University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201merge of cover 19-6 December 2022721410.22111/ijfs.2022.7214ENJournal Article20221107https://ijfs.usb.ac.ir/article_7214_47884a67ba2e5496e690b8c7e259bf97.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Numerical solution for interval initial value problems based on interactive arithmetic112720610.22111/ijfs.2022.7206ENE.EsmiDepartment of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, BrazilC.SacilottoDepartment of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, BrazilV. F.WasquesIlum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, BrazilL. C.BarrosDepartment of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, BrazilJournal Article20221106This work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative ($gH$-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the $gH$-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for intervals. The arithmetic considered here is obtained using sup-$J$ extension principle, where $J$ is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via $gH$-derivative. To illustrate the results, the paper focuses in the decay Malthusian model.https://ijfs.usb.ac.ir/article_7206_d8d2eddb4302aa89fe38bcf111c89b98.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Distributivity between 2-uninorms and Mayor's aggregation operators1327720710.22111/ijfs.2022.7207END.JocicMathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, SerbiaI.Stajner-PapugaDepartment of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, SerbiaJournal Article20221106The issue of distributivity of aggregation operators is crucial for many different areas such as the utility theory and the integral theory. The topic of this paper is distributivity between 2-uninorms and Mayor's aggregation operators. The presented research is an extension and upgrade of<br />the previously obtained results. The full characterization of distributive pairs of operators is given.https://ijfs.usb.ac.ir/article_7207_e602acdb626efa64ab9c74330a357755.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201A new method to solve linear programming problems in the environment of picture fuzzy sets2949720810.22111/ijfs.2022.7208ENM.AkramDepartment of Mathematics, University of the Punjab, New Campus, Lahore 4590, PakistanI.UllahDepartment of Mathematics, University of the Punjab, New Campus, Lahore 4590, PakistanT.AllahviranlooFaculty of Engineering and Natural Sciences, Istinye University, Istanbul, TurkeyJournal Article20221106Picture fuzzy set is characterized by neutral membership function along with the membership and non-membership functions, and is, therefore, more general than the intuitionistic fuzzy set which is only characterized by membership and non-membership functions. In this paper, first, we are going to point out a drawback and try to fix it by the existing trapezoidal picture fuzzy number. Furthermore, we define an $LR$ flat picture fuzzy number, which is a generalization of trapezoidal picture fuzzy numbers. We also discuss a linear programming model with $LR$ flat picture fuzzy numbers as parameters and variables and present a method to solve these type of problems using a generalized ranking function.https://ijfs.usb.ac.ir/article_7208_628fc90d5c0488b5c42d98c4c9c85655.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201A new model to protect an important node against two threatening agents5160720910.22111/ijfs.2022.7209ENZ.MalekiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranH. R.MalekiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranR.AkbariDepartment of Computer Engineering and Information Technology, Shiraz University of Technology, Shiraz, IranJournal Article20221106One of the main goals of network planners is the protection of important nodes in a network against natural disasters, security threats, attacks, and so on.<br /> Given the importance of this issue, a new model is presented in this paper for protecting an important node in a typical network based on a defensive location problem where the two agents threaten this node. The protecting facilities location problem with two agents is formulated as a three-level programming problem. The decision maker in the upper level is a network planner agent. The planner agent wants to find the best possible location of protecting facilities to protect the important node against threatening agents. The second and third levels problems are stated as the shortest path problems in the network in which the edges are weighted with positive values. In this work, the genetic, variable neighborhood search, simulated annealing algorithms are used to solve the problem. The performance of the used metaheuristic algorithms on this class of problems is investigated by a test problem that is generated randomly. Then, t-test are used to compare the performance of these algorithms. The best results are obtained by the variable neighborhood search algorithm.https://ijfs.usb.ac.ir/article_7209_f0fb130c099655bef5b074a10a51b3e1.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Pseudo L-algebras6173721010.22111/ijfs.2022.7210ENX. L.XinSchool of Science, Xi'an Polytechnic University, Xi'an 710048, ChinaX. F.YangSchool of Science, Xi'an Polytechnic University, Xi'an 710048, ChinaY. C.MaSchool of Science, Xi'an Polytechnic University, Xi'an 710048, ChinaJournal Article20221106We introduce generalized structures of L-algebras, called pseudo L-algebras, which are the multiplication reduct of pseudo hoops and are structures combining two L-algebras with one compatible order. We prove that every pseudo hoop gives rise to a pseudo L-algebra and every pseudo effect algebra gives rise to a pseudo L-algebra. The self-similarity is the most important property of an L-algebra $L$, which guarantees to induce a multiplication on $L$. We introduce a notion of self-similar pseudo L-algebras and prove that a self-similar pseudo L-algebra becomes an L-algebra if and only if the multiplication $\odot$ is commutative. We get some interesting results for self-similar pseudo L-algebras: (1) The negative cone $G^-$ of an $\ell$-group $G$ can be seen as a self-similar pseudo L-algebra. (2) Every self-similar pseudo L-algebra is a pseudo hoop. Next, we introduce the notion of self-similar closures of pseudo L-algebras and obtain a self-similar closure by a recursive method. Given a pseudo L-algebra $(L, \rightarrow, \rightsquigarrow ,1)$, we can generate a free semigroup $(A, \ast)$ by the set $L\setminus \{1\}$. Furthermore, we let $S(L)=A\cup\{1\}$ and define a binary operation $\odot$ on $S(L)$. Then we extend the operations $\rightarrow$ and $\rightsquigarrow$ from $L$ to $S(L)$, and prove that $(S(L), \rightarrow, 1)$ and $(S(L), \rightsquigarrow, 1)$ are two cycloids, respectively. Furthermore, under some conditions, $(S(L), \rightarrow, \rightsquigarrow, 1)$ becomes a self-similar pseudo L-algebra. Finally, we introduce the notion of the structure group of pseudo L-algebras, and give an interesting example to show how to extend a pseudo L-algebra $L$ into the pseudo self-similar closure $S(L)$, and furthermore, derive it's structure group $G(L)$.https://ijfs.usb.ac.ir/article_7210_904114994177871109c4da5605b2e7ac.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Fuzzy product rule with applications7592721110.22111/ijfs.2022.7211ENM.ZeinaliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranF.MaheriDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20221106In this paper, we establish the GH-derivative of multiplication of fuzzy functions, the so-called product rule. For the first time, a product rule is constructed while both of the multiplied functions are assumed to be fuzzy without any restriction on the signs of multiplied functions. The rule is extracted based on the MCE-product and its property of distributivity. Then, we propose two important applications of the fuzzy product rule: An integration by parts formula for fuzzy functions and solving a nonlinear fuzzy differential equation. Some illustrative examples are given to verify the theoretical results.https://ijfs.usb.ac.ir/article_7211_4598aa875b2cd49d227bd712371d2bd8.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Connections between commutative rings and some algebras of logic93110721310.22111/ijfs.2022.7213ENC.FlautFaculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527, Constanta, RomaniaD.PiciuFaculty of Science, University of Craiova, A.I. Cuza Street, 13, 200585, Craiova, RomaniaJournal Article20221107In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings A in which Id(A) is an MV-algebra, a Heyting algebra or a Boolean algebra and we establish connections between these types of rings. We are very interested in the finite case and we present summarizing statistics. We show that the lattice of ideals in a finite commutative ring of the form $A=\mathbb{Z} _{k_{1}}\times \mathbb{Z}_{k_{2}}\times ...\times \mathbb{Z}_{k_{r}},$ where $k_{i}=p_{i}^{\alpha _{i}}$ and $p_{i}$ a prime number, for all $i\in \{1,2,...,r\}$, is a Boolean algebra or an MV-algebra (which is not Boolean). Using this result we generate the binary block codes associated to the lattice of ideals in finite commutative rings and we present a new way to generate all (up to an isomorphism) finite MV-algebras using rings.https://ijfs.usb.ac.ir/article_7213_43bce92b52b9a67d396d63a83a1dbcd3.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Algorithm for multiple attribute decision-making using T-spherical fuzzy Maclaurin symmetric mean operator111124721510.22111/ijfs.2022.7215ENH.GargSchool of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala-147004, Punjab, IndiaA.AhmadDepartment of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000, Lahore, PakistanK.UllahDepartment of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University (Lahore Campus), 54000, Lahore, PakistanT.MahmoodDepartment of Mathematics and Statistics, International Islamic University Islamabad-44000, PakistanZ.AliDepartment of Mathematics and Statistics, International Islamic University Islamabad-44000, PakistanJournal Article20221107The conception of T-spherical fuzzy set (TSFS) is a recent phenomenon in the environment of fuzzy notions that describe opinion about some certain objects under uncertainties with the help of four types of degrees known as the degree of membership (DM), degree of abstinence (DA), degree of non-membership (DNM) and degree of refusal (DR). The focus of this manuscript, to examine the interrelationship among any numbers of T-spherical fuzzy numbers (TSFNs) by the use Maclaurin symmetric mean (MSM) operators. We investigate and develop T-spherical fuzzy (TSF) MSM (TSFMSM) operator, TSF weighted MSM (TSFWMSM) operator, TSF dual MSM (TSFDMSM) operator, TSF weighted dual MSM (TSFWDMSM) operator. By using these investigated operators, some special cases of the explored operators are also developed, and their properties are examined. In addition, an algorithm for handling multi attribute decision making (MADM) problems based MSM operators in TSF setting. An illustrative example to check the applicability of the MSM operators of TSFSs is presented where the evaluation of technology commercialization is observed. To show the superiority of the newly established MSM operators, a comprehensive comparative study is designed numerically. In view of the comparative analysis, some advantages of the new MSM operators of the TSFNs are stated.https://ijfs.usb.ac.ir/article_7215_e634dad6426c2ff0d7d2e7c6b909f79f.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201A quadratic optimization problem with bipolar fuzzy relation equation constraints125140721610.22111/ijfs.2022.7216ENA.Abbasi MolaiSchool of Mathematics and Computer Sciences,Damghan University, P.O.Box 36715-364, Damghan, IranJournal Article20221107This paper studies the quadratic programming problem subject to a<br />system of bipolar fuzzy relation equations with the max-product<br />composition. A characterization of structure of its feasible domain is presented using the lower and upper bound vector on its solution set. A sufficient condition is proposed which under the condition, a component of one of its optimal solutions is the corresponding component of either the lower or upper bound vector. Some sufficient conditions are suggested to reveal one of its optimal solutions without resolution of the problem. Furthermore, some sufficient conditions are then given to determine some components from one of its optimal solutions. Based on these conditions, we can simplify the problem and reduce its dimensions. The simplified problem can be reformulated to an 0-1 mixed integer programming problem. Other unknown variables can be found by solving the current problem.https://ijfs.usb.ac.ir/article_7216_f729f77e33fb3186ce5979c7669851b7.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201A parametric similarity measure for extended picture fuzzy sets and its application in pattern recognition141160721710.22111/ijfs.2022.7217ENB.FarhadiniaDepartment of Mathematics, Quchan University of Technology, Iran, Department of Computing and Information Systems, University of Melbourne, AustraliaU.AickelinDepartment of Computing and Information Systems, University of Melbourne, AustraliaH. A.KhorshidiDepartment of Computing and Information Systems, University of Melbourne, AustraliaJournal Article20221107This article advances the idea of extended picture fuzzy set (E-PFS), which is especially an augmentation of generalised spherical fuzzy set (GSFS) by releasing the restricted selection of $p$ in the description of GSFSs.<br />Moreover, by the use of triangular conorm term in the description of E-PFS, it indeed widens the scope of E-PFS not only compared to picture fuzzy set (PFS) and spherical fuzzy set (SFS), but also to GSFS. In the sequel, a given fundamental theorem concerning E-PFS depicts its more ability in comparison with the special types to deal with the ambiguity and uncertainty.<br />Further, we propose a parametric E-PFS similarity measure which plays a critical role in information theory.<br />In order for revealing the advantages and authenticity of E-PFS similarity measure, we exhibit its applicability in multiple criteria decision making entitling the recognition of building material, the recognition of patterns, and the selection process of mega project(s) in developing countries.<br />Furthermore, through the experimental studies, we demonstrate that E-PFS is able to handle uncertain information in real-life decision procedures with no extra parameter, and it has a prominent role in decision making whenever the concepts of PFS, SFS and GSFS do not make sense.https://ijfs.usb.ac.ir/article_7217_8c881b259cecebf5a82195a07be0d71c.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Picture m-polar fuzzy soft sets and their application in decision-making problems161173721810.22111/ijfs.2022.7218END.AhmedSchool of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. ChinaB.DaiSchool of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. ChinaA. M.KhalilDepartment of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, EgyptJournal Article20221107The aim of this paper is to introduce a new multiple attribute decision-making model named picture m-polar fuzzy soft sets, which is a combination of the soft sets and picture m-polar fuzzy set. Some operations and properties of the new model, including subset, equality, union, intersection, and complement are discussed.<br />Further, the basic six definitions, three theorems, and six examples on picture m-polar fuzzy soft sets are explained. Lastly, we construct a new methodology to extend the TOPSIS to picture m-polar fuzzy soft sets (i.e., an application of picture m-polar fuzzy soft sets) in which capable of different objects recognizing belonging to the same family is constructed and illustrated its applicability via a numerical example.https://ijfs.usb.ac.ir/article_7218_04f9ac1ef3be52f5e06ade4df778c5b2.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201A novel hesitant fuzzy linguistic term sets approach and its application on acceptance sampling plans175192721910.22111/ijfs.2022.7219ENG.IsikDepartment of Industrial Engineering, Bursa Technical University, Bursa, TurkiyeI.KayaDepartment of Industrial Engineering, Yildiz Technical University, stanbul, TurkiyeJournal Article20221107Hesitant fuzzy linguistic term set (HFLTS) is an approach giving ability to obtain more flexible decision-making (DM) process by integrating linguistic fuzzy modeling (LFM) with hesitative expert judgments. Although HFLTS is widely-studied in the literature and many enhancements are made on HFLTS procedure, none of these enhancements gives ability to continue with precise fuzzy modeling (PFM) in decision process. LFM has a big drawback about accuracy because of the dependency between the size of term set and the comprehensiveness of fuzzy sets (FSs). This issue creates a very critical difficulty in modeling of DM problems that need sensitive evaluations by using HFLTS. This paper aims to solve this problem by proposing a novel HFLTS methodology that is usable for DM problems that need sensitive calculations in the decision stage. The proposed methodology integrates 2-tuple LFM and linguistic fuzzy modifiers with HFLTS to overcome the accuracy problem and obtain more sensitive and flexible decision procedure. This paper also presents an envelopment transformation technique to aggregate expert assessments as a fuzzy membership function instead of membership grades. It becomes possible to keep interpretability in a certain level and achieve sensitive results at the same time with the help of these modifications. The proposed HFLTS approach is analyzed on a real case example from manufacturing industry for acceptance sampling plans (ASP) that is a DM problem requiring sensitive calculations. As another originality of the paper, the main formulations of ASP are derived based on hesitant fuzzy defectiveness information. The obtained results are also compared with some existing enhancements of the HFLTS and the success of the proposed methodology is proved in terms of sensitive calculation.https://ijfs.usb.ac.ir/article_7219_555aefc7dfca4e8e9a9efde717f320aa.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201Merge of translate 19-6 December 2022195206722010.22111/ijfs.2022.7220ENJournal Article20221107https://ijfs.usb.ac.ir/article_7220_f286fdc454fc2a8b86f17e30ae212cb2.pdf