University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801cover merge 17-4 August 2020540210.22111/ijfs.2020.5402ENJournal Article20200526https://ijfs.usb.ac.ir/article_5402_98dd2c7ad725dd425a4bbe985512e2b2.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Product operation and joint interval valued observable16540110.22111/ijfs.2020.5401ENK.CunderlkovaMathematical Institute, Slovak Academy of Sciences, Stefanikova 49, 814 73 Bratislava, SlovakiaJournal Article20200526The aim of this paper is to define the product<br />operation on a family of interval valued events and the notion of<br />joint interval valued observable. We show the connection between<br />product operations for interval valued events and intuitionistic<br />fuzzy events, too. We display the relation between joint interval<br />valued observable and joint intuitionistic fuzzy observable. We<br />define a function of several interval valued observables with help<br />of a Borel function and a joint interval valued observable, too.https://ijfs.usb.ac.ir/article_5401_f43f84c98f57307391b63e859f6d9862.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Fuzzy particle swarm optimization with nearest-better neighborhood for multimodal optimization724540310.22111/ijfs.2020.5403ENM. B.DowlatshahiDepartment of Computer Engineering, Faculty of Engineering, Lorestan University, Khoramabad, Iran.V.DerhamiDepartment of Computer Engineering, Faculty of Engineering, Yazd University, Yazd, Iran.H.Nezamabadi-pourDepartment of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20200526In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing performance. Hence, this paper has two main contributions. First, two novel parameter-free neighborhood structures named Topological Nearest-Better (TNB) neighborhood and Distance-based Nearest-Better (DNB) neighborhood are proposed in the topological space and decision space, respectively. Second, two proposed neighborhoods are combined with Fuzzy PSO (FPSO) and two novel niching algorithms, called TNB-FPSO and DNB-FPSO, are proposed for solving multimodal optimization problems. It should be noted that we use a zero-order fuzzy system to balance between exploration and exploitation in the proposed algorithms. To evaluate the performance of proposed algorithms, we performed a detailed empirical evaluation on the several standard multimodal benchmark functions. Our results show that DNB-FPSO statistically outperforms the other compared multimodal optimization algorithms.https://ijfs.usb.ac.ir/article_5403_d00a4d5c65b37f42df87e8c29b9a001e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Solving matrix games with hesitant fuzzy pay-offs2540540410.22111/ijfs.2020.5404ENM. R.SeikhDepartment of Mathematics, Kazi Nazrul University, Asansol-713 340, IndiaS.KarmakarDepartment of Mathematics, Kazi Nazrul University, Asansol-713 340, IndiaM.XiaSchool of Economics and Management, Beijing University, Beijing, ChinaJournal Article20200526The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems into two non-linear multi-objective programming problems with triangular fuzzy numbers (TFNs). Finally, the Lexicographic method is used to solve these two multi-objective programming problems. A market share problem is considered to show the validity and applicability of the proposed methodology.https://ijfs.usb.ac.ir/article_5404_818b1208ac6da1403947ed88eef552e3.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801General definitions for the union and intersection of ordered fuzzy multisets4154540510.22111/ijfs.2020.5405ENÁ.RiesgoDepartment of Statistics and O. R., University of Oviedo, SpainP.AlonsoDepartment of Mathematics, University of Oviedo, SpainI.DíazDepartment of Computer Science, University of Oviedo, SpainS.MontesDepartment of Statistics and O. R., University of Oviedo, SpainJournal Article20200526Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membership, the key difference being that the fuzzy multisets allow for repeated membership values whereas the hesitant fuzzy sets do not. But in neither case are these collections of values ordered, as they are simply represented through multisets or sets. In this paper, we study ordered fuzzy multisets, where the membership value can be an ordered $n$-tuple of values, thus accounting for both order and repetition. We present some basic definitions and results and explore the relation between these ordered fuzzy multisets and the fuzzy multisets and hesitant fuzzy sets.https://ijfs.usb.ac.ir/article_5405_72f81348e828cf69f89e9e6f64028fbf.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Multi-criteria IT personnel selection on intuitionistic fuzzy information measures and ARAS methodology5568540610.22111/ijfs.2020.5406ENA.Raj MishraDepartment of Mathematics, Govt. College Jaitwara, Satna, M P, IndiaG.SisodiaDepartment of Computer Science \& Engineering, ITM University, Gwalior-474001, MP, IndiaK.Raj PardasaniDepartment of Mathematics, Bioinformatics and Computer Applications, MANIT, Bhopal-462051, M P, IndiaK.SharmaDepartment of Computer Science \& Engineering, ITM University, Gwalior-474001, MP, IndiaJournal Article20200526Global challenge and the speedy growth of information technologies compel organizations to constantly change their ways. At the present time, associations need IT personnel who create a difference by creative thoughts and who preserve with the rapid amendments. Since the evaluation of IT personnel selection (ITPS) consists of different alternatives and criteria, therefore, IT personnel selection could be regarded as a multi-criteria decision making (MCDM) problem. The doctrine of intuitionistic fuzzy sets (IFSs) is an effective tool to elucidate the uncertain information in an MCDM problem. The main objective of the paper is to choose the best IT personnel candidate by integrating intuitionistic fuzzy Additive Ratio Assessment (IF-ARAS) method with divergence measure, improved score function and IF-aggregation operators. In the developed methodology, the weights of criteria and decision experts (DEs) are computed based on proposed IF-divergence measure method intuitionistic fuzzy preference evaluation method, respectively. Next, the decision experts’ judgments are aggregated of the proposed method to evade the loss of data. Finally, the proposed IF-ARAS method is implemented to solve the IT-personnel selection (ITPS) problem to indicate the applicability of the presented approach. In addition, a comparative analysis is provided to discuss the obtained results for validating the developed methodology. The analysis illustrates that the IF-ARAS method is effective and well consistent with the existing ones.https://ijfs.usb.ac.ir/article_5406_773e304765eced9372865246c596bf2a.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Uncertainty analysis of hierarchical granular structures for multi-granulation typical hesitant fuzzy approximation space6984540710.22111/ijfs.2020.5407ENH. Y.ZhangSchool of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaan'xi Province, P.R. ChinaS. Y.YangSchool of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaan'xi Province, P.R. ChinaJournal Article20200526Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measures in typical hesitant fuzzy backgrounds. Firstly, we propose the parameterized scalar cardinalities of typical hesitant fuzzy elements, typical hesitant fuzzy sets and typical hesitant fuzzy relations based on a more reasonable partial orders with a disjunctive semantic meaning, respectively, where the parameters represent the decision makers' risk preferences.<br /> Secondly, we present four ordered relations for typical hesitant fuzzy space and four uncertainty measures to characterize the ambiguity in typical hesitant fuzzy approximation space and discuss their relationships. Thirdly, the hierarchical structures of a multi-granulation typical hesitant fuzzy space are analyzed by various multi-granulation typical hesitant fuzzy knowledge bases. In addition, we construct the framework of multi-granulation typical hesitant fuzzy rough sets in terms of optimistic and pessimistic attitudes. Finally, we study the uncertainty<br /> measures for the multi-granulation typical hesitant fuzzy approximation space based on the maximal and minimal knowledge bases, respectively.https://ijfs.usb.ac.ir/article_5407_533901062f340cdf6ae70f53c9bf36e7.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Refining membership degrees obtained from fuzzy C-means by re-fuzzification85104540810.22111/ijfs.2020.5408ENM.JavadianDepartment of Computer Engineering, Faculty of Information Technology, Kermanshah University of Technology, Kermanshah, IranR.VaziriIslamic Azad University Central Tehran Branch, Tehran, IranS.Haghzad KlidbaryDepartment of Computer Engineering, Faculty of Engineering, University of Zanjan, Zanjan, IranA.MalekzadehDepartment of Computer Science and Statistics, Faculty of Mathematics, K.N. Toosi University of Technology, Tehran, IranJournal Article20200526Fuzzy C-mean (FCM) is the most well-known and widely-used fuzzy clustering algorithm. However, one of the weaknesses of the FCM is the way it assigns membership degrees to data which is based on the distance to the cluster centers. Unfortunately, the membership degrees are determined without considering the shape and density of the clusters. In this paper, we propose an algorithm which takes the FCM clustering results and re-fuzzifies them by taking into account the shape and density of the clusters. The algorithm first defuzzifies the FCM clustering results. Then the crisp result is fuzzified again. Re-fuzzification in our algorithm has some advantages. The main advantage is that the fuzzy membership degrees of data points are obtained based on the shape and density of clusters. Adding the ability to eliminate noise and outlier data is the other advantage of our algorithm. Finally, our proposed re-fuzzification algorithm can slightly improve the FCM clustering quality, because the data points change their clusters according to similarity to the shape and density of their respective clusters. These advantages are supported by simulations on real and synthetic datasets.https://ijfs.usb.ac.ir/article_5408_7b1b6695ca9181bf2c0a10bec6c836af.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801A robust least squares fuzzy regression model based on kernel function105119540910.22111/ijfs.2020.5409ENA. H.KhammarDepartment of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, IranM.ArefiDepartment of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, IranM. G.AkbariDepartment of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, IranJournal Article20200526In this paper, a new approach is presented to fit a<br />robust fuzzy regression model based on some fuzzy quantities. In<br />this approach, we first introduce a new distance between two fuzzy<br />numbers using the kernel function, and then, based on the least<br />squares method, the parameters of fuzzy regression model is<br />estimated. The proposed approach has a suitable performance to<br />present the robust fuzzy model in the presence of different types<br />of outliers. Using some simulated data sets and some real data<br />sets, the application of the proposed approach in modeling some<br />characteristics with outliers, is studied.https://ijfs.usb.ac.ir/article_5409_9f42718415f1e2c77d90e77b0b65b9f7.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Alternative approaches to obtain t-norms and t-conorms on bounded lattices121138541010.22111/ijfs.2020.5410ENE.AsiciDepartment of Software Engineering, Faculty of Technology, Karadeniz Technical University,
61830 Trabzon, TurkeyR.MesiarDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinskeho, 11, 81005 Bratislava, SlovakiaJournal Article20200526Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for the clarity. Finally, we show that our construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on an arbitrary bounded lattice, respectively.https://ijfs.usb.ac.ir/article_5410_70ae4886f8ae63e19b1d2a4ec3717c74.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Fuzzy convergence structures in the framework of L-convex spaces139150541110.22111/ijfs.2020.5411ENZ. Y.XiuCollege of Applied Mathematics, Chengdu University of Information Technology, Chengdu, ChinaQ. H.LiSchool of Mathematics and Information Sciences, Yantai University, Yantai, ChinaB.PangSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing, ChinaJournal Article20200526In this paper, fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the category of $L$-convex spaces can be embedded in that of $L$-convergence spaces as a reflective subcategory. Finally, the concepts of convex and preconvex $L$-convergence spaces are introduced and it is shown that the resulting categories are isomorphic to the categories of $L$-convex spaces and $L$-preconvex remote-neighborhood spaces, respectively.https://ijfs.usb.ac.ir/article_5411_9d3ab259910efced25e1b09b291322cf.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801A modification of probabilistic hesitant fuzzy sets and its application to multiple criteria decision making151166541210.22111/ijfs.2020.5412ENB.FarhadiniaDepartment of Mathematics, Quchan University of Technology, Iran.0000000325808789E.Herrera-ViedmaAndalusian Research Institute in Data Science and Computational Intelligence, University of Granada, Granada 18071, SpainJournal Article20200526Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of PHFS, we propose a class of T-norm-based and S-norm-based operations for PHFSs together with a number of aggregation operators. Eventually, on the basis of the new operators, the effectiveness and practicality of re-defined PHFS will be tested using {three} multiple criteria decision making (MCDM) problems concerning the automotive industry safety evaluation, the evaluation of Chines hospitals and<br />the evaluation of alternatives in an investment company.https://ijfs.usb.ac.ir/article_5412_057e5deb1ffd05ff70caf7c0f6bcc02c.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801A novel fuzzy multi-criteria decision-making methodology based upon the spherical fuzzy sets with a real case study167177541310.22111/ijfs.2020.5413ENA.BalinIstanbul University, Department of Transportation and Logistics, Istanbul/TurkeyJournal Article20200526The choice of roll stabilization system is critical for many types of ships. For warships where operational activities are fast and the concept of time is very effective, determining the most appropriate of these systems is of particular importance. Some operations, such as the landing of the helicopter on board, are critical for naval ships. Unwanted rolling motion makes this difficult. In addition, the performance of the crew may be insufficient due to the effect of roll movement. Therefore, the determination of the most effective stabilizing device for naval ships was highly related to the rapid reduction of roll motion. With increasing technological studies, it became important which type of stabilizing system is more suitable for which type of naval ship. This study evaluates the relationship between criteria and alternatives and selects the most effective roll stabilizer system for naval ships according to expert opinion. Extension of TOPSIS method with interval-valued spherical fuzzy sets used to list the stabilizing systems alternatives for naval ships. When the obtained results were evaluated, the effect of the criteria on the alternative system types examined, Active Fin found to be the most functional alternative.https://ijfs.usb.ac.ir/article_5413_fc54157f0348662a307191ddafb609bb.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Reliable hub-and-spoke network design problems under uncertainty through multi-objective programming179198541410.22111/ijfs.2020.5414ENJ.NematianDepartment of Industrial Engineering, University of Tabriz, P.O.Box 51666-14766, Tabriz, IranJournal Article20200526HLP (hub location problem) tries to find locations of hub facilities and assignment of nodes to extended facilities. Hubs are facilities to collect, arrange, and distribute commodities in telecommunication networks, cargo delivery systems, etc. Hubs are very crucial and their inaccessibility impresses on network whole levels. In this paper, first, total reliability of the network is defined based on considering the reliability values of nubs and arcs. Then, a reliable hub-and-spoke network design problem under uncertainty is introduced through the multi - objective programming method in which the parameters are random fuzzy variables. Indeed, we are making effort to either maximize the average reliability or minimize total cost. Then, the proposed reliable multi - objective hub-and-spoke network design problem under uncertainty is solved by a new method using Zimmermann fuzzy multi - objective programming and random fuzzy chance-constrained programming based on possibility theory. Finally, some benchmark problems are solved as numerical examples to clarify the described method and show its efficiency.https://ijfs.usb.ac.ir/article_5414_dedc9e1946aadf32cc69354dae01612c.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417420200801Persian-translation 17-4 August 2020201213541510.22111/ijfs.2020.5415ENJournal Article20200526https://ijfs.usb.ac.ir/article_5415_79bde181334cfe5a7e2939fc9733e24b.pdf