campus Riu Sec, 12071-Castello, Spain
10.22111/ijfs.2018.3753
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.
Fuzzy-number,Fuzzy analysis,Function space,Pointwise convergence,Dual map,Evaluation map,Fr'echet space,Grothendieck's theorem,Cardinal function
http://ijfs.usb.ac.ir/article_3753.html
http://ijfs.usb.ac.ir/article_3753_2b8058838050761d26d4f9d8d6a43cfd.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS
23
40
EN
Chong
Shen
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
shenchong0520@163.com
Fu-Gui
Shi
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
fuguishi@bit.edc.cn
10.22111/ijfs.2018.3754
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.
$L$-convex system,Scott-hull space,Induced $L$-convex structure,Quotient system
http://ijfs.usb.ac.ir/article_3754.html
http://ijfs.usb.ac.ir/article_3754_de43053a691df5ee38c5df21e874a1b9.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
BASES AND CIRCUITS OF FUZZIFYING MATROIDS
41
52
EN
Shao-Jun
Yang
The Fujian Provincial Key Laboratory of Network Security and
Cryptology, School of Mathematics and Computer Science, Fujian Normal University,
Fuzhou 350007, P.R. China
shaojunyang@outlook.com
Fu-Gui
Shi
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
fuguishi@bit.edc.cn
10.22111/ijfs.2018.3755
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.
Fuzzifying matroid,Fuzzifying base-map,Fuzzifying basis axiom,Fuzzifying circuit-map,Fuzzifying circuit axiom
http://ijfs.usb.ac.ir/article_3755.html
http://ijfs.usb.ac.ir/article_3755_3eb0a96d3cd8eee16ffe525dc4b0db85.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
QUANTALE-VALUED SUP-ALGEBRAS
53
73
EN
Radek
Slesinger
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic
10.22111/ijfs.2018.3759
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.
$Q$-order,$Q$-sup-lattice,$Q$-ordered algebra,$Q$-sup-algebra,Quotient,Subalgebra
http://ijfs.usb.ac.ir/article_3759.html
http://ijfs.usb.ac.ir/article_3759_15a2e675b28ad7601164f7c1adefa982.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES
75
87
EN
Zhen-Yu
Xiu
College of Applied Mathematics, Chengdu University of Information
Technology, Chengdu 610225, P.R.China
xyz198202@163.com
Bin
Pang
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
pangbin1205@163.com
10.22111/ijfs.2018.3760
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.
$M$-fuzzifying convex structure,Base axiom,Subbase axiom,CP mapping,CC mapping
http://ijfs.usb.ac.ir/article_3760.html
http://ijfs.usb.ac.ir/article_3760_b615cc331d0d71e72929cb7e6d511ca6.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
89
108
EN
Hui
Li
School of Information and Engineering, Wuchang University of Technology,
Wuhan, 430223, China
ximuhuizi@163.com
Bo
Zhang
School of Statistics and Mathematics, Zhongnan University of Economics
and Law, Wuhan, 430073, China
bzhang3@masonlive.gmu.edu
Jin
Peng
Institute of Uncertain Systems, Huanggang Normal University, Huang-
gang, 438000, China
pengjin01@tsinghua.org.cn)
10.22111/ijfs.2018.3761
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.
Uncertainty theory,Uncertain measure,Maximum matching,Matching number,Uncertain graph
http://ijfs.usb.ac.ir/article_3761.html
http://ijfs.usb.ac.ir/article_3761_843af24ca521b1d9f207a6a79751dcc4.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
RESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION EQUATION CONSTRAINTS USING GENETIC ALGORITHM
109
131
EN
Hassan Dana
Mazraeh
School of Mathematics and Computer Sciences, Damghan
University, Damghan, Iran
Ali Abbasi
Molai
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
a abbasimolai@du.ac.ir
10.22111/ijfs.2018.3762
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.
Bipolar fuzzy relation equations,Max-min composition,Nonlinear optimization,Genetic algorithm
http://ijfs.usb.ac.ir/article_3762.html
http://ijfs.usb.ac.ir/article_3762_2154eb21dc0b0710dca0c101b1419ad8.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
SOME PROPERTIES OF UNCERTAIN INTEGRAL
133
142
EN
Cuilian
You
College of Mathematics and Information Science, Hebei University,
Baoding 071002, China
yycclian@163.com
Na
Xiang
College of Mathematics and Information Science, Hebei University, Baoding 071002, China
xiangnahbu@126.com
10.22111/ijfs.2018.3764
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.
Uncertain variable,Uncertain process,Uncertain integral,Monotonicity
http://ijfs.usb.ac.ir/article_3764.html
http://ijfs.usb.ac.ir/article_3764_a8b8715f896bcb2aeaba59a2dcf9c552.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS
143
163
EN
J.
Mockor
University of Ostrava, Institute for Research and Applications of Fuzzy
Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
10.22111/ijfs.2018.3765
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.
Extensional fuzzy sets,Powerset operators,Monads in categories
http://ijfs.usb.ac.ir/article_3765.html
http://ijfs.usb.ac.ir/article_3765_d621b021f19eac714bf7d16a69c7da75.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
29
GENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM
165
182
EN
S. P.
Tiwari
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
I.
Perfilieva
University of Ostrava, Institute for Research and Applications of
Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
irina.perﬁlieva@osu.cz
A. P.
Singh
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
10.22111/ijfs.2018.3766
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.
Generalized residuated lattice,Fuzzy partition,Direct $F$-transform,Inverse $F$-transform
http://ijfs.usb.ac.ir/article_3766.html
http://ijfs.usb.ac.ir/article_3766_2e1aae518019f70a853a251e8e71e464.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
15
2
2018
04
01
Persian-translation Vol.15, No.2 April 2018
185
194
EN
10.22111/ijfs.2018.3767
http://ijfs.usb.ac.ir/article_3767.html
http://ijfs.usb.ac.ir/article_3767_5165ec122a668e255726ff4271fa0e61.pdf