University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601cover IJFS-Vol 18-No 3-June 2021609010.22111/ijfs.2021.6090ENJournal Article20210412https://ijfs.usb.ac.ir/article_6090_d47d0ec438c0fea76656b7cd35bcd0bf.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Fuzzy logic and enriched categories111607710.22111/ijfs.2021.6077ENS.DautovicMathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, SerbiaM.ZekicMathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, SerbiaJournal Article20210412We consider a category C enriched over the segment [0,1] whose hom-objects are real numbers from [0,1]. For a suitably defined function $\hat{v}$ assigning to each formula $\varphi$ some object of $\C$, the hom-object $\C(\hat{v} (\varphi),\hat{v}(\psi))$ represents the degree of derivability of $\psi$ from $\varphi$. We reformulate completeness result for intuitionistic propositional logic, as well as H\' ajek's completeness results concerning the product, G\" odel and \L ukasiewicz fuzzy logic in the context of enriched category theory.https://ijfs.usb.ac.ir/article_6077_9fa789612cdfd958226861183fbceac4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-0654183202106012-set-based extended functions1326607810.22111/ijfs.2021.6078ENR.MesiarDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology,
Radlinskeho 11, 810 05 Bratislava, SlovakiaA.KolesarovaInstitute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak
University of Technology, Radlinskeho 9, 812 37 Bratislava, SlovakiaS.BorkotokeyDepartment of Mathematics, Dibrugarh University, Dibrugarh - 786004, IndiaJournal Article20210412We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular, 2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.https://ijfs.usb.ac.ir/article_6078_a34007ed93611143cb6efbd277e9a6cd.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Using a fuzzy expert system as a decision support system to decrease time consumption in the UAST development process: A case study2738607910.22111/ijfs.2021.6079ENA.Alinezhad EsboeiUniversity of Applied Science and Technology, Tehran, IranM. H.Karimi GavareshkiDepartment of Management and Industrial Engineering, Malek Ashtar University of Technology, Tehran, IranJournal Article20210412Always the decision of the government to the private sector is faced with the challenges and high level of importance, because these decisions should be taken at the meeting of standards and functional requirements to overcome investors' interests. These decisions include education, and due to the governance nature of education and the governments' strategies in this area, the private sectors who act in it, have been affected by the consequences of different decisions. \\<br />In this paper, our motivation is to propose a system to decide on how to develop applied academic educations at the Applied Science<br />Education Centers (ASEC's) which are supervised by the University of Applied Science and Technology (UAST) in Iran. The method used is the<br />Fuzzy Inference System (FIS) to reach this goal. The model performed in this study consists of a two-part FIS for two purposes straight ahead.<br />The first concerns the quantitative development of higher applied education, including the number of Course Request (CR) for each ASEC with 4 inputs and 242 rules. The latter, is related to the qualitative development of higher applied education, including the assessment of the capability and competence of each ASEC for specific CR with the course and student admission background, specialty, committee's and council’s opinion, and frequency of course in city or province with 9 inputs, 350 rules, and an output. Each section has its inputs and rules that are determined and used by experts in this domain. \\<br />Our results show that using this method, provides some cost and time savings. This model analyzes in less than 2 minutes, while in practice it could be gain within 1650 person /hours work in different committees that all of them have their costs. Also, results are very close to reality with the advantage that there is no way to apply personal preferences, which largely meets the needs of research.https://ijfs.usb.ac.ir/article_6079_a6b772899ce3993c1adc8c6b987a7e7a.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601A credibility approach on fuzzy slacks based measure (SBM) DEA model3949608010.22111/ijfs.2021.6080END.MahlaDepartment of Mathematics, Birla Institute of Technology and Science, Pilani, IndiaS.AgarwalDepartment of Mathematics, Birla Institute of Technology and Science, Pilani, IndiaJournal Article20210412Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal with many real-life problems, mostly in nonprofit organizations. The slacks-based measure (SBM) model is one of the DEA model used to assess the relative efficiencies of decision-making units (DMUs). The SBM DEA model directly used input slacks and output slacks to determine the relative efficiency of DMUs. In order to deal with qualitative or uncertain data, a fuzzy SBM DEA model is used to assess the performance of DMUs in this study. The credibility measure approach, transform the fuzzy SBM DEA model into a crisp linear programming model at different credibility levels is used. The results came from the fuzzy DEA model are more rational to the real-world situation than the conventional DEA model. In the end, the data of Indian oil refineries is collected, and the efficiency behavior of the companies obtained by applying the proposed model for its numerical illustration.https://ijfs.usb.ac.ir/article_6080_e93c2f6b1f780c670de2b478eeae076b.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601On the fuzzy solutions of time-fractional problems5166608110.22111/ijfs.2021.6081ENM.GhaffariDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranT.AllahviranlooDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranS.AbbasbandyDepartment of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranM.AzhiniDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranJournal Article20210412The main purpose of this paper is to obtain an analytical solution for the time-fractional fuzzy equation. To do this, the time-fractional equation is transformed into an algebraic equation using the fuzzy Laplace and Fourier transforms. The fractional derivatives are described in the Caputo gH-differentiability. In addition, to demonstrate the efficiency of the method some various examples are solved.https://ijfs.usb.ac.ir/article_6081_fa6b3ba80a9d1e6f84b485dccb947da2.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601C-continuous fuzzy posets6780608210.22111/ijfs.2021.6082ENY. J.ZhangSchool of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, P.R. ChinaB.ZhaoSchool of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, P.R. ChinaJournal Article20210412In this paper, we develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral quantale.<br />The main results are: (1) The set of all C-compact elements of a complete<br />Q-ordered set is irreducible complete; (2) The Scott Q-cotopology<br /> of a Q-ordered set under the fuzzy inclusion order is C-continuous, even<br />C-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.https://ijfs.usb.ac.ir/article_6082_ca19ba3eaf7a2ec028b5b3aafb3d7316.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Construction methods for triangular norms and triangular conorms on appropriate bounded lattices8198608310.22111/ijfs.2021.6083ENE.AsiciDepartment of Software Engineering, Faculty of Technology, Karadeniz Technical University, 61830 Trabzon, TurkeyJournal Article20210412In this study, new methods to construct triangular norms and triangular conorms on appropriate bounded lattices are introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and some other approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on appropriate bounded lattices. And some illustrative examples are given.https://ijfs.usb.ac.ir/article_6083_0947d2e3e598ccd65f53ad2fd50896a4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Jensen's inequalities for pseudo-integrals99109608410.22111/ijfs.2021.6084END.ZhangCollege of Mathematics, Changchun Normal University, Changchun 130032, Jilin, PR ChinaE.PapSingidunum University, 11000 Belgrade, SerbiaJournal Article20210412In this paper, we introduce a general<br />$(\oplus,\otimes)$-convex function based on semirings $([a,b],<br />\oplus, \otimes)$ with pseudo-addition $\oplus$ and<br />pseudo-multiplication $\otimes.$ The generalization of the finite<br />Jensen's inequality, as well as pseudo-integral with respect to<br />$(\oplus,\otimes)$-convex functions, is obtained.<br /> This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and \v{S}trboja \cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], \sup, \otimes)$<br />with respect to nondecreasing functions and present corresponding<br />results for generalized fuzzy integrals. <br /> https://ijfs.usb.ac.ir/article_6084_fc82d15ffde749f2e3f40b3418123c62.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601New results on the migrativity properties for overlap (grouping) functions and uninorms111128608510.22111/ijfs.2021.6085ENW. H.LiSchool of Mathematics and Statistics, Jiangxi Normal University, 330022 Nanchang, PR ChinaF.QinSchool of Mathematics and Statistics, Jiangxi Normal University, 330022 Nanchang, PR ChinaJournal Article20210412Functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory. That the migrativity equation as a kind of restricted general associative equation have been proven to be useful in a wide range of fields like decision making, aggregation of information, image processing and so on. In the literature, the already existing results concerning the migrativity equation between overlap (grouping) functions and uninorms are based on the assumption that uninorms belong to one of the most studied classes. In this study we will explore it involving uninorms in a more general setting. To be specific, we investigate the migrativity properties between overlap (grouping) functions and uninorms in the case when uninorms have continuous underlying operators. We will show along the paper that many new solutions to the equation are characterized from this new point of view.https://ijfs.usb.ac.ir/article_6085_e18e2197be3037d9641fb7e032c53cb6.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Milstein method for solving fuzzy differential equation129141608610.22111/ijfs.2021.6086ENL. Y.JiCollege of Mathematics and Information Science, Hebei
University, Baoding 071002, ChinaC. L.YouCollege of Mathematics and Information Science, Hebei
University, Baoding 071002, ChinaJournal Article20210412To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analyzed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.https://ijfs.usb.ac.ir/article_6086_e90293a7ef158a6db557a804297bb205.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Hyers-Ulam-Rassias stability of quaternion multidimensional fuzzy nonlinear difference equations with impulses143160608710.22111/ijfs.2021.6087ENZ.LiDepartment of Mathematics, Yunnan University, Kunming, Yunnan, ChinaC.WangDepartment of Mathematics, Yunnan University, Kunming, Yunnan, ChinaR. P.AgarwalDepartment of Mathematics, Texas A\&M University-Kingsville, TX, USAR.SakthivelDepartment of Applied Mathematics, Bharathiar University, Coimbatore, IndiaJournal Article20210412In this paper, we consider the Hyers-Ulam-Rassias stability of the<br />impulsive fuzzy nonlinear difference equations in the multidimensional fuzzy quaternion space.<br />Some sufficient conditions of the Hyers-Ulam-Rassias stability are established for the quaternion multidimensional fuzzy nonlinear difference equations with impulses and several examples are demonstrated to show the feasibility of our obtained results.https://ijfs.usb.ac.ir/article_6087_a579c5b51068f724c02ceacb69470f6e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601A bilateral fuzzy support vector machine hybridizing the Gaussian mixture model161177608810.22111/ijfs.2021.6088ENM.MohammadiDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranM.SarmadDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20210412The fuzzy support vector machine is one of the most exceptional methods to deal with uncertainty in the classification problem. The membership function is a proper way to model uncertainty. The goal of the membership function is to distinguish the different points in terms of their importance. The ordinary design of the membership function relies on the distance of the observations to the class center. However, the class center is affected by the presence of outliers. To prevent this effect, we utilized an unsupervised learning method called the Gaussian mixture model in the structure of the membership function. The proposed membership function is presented in two different categories distance-based and Bayes-based. Unlike the classical membership function, the contribution of outliers in the training phase decreased by diminishing their degree of importance. Hybridizing the classic fuzzy support vector machine classifier with the Gaussian mixture model will enhance the classification accuracy and also will prevent overfitting problems. The superiority of the proposed methods assessed by the synthetic and benchmarking dataset. The statistical significance is assessed by using the non-parametric Friedman and post-hoc Nemenyi tests.https://ijfs.usb.ac.ir/article_6088_81cff20e23477cda672692983dc5f7de.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601Improved fuzzy clustering algorithm using adaptive particle swarm optimization for nonlinear system modeling and identification179196608910.22111/ijfs.2021.6089ENL.HoucineDepartment of GTER ISET Tataouine. Laboratory for Engineering of Industrial Systems and Renewable
Energies (LISIER),University of Tunisia, ENSIT, Tunisia National Higher Engineering School of Tunisia (ENSIT), BP 56, 1008, TunisiaM.BouzbidaLaboratory for Engineering of Industrial Systems and Renewable Energies (LISIER), University of Tunis, ENSIT, TunisiaA.ChaariLaboratory for Engineering of Industrial Systems and Renewable Energies (LISIER), University of Tunis, ENSIT, TunisiaJournal Article20210412In this paper, an improved Type2-PCM clustering algorithm based on improved adaptive particle swarm optimization called Type2-PCM-IAPSO is proposed. Firstly, a new clustering algorithm called Type2-PCM is proposed. The Type2-PCM algorithm can solve the problems encountered by fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm (G-K), possibilistic c-means algorithm (PCM) and NPCM (sensitivity to noise or aberrant points and local minimal sensitivity). . . etc. Secondly, we combined our Type2-PCM algorithm with the improved adaptive particle swarm optimization algorithm (IAPSO) to ensure proper convergence to a local minimum of the objective function. The effectiveness of the two proposed algorithms Type2-PCM and Type2-PCM-IAPSO was tested on a system described by a different equation, Box-Jenkins gas furnace, dryer system and the convection system. The validation tests used showed good performance of these algorithms. However, their average square error test (MSE) shows a better behaviour of the Type2-PCM-IAPSO algorithm compared to the FCM, G-K, PCM, FCM-PSO, Type2-PCM-PSO, RKPFCM and RKPFCM-PSO algorithms.https://ijfs.usb.ac.ir/article_6089_83c6685980383525c2cfd82103059683.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418320210601translations IJFS-Vol 18-No 3-June 2021199211609110.22111/ijfs.2021.6091ENJournal Article20210412https://ijfs.usb.ac.ir/article_6091_35452fcdc751a41853312271aa86863e.pdf