University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180401Cover vol. 15, no. 2, April 20180375610.22111/ijfs.2018.3756ENJournal Article20180407https://ijfs.usb.ac.ir/article_3756_a827a8e2afdf2fe8eb4bb7c5a5bd0217.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS121375310.22111/ijfs.2018.3753END. R.JardonAcademia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa s/n, Col. Lomas de Zaragoza 09620, Ciudad de Mexico ,
MexicoM.SanchisInstitut de Matematiques i Aplicacions de Castello (IMAC), Universitat
Jaume I, Campus Riu Sec, 12071-Castello, SpainJournal Article20160807We study the space of all continuous fuzzy-valued functions from a space $X$ into the space of fuzzy numbers $(\mathbb{E}\sp{1},d\sb{\infty})$ 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.https://ijfs.usb.ac.ir/article_3753_2b8058838050761d26d4f9d8d6a43cfd.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS2340375410.22111/ijfs.2018.3754ENChongShenSchool of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. ChinaFu-GuiShiSchool of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. ChinaJournal Article20161107The 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.https://ijfs.usb.ac.ir/article_3754_de43053a691df5ee38c5df21e874a1b9.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429BASES AND CIRCUITS OF FUZZIFYING MATROIDS4152375510.22111/ijfs.2018.3755ENShao-JunYangThe Fujian Provincial Key Laboratory of Network Security and
Cryptology, School of Mathematics and Computer Science, Fujian Normal University,
Fuzhou 350007, P.R. ChinaFu-GuiShiSchool 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. ChinaJournal Article20161007In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievable<br />example is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for the<br />basis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroid<br />is equivalent to a mapping which satisfies the basis axioms or circuit axioms.https://ijfs.usb.ac.ir/article_3755_3eb0a96d3cd8eee16ffe525dc4b0db85.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429QUANTALE-VALUED SUP-ALGEBRAS5373375910.22111/ijfs.2018.3759ENRadekSlesingerDepartment of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech RepublicJournal Article20160908Based 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.https://ijfs.usb.ac.ir/article_3759_15a2e675b28ad7601164f7c1adefa982.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES7587376010.22111/ijfs.2018.3760ENZhen-YuXiuCollege of Applied Mathematics, Chengdu University of Information
Technology, Chengdu 610225, P.R.ChinaBinPangSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.ChinaJournal Article20161008Based 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.https://ijfs.usb.ac.ir/article_3760_b615cc331d0d71e72929cb7e6d511ca6.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH89108376110.22111/ijfs.2018.3761ENHuiLiSchool of Information and Engineering, Wuchang University of Technology,
Wuhan, 430223, ChinaBoZhangSchool of Statistics and Mathematics, Zhongnan University of Economics
and Law, Wuhan, 430073, ChinaJinPengInstitute of Uncertain Systems, Huanggang Normal University, Huang-
gang, 438000, ChinaJournal Article20161108Uncertain graphs are employed to describe graph models with indeterministic<br />information that produced by human beings. This paper aims to study the<br />maximum matching problem in uncertain graphs.<br />The number of edges of a maximum matching in a graph is called matching number<br />of the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain variable.<br />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 $k$).<br />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 transformed<br />into a simplified form. What is more, a polynomial time algorithm to numerically calculate the uncertain measure is derived from the simplified form.<br />Finally, some numerical examples are illustrated to show the application and efficiency of the algorithm.https://ijfs.usb.ac.ir/article_3761_843af24ca521b1d9f207a6a79751dcc4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429RESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION EQUATION CONSTRAINTS USING GENETIC ALGORITHM109131376210.22111/ijfs.2018.3762ENHassan DanaMazraehSchool of Mathematics and Computer Sciences, Damghan
University, Damghan, IranAli AbbasiMolaiSchool of Mathematics and Computer Sciences, Damghan University, Damghan, IranJournal Article20161208This 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.https://ijfs.usb.ac.ir/article_3762_2154eb21dc0b0710dca0c101b1419ad8.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429SOME PROPERTIES OF UNCERTAIN INTEGRAL133142376410.22111/ijfs.2018.3764ENCuilianYouCollege of Mathematics and Information Science, Hebei University,
Baoding 071002, ChinaNaXiangCollege of Mathematics and Information Science, Hebei University, Baoding 071002, ChinaJournal Article20161208Uncertainty theory is a mathematical methodology for dealing with<br />non-determinate phenomena in nature. As we all know, uncertain<br />process and uncertain integral are important contents of uncertainty<br />theory, so it is necessary to have deep research. This paper<br />presents the definition and discusses some properties of strong<br />comonotonic uncertain process. Besides, some useful formulas of<br />uncertain integral such as nonnegativity, monotonicity, intermediate<br />results are studied.https://ijfs.usb.ac.ir/article_3764_a8b8715f896bcb2aeaba59a2dcf9c552.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS143163376510.22111/ijfs.2018.3765ENJ.MockorUniversity of Ostrava, Institute for Research and Applications of Fuzzy
Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech RepublicJournal Article20161208Powerset 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.https://ijfs.usb.ac.ir/article_3765_d621b021f19eac714bf7d16a69c7da75.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429GENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM165182376610.22111/ijfs.2018.3766ENS. P.TiwariDepartment of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, IndiaI.PerfilievaUniversity of Ostrava, Institute for Research and Applications of
Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech RepublicA. P.SinghDepartment of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, IndiaJournal Article20151208The 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.https://ijfs.usb.ac.ir/article_3766_2e1aae518019f70a853a251e8e71e464.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180401Persian-translation Vol.15, No.2 April 2018185194376710.22111/ijfs.2018.3767ENJournal Article20180408https://ijfs.usb.ac.ir/article_3767_5165ec122a668e255726ff4271fa0e61.pdf