University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801cover IJFS-Vol 18-No 4-August 2021617210.22111/ijfs.2021.6172ENJournal Article20210522https://ijfs.usb.ac.ir/article_6172_c9af5e7d59149355779f1ccf41fbe7cc.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights117617310.22111/ijfs.2021.6173ENO.PavlackaDepartment of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palack'y University in Olomouc, Czech RepublicM.PavlackovaDepartment of Computer Science and Applied Mathematics, Moravian College Olomouc, Czech RepublicJournal Article20210522Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for aggregation operators -- identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples.https://ijfs.usb.ac.ir/article_6173_97e5e9d3db17c8b02c64af90288bbd34.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801F-transforms determined by implicators1936617410.22111/ijfs.2021.6174ENA.TripathiDepartment of Mathematics \& Computing, Indian Institute of Technology (ISM) Dhanbad-826004, IndiaS. P.TiwariDepartment of Mathematics \& Computing, Indian Institute of Technology (ISM) Dhanbad-826004, IndiaI.PerfilievaUniversity of Ostrava, Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03, Ostrava 1, Czech RepublicJournal Article20210522This work aims to study F-transforms based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of F-transforms fail to hold in the case of implicators, such as S- and QL-implicators. {Further, we establish an equivalence between L-fuzzy transformation systems and F-transforms}.https://ijfs.usb.ac.ir/article_6174_fa78527f0e20231de643933ebaac58b4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices3749617510.22111/ijfs.2021.6175ENR. A.AlievJoint MBA Program, Georgia State University, USA, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010 Baku, AzerbaijanB. G.GuirimovState Oil Company of Azerbaijan Republic, SOCAR, SOCAR Tower, 121, H.Aliyev Ave., Baku, Azerbaijan, AZ 1029O. H.HuseynovResearch Laboratory of Intelligent Control and Decision Making Systems in Industry and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, AzerbaijanR. R.AliyevResearch Laboratory of Intelligent Control and Decision Making Systems in Industry and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, AzerbaijanJournal Article20210522The notion of consistency is used to estimate the quality of preference knowledge and its stability for reliable evaluation of decision alternatives. It is well-known that a set of strict consistency conditions are used to keep the rationality of preference intensities between compared elements. These requirements are not achievable in the real situations when decision maker has limited rationality and partially reliable preferences. In this study, we propose an approach to deriving consistency-driven preference degrees for such kind of situations. A preference degree is described by a Z-number to reflect imprecision and partial reliability of preference knowledge. An optimization problem with Z-number valued variables is used to formulate design of consistent preferences. A real-world decision making problem is considered to illustrate application of the proposed method and conduct comparison with an existing technique.https://ijfs.usb.ac.ir/article_6175_9d91cb1069a4db5878878b58d0503e6e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801Preference implication-based approach to ranking fuzzy numbers5168617610.22111/ijfs.2021.6176ENJ.DombiInstitute of Informatics, University of Szeged, Szeged, HungaryT.JonasInstitute of Business Economics, Eotvos Lorand University, Budapest, HungaryJournal Article20210522Dombi and Baczy'{n}ski presented a new approach to the problem of implication operation by introducing the preference implication, which has very advantageous properties. In this paper, it is presented how the preference implication is connected with soft inequalities and with sigmoid functions. Utilizing this connection the preference implication-based preference measure for two fuzzy numbers is introduced and its key properties, including the reciprocity, are described. Then, the exact expression for computing the new preference measure for trapezoidal fuzzy numbers is presented. Here, using the new preference measure, two crisp relations over trapezoidal fuzzy numbers are introduced. It is shown that one of them is a strict (but not a total) order relation, and the other one is an equivalence relation. The strict order relation can be used to rank comparable fuzzy numbers, while the equivalence relation, which we call the indifference relation, expresses that the order of some fuzzy numbers is indifferent. These two crisp relations can be used to rank a collection of trapezoidal fuzzy numbers. Lastly, the proposed ranking method is compared with some well-known existing fuzzy number ranking methods.https://ijfs.usb.ac.ir/article_6176_7638c6f7016ba62cef19047cef0947af.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801Sensitivity and strong sensitivity on induced dynamical systems6978617710.22111/ijfs.2021.6177END.JardonAcademia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa S/N, Col. Lomas de
Zaragoza 09620, Mexico City, Mexico.I.SanchezDepartamento de Matematicas, Universidad Autonoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Del.
Iztapalapa, C.P. 09340, Mexico City, MexicoJournal Article20210522Given a metric space X, we consider the family of all normal upper semicontinuous fuzzy sets on X, denoted by $mathcal{F}(X)$, and a discrete dynamical system $(X,f)$. In this paper, we study when $(mathcal{F}(X), widehat{f})$ is (strongly) sensitive, where $widehat{f}$ is the Zadeh's extension of f and $mathcal{F}(X)$ is equipped with different metrics: The uniform metric, the Skorokhod metric, the sendograph metric and the endograph metric. We prove that the sensitivity in the induced dynamical system $(mathcal{K}(X),overline{f})$ is equivalent to the sensitivity in $ widehat{f} :mathcal{F}(X)to mathcal{F}(X) $ with respect to the uniform metric, the Skorokhod metric and the sendograph metric. We also show that the following conditions are equivalent:<br />item {rm a)} $(X,f)$ is strongly sensitive;<br />item {rm b)} $(mathcal{F}(X), widehat{f})$ is strongly sensitive, where $mathcal{F}(X)$ is equipped with the uniform metric;<br />item {rm c)} $(mathcal{F}(X), widehat{f})$ is strongly sensitive, where $mathcal{F}(X)$ is equipped with the Skorokhod metric;<br />item {rm d)} $(mathcal{F}(X), widehat{f})$ is strongly sensitive, where $mathcal{F}(X)$ is equipped with the sendograph metric.https://ijfs.usb.ac.ir/article_6177_fb318d654462c7dc4d32cb53d08091ee.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801Disturbance estimator based dynamic compensator design for fractional order fuzzy control systems7993617810.22111/ijfs.2021.6178ENS.KanakalakshmiDepartment of Mathematics, Anna University Regional Campus, Coimbatore 641046, IndiaR.SakthivelDepartment of Applied Mathematics, Bharathiar University, Coimbatore 641046, IndiaL.Susana RamyaDepartment of Mathematics, Anna University Regional Campus, Coimbatore 641046, IndiaA.ParivallalDepartment of Mathematics, Anna University Regional Campus, Coimbatore 641046, IndiaA.LeelamaniDepartment of Mathematics, Anna University Regional Campus, Coimbatore 641046, IndiaJournal Article20210522The robust stabilization problem for singular fractional order time delay T-S fuzzy systems with nonlinearities and unknown external disturbances is addressed in this paper. An equivalent-input-disturbance (EID) estimator is used to estimate the impact of external disturbances and nonlinearities on the system output. Based on this EID approach, a dynamic compensator is designed to solve the stabilization problem of the considered system. Moreover, by considering a relevant Lyapunov-Krasovskii functional candidate and by using Lyapunov technique, the stability conditions in terms of LMIs are acquired for the considered closed-loop system. At last, to validate the effectiveness of the proposed result, two numerical examples are provided.https://ijfs.usb.ac.ir/article_6178_7f57419e01afeaf374e015f4a6ed437e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801An interactive fuzzy programming approach for a new multi-objective multi-product oil pipeline scheduling problem95112617910.22111/ijfs.2021.6179ENF.Khalili GoudarziDepartment of Mathematics, Faculty of Applied Mathematics, Shiraz University of Technology, Shiraz, IranH. R.MalekiDepartment of Mathematics, Faculty of Applied Mathematics, Shiraz University of Technology, Shiraz, IranS.NiroomandDepartment of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, IranJournal Article20210522In this paper, a new fuzzy multi-objective multi-product pipeline scheduling problem is introduced. The system consists of a single refinery, a unique distribution center, and a multi-product pipeline. Restrictions such as batch<br />sizing, discharging rate, forbidden sequences, batch volumetric, etc. are considered. Due to the uncertain nature of real-world problems, some parameters of the system are considered as fuzzy values. Tardiness and earliness penalties are considered with a time dependent non-linear function. The basic aim of this scheduling problem is to achieve the optimal sequence for pumping batches of oil products to maximize the financial benefit and simultaneously satisfies the customers with on-time delivery as a multi-objective problem. To tackle this problem, a two-stage methodology is proposed. In the first stage, the fuzzy formulation is converted to its equivalent crisp form by a credibility-based chance-constrained programming approach. In the second stage, the multi-objective crisp formulation is solved by some well-known approaches in the literature. Some test problems are generated and solved by the proposed approaches and the obtained Pareto-optimal solutions are analyzed and compared using some distance-based comparison metrics.https://ijfs.usb.ac.ir/article_6179_a4fb471439035a40cb4202e128549bf5.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801On the symmetric quintuple implicational method of fuzzy reasoning113129618010.22111/ijfs.2021.6180ENY. M.TangSchool of Computer and Information,
Hefei University of Technology, Hefei, 230009, P.R.ChinaG. Q.BaoSchool of Computer and Information,
Hefei University of Technology, Hefei, 230009, P.R.ChinaJ. J.ChenSchool of Computer and Information,
Hefei University of Technology, Hefei, 230009, P.R.ChinaW.PedryczDepartment of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6R 2V4, CanadaJournal Article20210522A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) method<br />is put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the QIP method. Then unified optimal solutions of the SQI method are obtained for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens), meanwhile corresponding reversible properties are verified. Furthermore, focusing on the case of multiple rules, optimal solutions of the SQI method are achieved, which involves two general approaches, i.e., FITA (first-infer-then-aggregate) and FATI (first-aggregate-then-infer). Equivalence relation of continuity and interpolation is analyzed for both FITA and FATI under the environment of the SQI method. Finally, one computing example arising in the field of affective computing is given for the SQI method with FATI. It is found that the SQI method preserves the same properties as the QIP method.https://ijfs.usb.ac.ir/article_6180_07619a5c6dff0d7e4ebae77ced45ab10.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801A multi-attribute assessment of fuzzy regression models131148618110.22111/ijfs.2021.6181ENJ.ChachiFaculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranA.KazemifardFaculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranM.JalalvandFaculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20210522Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models.<br />These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers.<br />Therefore, this paper develops a new multi-objective two-stage optimization and decision technique for fuzzy regression modeling problems in order to handle both of the criticisms.<br />To handle the outlier problems, in the first stage, dynamic robust to outlier objective functions is considered in the estimation problem.<br />The estimation problem is solved by running an algorithm which generates a set of fuzzy regression models.<br />Then, in the next stage, we design a decision schema by employing Multi-Attribute Decision Making (MADM) problem.<br />Here, the VIKOR method is employed as a proper means to provide a design to rank the generated fuzzy regression models by the first stage to introduce the most desirable model.<br />We include simulation numerical results and a real-world house price problem in order to highlight the advantages of the proposed method in a comparison study.<br />The results demonstrate the effectiveness of the proposed multi-objective optimization method to handle outlier detection problem while the prediction accuracy of the model is improved.https://ijfs.usb.ac.ir/article_6181_1cd8aaf61e7774888f201dc148012ed0.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801On matrix games with 2-tuple intuitionistic fuzzy linguistic payoffs149167618210.22111/ijfs.2021.6182ENR.VermaDepartment of Management Control and Information Systems, University of Chile, Av. Diagonal Paraguay 257, 8330015 Santiago, ChileA.AggarwalUniversity School of Basic and Applied Sciences\\ Guru Gobind Singh Indraprastha University Delhi-110078, IndiaJournal Article20210522In real-world decision-making problems, experts often prefer to express their views, regarding problem parameters, in a natural language rather than precise numerical form. Linguistic representation models have been widely used to solve many decision-making problems with qualitative information. Game theory has been found successful applications in a wide range of areas. This paper presents an extensive study of matrix games with qualitative payoffs. The work uses 2-tuple intuitionistic fuzzy linguistic values (2-TIFLVs) to represent the payoffs of the matrix game. We develop the mathematical formulation and concepts of the solutions for matrix games with payoffs represented by 2-TIFLVs. Paper also shows that matrix games with payoffs of 2-TIFLVs have solutions that can be obtained by transforming the matrix game in a pair of linear/nonlinear programming problems. Finally, a real-life numerical is given to illustrate the developed method.https://ijfs.usb.ac.ir/article_6182_801e5ffd2aaeae70c1b69d5e04a85514.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801Developing a fuzzy programming model for improving outpatient appointment scheduling169184618310.22111/ijfs.2021.6183ENB.FarahbakhshDepartment of Industrial Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, IranS. H.MoosaviradDepartment of Industrial Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, IranY.AsadiDepartment of Industrial Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, IranA.AmirbeigiSurgery Department, Faculty of Medicine, Kerman University of Medical Sciences, Kerman, IranJournal Article20210522Appointment scheduling for outpatient services is a challenge in the healthcare sector. For addressing this challenge, most studies assumed that patients’ unpunctuality and the duration of service have constant values or a specific probability distribution function. Consequently, there is a research gap to consider the uncertainty of both patients’ unpunctuality and the duration of service in terms of fuzzy sets. Therefore, this research aims to consider fuzzy values for both unpunctuality and duration of service have to improve an outpatient appointment scheduling (the time interval between two patients) in a referral clinic with the objective of reducing the total weight of waiting time, idle time, and overtime. Four different fuzzy linear programming models and 36 scenarios have been developed based on the show, no-show of patients, single-book, and double-book by using GAMS software. These four models are as follows: (1) probability of no-show equal to zero, (2) probability of no-show equal to 20%, (3) probability of no-show equal to zero and with double-book factor, and (4) probability of no-show equal to 20% and with double-book factor. The results of the first, second, third, and fourth models, respectively, present the scenarios considering 10, 5, 15, and 15 minutes for the time interval between two patients that have the minimum total weight of patient waiting times, physician idle times, and physician overtime. By considering these findings, the investigated referral clinic can improve its appointment system’s performance. Moreover, other similar clinics can apply the proposed model for improving their appointment systems' performance.https://ijfs.usb.ac.ir/article_6183_a1cac6860f21864cca4e9cbe9a7a4d10.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801Continuous probability-interval valued fuzzy preference relations and its application in group decision making185200618410.22111/ijfs.2021.6184ENJ.MoSchool of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, P.R. ChinaH. L.HuangSchool of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, P.R. ChinaJournal Article20210522Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements.<br />The probabilistic hesitant fuzzy preference relations can more effectively express the<br />hesitant preference information of decision makers.<br />But in the existing research, all of them are based on discrete probability distribution.<br />In order to give decision maker more evaluation space,<br />continuous probability distribution is necessary to be considered.<br />Therefore, in this paper, the continuous probability-interval valued fuzzy set<br />is defined and its probability is represented by a probability density function.<br />A method of converting probabilistic hesitant fuzzy set into continuous probability-interval valued fuzzy set<br />is developed to transform discrete data into continuous data.<br />Then, the continuous probability-interval valued fuzzy preference relations is presented.<br />In order to consider the consistency of continuous probability-interval valued fuzzy preference relations, the multiplication consistent expected preference relations is proposed.<br />The individual consistency index and group consensus index are also presented to determine the consistency level.<br />And then, an algorithm is introduced for checking and improving the individual consistency level and<br />group consensus level.<br />Finally, a numerical example is shown to the effectiveness of proposed algorithm,<br />the comparative analysis is given with the existing methods to<br />show the superiority of this algorithm.https://ijfs.usb.ac.ir/article_6184_367f212dbce02618182b52e7321ffc50.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065418420210801translate vol.18-no.4-August 2021201214618510.22111/ijfs.2021.6185ENJournal Article20210522https://ijfs.usb.ac.ir/article_6185_eaee52a18d1fec6593b7a20930f6f731.pdf