University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Distributivity laws for quasi-linear means111654710.22111/ijfs.2022.6547END.JocicMathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, SerbiaI.Stajner-PapugaDepartment of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovica 4, 21000 Novi Sad, SerbiaJournal Article20211218Aggregation operations play a fundamental role in a large number of disciplines, from mathematics and natural sciences to economics and social sciences. This paper is focused on the problem of distributivity for some special classes of aggregation operations, and quasi-linear means. Characterization of distributivity pairs for uninorms, semi-uninorms and associative a-CAOA vs quasi-linear means is given.https://ijfs.usb.ac.ir/article_6547_0b86d326c08660c16694d0edaa3e8a84.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Design and analysis of process capability indices cpm and cpmk by neutrosophic sets1330654810.22111/ijfs.2022.6548ENS.YalcinDepartment of Industrial Engineering, Beykent University, 34398, Sariyer, Istanbul, TurkeyI.KayaDepartment of Industrial Engineering, Yildiz Technical University, 34349, Yildiz, Istanbul, TurkeyJournal Article20211218Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices C_{pm} and C_{pmk} have been developed to consider customers' ideal value that called target value ( T ). Although, these indices have similar features of the well-known indices C_{p} and C_{pk} , one of the most important differences is to consider \textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices C_{pm} and C_{pmk} have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} have been obtained and the main formulas of them have been produced. Additionally, the proposed \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} have been applied on real case studies from manufacturing industry. The obtained results show that the indices \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} include more informative and flexible results to evaluate capability of process.https://ijfs.usb.ac.ir/article_6548_e98cfe7416bb8c70e2264f1b97bfab6d.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Type 2 adaptive fuzzy control approach applied to variable speed DFIG based wind turbines with MPPT algorithm3145654910.22111/ijfs.2022.6549ENS. M.HosseiniElectrical and Electronic Engineering Department, Shahed University, Tehran, IranM.ManthouriElectrical and Electronic Engineering Department, Shahed University, Tehran, IranJournal Article20211218In this research, a Type 2 adaptive fuzzy controller approach is formulated and designed to be applied to variable speed doubly fed induction generator-based wind turbines directly connected to the grid. It brings this study to evaluate the whole operation of the system to capture the highest rate of power in the wind turbines. The controlling approach is considered to keep the stator reactive power to the ideal value. In contrast to the other researches, here the controlling technique is developed through the nonlinear systems. By the aim of making progress in system operation, in contrast with the Type 1 adaptive fuzzy system, type two adaptive fuzzy theory is proposed to approximate a large number of uncertainties and the dynamic nonlinearities, exists in tracking errors which may limit the system performance. Feedback linearization control approach helps us to algebraically alter the system into a linearized plant. Thanks to the Lyapunov theorem, the introduced type two adaptive fuzzy approach is proved to meet the uniformly ultimately boundness (UUB) property. On the other hand, it results better tracking function. The simulation outputs represent that the proposed technique is robust enough in presence of parameter variations and unstructured uncertainties.https://ijfs.usb.ac.ir/article_6549_30a0437f028dfb84047c69beee683079.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Solvability of fuzzy fractional stochastic Pantograph differential system4760655010.22111/ijfs.2022.6550ENJ.PriyadharsiniDepartment of Mathematics, Faculty of Mathematics, The Gandhigram Rural Institute - Deemed to be University,
Gandhigram - 624 302, Dindigul, Tamil Nadu, IndiaP.BalasubramaniamDepartment of Mathematics, Faculty of Mathematics, The Gandhigram Rural Institute - Deemed to be University,
Gandhigram - 624 302, Dindigul, Tamil Nadu, IndiaJournal Article20211218In this paper, a new type of equation namely fuzzy fractional stochastic Pantograph delay differential system (FSPDDS) is proposed. In our previous work, a first extension of fuzzy stochastic differential system into fuzzy fractional stochastic differential system by using Granular differentiability has been established. Here we study the existence and uniqueness results for the fuzzy FSPDDS which are obtained by using generalized Granular differentiability and contraction principle with weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.https://ijfs.usb.ac.ir/article_6550_9556add429d3b6cd7b85805c3c6b35e9.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201A fuzzy non-parametric time series model based on fuzzy data6172655110.22111/ijfs.2022.6551ENG.HesamianDepartment of Statistics, Payame Noor University, Tehran 19395-3697, IranF.TorkianDepartment of Statistics, Payame Noor University, Tehran 19395-3697, IranM.YarmohammadiDepartment of Statistics, Payame Noor University, Tehran 19395-3697, IranJournal Article20211218Parametric time series models typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. However compared with parametric methods, nonparametric time series models often provide a very flexible approach to bring out the features of the observed time series. This paper suggested a novel fuzzy nonparametric method in time series models with fuzzy observations. For this purpose, a fuzzy forward fit kernel-based smoothing method was introduced to estimate fuzzy smooth functions corresponding to each observation. A simple optimization algorithm was also suggested to evaluate optimal bandwidths and autoregressive order. Several common goodness-of-fit criteria were also extended to compare the performance of the proposed fuzzy time series method compared to other fuzzy time series model based on fuzzy data. Furthermore, the effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results indicate that the proposed model performs better than the previous ones in terms of both scatter plot criteria and goodness-of-fit evaluations.https://ijfs.usb.ac.ir/article_6551_36a0046be4e364dbce4bd7255957fbae.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201A note on divisible discrete triangular norms7381655210.22111/ijfs.2022.6552ENF.KouchakinejadDepartment of Statistics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, IranA.StupnanovaDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology,
Radlinskeho 11, 810 05 Bratislava, SlovakiaA.SeligaDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology,
Radlinskeho 11, 810 05 Bratislava, SlovakiaJournal Article20211218Triangular norms and conorms on [0,1] as well as on finite chains are characterized by 4 independent properties, namely by the associativity, commutativity, monotonicity and neutral element being one of extremal points of the considered domain (top element for t-norms, bottom element for t-conorms). In the case of [0,1]domain, earlier results of Mostert and Shields on I-semigroups can be used to relax the latest three properties significantly, once the continuity of the underlying t-norm or t-conorm is considered. The aim of this short note is to show a similar result for finite chains, we significantly relax 3 basic properties of t-norms and t-conorms (up to the associativity) when the divisibility of a t-norm or of a t-conorm is considered.https://ijfs.usb.ac.ir/article_6552_212cf3ae3695a65bcb7510f17d629c1d.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Ordinal sum constructions for aggregation functions on the real unit interval8396655310.22111/ijfs.2022.6553ENA.Mesiarova-ZemankovaMathematical Institute, Slovak Academy of Sciences, 814 73 Bratislava, SlovakiaR.MesiarFaculty of Civil Engineering, Department of Mathematics, Slovak University of Technology, 81368 Bratislava, SlovakiaY.SuSchool of Mathematics Sciences, Suzhou University of Science and Technology, Suzhou 215009, ChinaJournal Article20211218We discuss ordinal sums as one of powerful tools in the aggregation theory serving, depending on the context, both as a construction method and as a representation, respectively. Up to recalling of several classical results dealing with ordinal sums, in particular dealing, e.g., with continuous t-norms, copulas, or recent results, e.g., concerning uninorms with continuous underlying functions, we present also several new results, such as the uniqueness of the link between t-norms or t-conorms, and related Archimedean components, problems dealing with the cardinality of the considered index sets in ordinal sums, or infinite ordinal sums of aggregation functions covering by one type of ordinal sums both t-norms and t-conorms ordinal sums.https://ijfs.usb.ac.ir/article_6553_6beeac25621da8d6e197c370d729fd2c.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle97114655410.22111/ijfs.2022.6554ENM.RanjbarDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranS. M.MiriDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranS.EffatiDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20211218A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.<br />Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic.<br />In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a new lattice operation on HFNs based upon extension principle and defining the Hamming distance on them.<br />Finally, the applications of them are explained on optimization and decision-making problems.https://ijfs.usb.ac.ir/article_6554_8f82ef516e925d7eb98e54e6f2a40f11.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Monte Carlo statistical test for fuzzy quality115124655510.22111/ijfs.2022.6555ENA.ParchamiDepartment of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranH.IranmaneshDepartment of Statistics, Factually of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranB.Sadeghpour GildehDepartment of Statistics, Factually of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20211218Testing the capability of a productive process on the basis of the flexible fuzzy quality using Yongting's index is proposed in this paper by the Monte Carlo simulation.<br />The theoretical approach and detailed steps of an algorithm are given to simulate the critical-value-based and also p-value-based approaches to statistical testing fuzzy quality. Also, the probability of type \textit{II} error of the quality test simulated by Monte Carlo approach. Moreover, a real-world case study is provided to show the performance of the proposed algorithm for triangular and trapezoidal fuzzy qualities.https://ijfs.usb.ac.ir/article_6555_ce35e74e892ec7df5d9e7179254f6fb8.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices125140655610.22111/ijfs.2022.6556ENE.AsiciDepartment of Software Engineering, Faculty of Technology, Karadeniz Technical University, 61830 Trabzon, TurkeyJournal Article20211218In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods by Ertu\u{g}rul, Kara\c{c}al, Mesiar \cite{Ertugrul} and \c{C}ayl{\i} \cite{Gul} as results. Also, we give some illustrative examples. Finally, we show that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices. This paper has further constructed the t-norms and t-conorms on bounded lattices from a mathematical viewpoint.https://ijfs.usb.ac.ir/article_6556_dbff86f25210038e3738de9c6c1263e4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Stability problem for Pexiderized Cauchy-Jensen type functional equations of fuzzy number-valued mappings141151655710.22111/ijfs.2022.6557ENM.MiahiFaculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, IranF.MirzaeeFaculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, IranH.KhodaeiFaculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, IranJournal Article20211218We investigate the stability problems of the $n$-dimensional Cauchy-Jensen type and the n-dimensional Pexiderized Cauchy-Jensen type fuzzy number-valued functional equations in Banach spaces by using the metric defined on a fuzzy number space.<br />Under some suitable conditions, some properties of the solutions for these equations such as existence and uniqueness are discussed. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.https://ijfs.usb.ac.ir/article_6557_1dc54cde393d7f75d581082c17d1132e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201An approach based on $\alpha$-cuts and max-min technique to linear fractional programming with fuzzy coefficients153169655810.22111/ijfs.2022.6558ENM.BorzaDepartment of Mathematical Sciences, Faculty of Science & Technology, UKM Bangi, Selangor 43600, MalaysiaA. S.RambelyDepartment of Mathematical Sciences, Faculty of Science & Technology, UKM Bangi, Selangor 43600, MalaysiaJournal Article20211218This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of $\alpha$-cut is used to tackle the fuzzy numbers in addition to rank them. Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPP is defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an $\epsilon$-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisons are made to show the efficiency.https://ijfs.usb.ac.ir/article_6558_f65f62b24b5980315eee9e714c6c736b.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201An identification model for a fuzzy time based stationary discrete process171188655910.22111/ijfs.2022.6559ENG.SirbiladzeDepartment of Computer Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, GeorgiaJournal Article20211218A new approach of fuzzy processes, the source of which are expert knowledge reflections on the states on Stationary Discrete Extremal Fuzzy Dynamic System (SDEFDS) in extremal fuzzy time intervals, are considered. A fuzzy-integral representation of a stationary discrete extremal fuzzy process is given.<br />A method and an algorithm for identifying the transition operator of SDEFDS are developed. The SDEFDS transition operator is restored by means of expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimator of the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states.https://ijfs.usb.ac.ir/article_6559_87e0ddf0d8f7773b6a5564a5b5aac42e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419120220201Construction of 2-uninorms on bounded lattices189200656010.22111/ijfs.2022.6560ENA.XieDepartment of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi, 330031, ChinaZ.YiCollege of Mathematics and Information Science, Nanchang Normal University, Nanchang, Jiangxi, 330031, ChinaJournal Article20211218Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U_1 and U_2, defined on sublattices [0,d] and [d,1], respectively, this paper presents two methods for constructing binary operators on L which extend both U_1 and U_2. We show that our first construction is a 2-uninorm on L if and only if U_2 is conjunctive and our second construction is a 2-uninorm on L if and only if U_1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0,d]^2 and [d,1]^2 are respectively U_1 and U_2.https://ijfs.usb.ac.ir/article_6560_9220983cc8033753db150b6234633b42.pdf