مجله پژوهش های نوین در ریاضی
پیاپی 32 (مهر و آبان 1400)

A bipolar fuzzy set is a powerful tool for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to the fuzzy model. We define certain notions, including a bipolar fuzzy number and bipolar fuzzy arithmetic. In this paper we propose the new fuzzy arithmetic operations based on on bipolar fuzzy numbers from [1,2]. We define 2- dipole fuzzy numbers and cutting them. The properties of these propose operations and their fundamental qualities are discussed in detail. Several illustrative examples were given to show the accomplishment and ability of the proposed method. At the end it is shown that the solution of the proposed method in comparison to other methods of solving fuzzy equations are more realistic, that is, they have smaller support. Further, we analyze our new approach to find the solutions of a bipolar fuzzy linear equations. In this paper, in addition to familiarity with bipolar fuzzy number operations based on transmission- average and presenting practical solutions for calculations in specific cases, this problem is identified.

In this paper, we first introduce some classes of fine non-abelian metacyclic 2-groups of nilpotency class two and nilpotency class at least three, which have been classified by Beuerle. Then, we define all representations of these groups as a finite non abelian two generators 2-group, namely Ɠ, so that this group covers all possible cases of the Beuerle’s classifications. Next, we compute the centralizers and the order of the centralizers of elements in the group Ɠ. Moreover, the conjugate type vector of the group, is obtained. Finally, as a direct application of the results, explicit formulas for the th commutativity degree of such groups are given. As a conclusion, it is found at the sizes of all the finite non-abelian metacyclic 2- groups of each type in Ɠ are the same. Also, we observe that the th commutativity degree of Ɠ has the same formula for all the group presentations.

Voltaire integral equations as the output of problems in basic sciences and engineering have a special application in advancing the solution of complex problems. One of the most widely used types, which consists of a random process under external motion, is the equations of random Volta integral. Solving this type of equation has always been a challenge for researchers. On the other hand, with the development of artificial intelligence and the presentation of fuzzy artificial neural network method as a model inspired by the process of thinking and analysis in the human brain, advanced models of algorithms have been designed. Some of these learning algorithms have been used in fuzzy artificial neural networks to solve equations. In this paper, using this method and designing a learning algorithm, the random equations of random Voltaire type is investigated. The method presented in this article, in addition to being more accurate than the previous methods, posseses more speed for solving problem. This topic provides an acceptable level of confidence for researchers when dealing with such issues.

Data envelopment analysis is a linear programming-based approach used to evaluate the relative performance of decision making units (DMU's) that perform the same tasks with multiple inputs and multiple outputs. Due to the optimistic view of the DEA in evaluating the performance of homogeneous decision making units, multiple units with a maximum relative efficiency score (equal to unit) are highly likely. Therefore, ranking models were presented to distinguish between efficient units. Cross efficiency evaluation is one of the most useful tools for ranking DMUs in data envelopment analysis. This model has two major flaws in implementation. First, it yields different results in the presence of optimal alternatives; and second, there is no compelling reason to use the arithmetic mean to integrate the cross-performance matrix results. In this paper, a new approach, inspired by the preferential voting process and the idea proposed in the TOPSIS method, is presented to combine cross-performance results in the presence of undesirable outputs. The results are then used to rank suppliers in the presence of undesirable outputs.

Every year, many people are killed and wounded due to traffic accidents on the roads of Iran and lot of families suffer from physical, mental and financial problems. Today, the problem of traffic accidents has become an important issue in Iran but all provinces are not same condition in this issue. Transport authorities and experts tend to know position of each state based on different criteria. They should know that which province has the good condition and which one are in the worst position because for more exact planning, this issue has some influences on their decisions. In this paper, provinces based on various criteria, equipment related to intelligent transportation systems, are ranked. This method indicates that the numbers of dead and injured are not appropriate criteria for ranking of states and different criteria must be considered. This priority is performed by using of Analytical Hierarchy process (AHP). Based on the obtained results, the most important indicators for assessing Iranian provinces to improve road safety are a number of relief bases, type of damage, intelligent transportation equipment and road traffic rate. Extracting the results was done using Expert Choice software.

In the present research, an optimization process was performed in Signoff unit of Saipa Corporation based on the discrete event simulation using a multiple objective function. The required information, including the operation classes (product inspection, adjustment, and reworking), the flow between different workstations, operation times, production cost identification, etc., were extracted from the actual data recorded for March 2018- March 2019 period. For the purpose of simulation, firstly, the model was built using the Arena software and all effective parameters and variables were introduced into the model following the planning of various scenarios. Upon a predetermined number of iterations, the bottleneck was identified and the model was verified. Next, in a primary phase, the OptQuest software was utilized to find the optimal number of workers for minimizing the production costs after 378 iterations (upon satisfaction of an automatic stop criterion), and the result was used as input for a secondary phase where the model was optimized for enhancing the operational capacity of the logistic units upon 303 iterations. Using the results of this research, it was anticipated to achieve 21.6% drop in the number of Operator along with 10% increase in the logistic capacity, 4% reduction in the production costs, and 2% increase in the production rate.

In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported. In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported.

Project-oriented organizations are one of the emerging organizational forms that are formed around projects and teams. These organizations have dynamic boundaries and fields of works, in which the number and size of projects of the organization are constantly changing. In this regard, the managers of these organizations are always faced with the issue of choosing the higher economic justification projects for their organizations, as well as, resource management (including resource leveling and resources allocation) for the selected projects. In this research, a mathematical model of renewable and non-renewable resource management for self-financing project-oriented organizations is presented. This means that financing of the selected projects within the organization is limited to the initial capital and the incomes of the completed projects. In this regard, the project portfolio theory is used to solve the problem of the selection and scheduling of the projects within the project-oriented organization considering the limitation of renewable and non-renewable resources, the existence of a prerequisite relationship between project activities, the time value of capital for financial resources and finally the application of reinvestment strategy. The multi-objective function maximizes the net present value of the investment as well as minimizes the amount of the idle renewable resources. The modeling is a mixed integer programming and after linearization of the model, the LP-metric method is used to solve the multi-objective function, and finally the results are examined on a numerical example.

Extension of Banach algebras defined by Cartesian product by a linear functional such as are called -Lau Banach algebras. Recently, this type of Banach algebras are interested by many researchers. Derivations play an important role in algebraic structures. By using this role, one can discover some of the properties of algebraic structures on which a derivation is defined, such as their semi simplicity. In this paper, we consider derivations that are defined on Lau product of Banach algebras and we characterize these derivations in some various cases. As a main characterization, for two Banach algebra , and , we show that is a derivation if and only if there are derivations , and a -derivation such that for all . We investigate the converse case of the above obtained result in some various cases and according to the obtained results related to characterization of derivations, we investigate and characterize the first cohomology of Banach algebras obtained by this product.

In this paper, we approximate the solution of two-dimensional Rayleigh-Stokes problem ‎for a heated generalized second grade fluid with fractional derivatives. This approximation is ‎based on the space-time radial basis functions (RBFs) and the Sinc quadrature rule. In this ‎method, we use Gaussian radial basis function and don't distinguish between time and place ‎variables and the collocation points have both the coordinates of time and space. We use the ‎Sinc quadrature rule with single exponential transformation to approximate the integral part of ‎fractional derivatives. The chosen fractional derivatives is Riemann – Liouville.‎This method is implemented on two examples with different values of the fractional ‎derivative order. Obtained results illustrate the effectiveness of our method and sh ow that ‎one can obtain accurate results with a small number of the collocation points for the radial ‎basis function. It should be noted that all calculations in this paper have been done using ‎Mathematica software.‎

A structure M is an o-minimal structure if every definable subset X of M is a finite union of intervals and points.Every o-minimal structure is a topological space. A definable set X in M is called a definably compact set if every definable curve in it is completable in X. The definable compactness of a definable set X is equivalent to be closed and bounded.A idea of definable space generalizes theorem of Robson for semialgebraic spaces, A definablespace is not a definable set but it looks like the definable sets. Indeed definable spaces are constructed by the gluing of sets which are not definable but they are relativ to definable sets. In this paper we will recall the concept of definable space and introduce the notion of definable compactness in it. We show that a definable set X in the housdorff definable space is definable compact if and only if it is closed and bounded.

Investigating the convergence of the Krylov subspace methods has been considered as one of the favorite subjects in the field of numerical linear algebra. Given that the DGMRES method is a Krylov subspace methods, there is not much work to be done on its convergence. In this article we will discuss parts of the convergence of this method. We show that for any non-decreasing sequence of negative numbers f(0)≥f(1)≥⋯≥f(m-1)>f(m)=⋯=f(n)=0, he set of {λ_1,…,λ_m,0,…,0} of the complex numbers and the arbitrary number α≤n-m can be a set of singular linear equations n×n, Ax=b with the index α and the set {λ_1,…,λ_m,0,…,0} as the spectrum of matrix A such that if the DGMRES method is used to solve this system, assuming ‖A^α r_0 ‖_2=f(0)‖_2 = f (0), for k=1,…,m-1, the k^th residual vector is ‖A^α 〖r 〗_k ‖_2=f(k), wherer_0=b-Ax_0 is the initial residual vector. We attempt to do this by constructing the complete coefficient matrix of the system (s).

One of the most important issues in managers' decisions is supplier selection and supply chain evaluation. Therefore, several studies have been conducted on supplier selection and evaluation by data envelopment analysis. But studies so far have focused on selecting suppliers and evaluating them. And there is no way to determine the number of suppliers in a supply chain. Therefore, in this article, we first express the concept of profit efficiency for supply chains and using the proposed model in this paper, the number and type of suppliers in a supply chain are determined simultaneously. Finally, 10 "supply chains" in the food industry were examined and the profit efficiency of each of them was calculated using the proposed model in this article, and then the number and type of suppliers in each chain were determined.

Evaluation of decision-making units is very importantin economic and management systems. Data envelopment analysis is one of the scientific and practical techniques for evaluating decision making units. In the conventional models of data envelopment analysis, the units are divided into efficient and inefficient categories, where the efficiency of each efficient unit is one and there is no distinction between efficient units.This study intends to propose a new way of ranking efficient units based on the concepts of cooperative game. The proposed method is that efficient units are considered as players of a cooperative game. A subset of these players is defined as the coalitionS.Then the sum of the efficiency of the inefficient units according to the production possibility set that is created by the inefficient units and the members of the coalitionS is defined as the characteristic function of S, which is used to determine the marginal effect of the efficient units in the various coalitions. Finally, the Shapley value is used to determine the cooperative game solution and rank the efficient units.In the same way that it is able to rank non-extreme units, inefficient units are also effective in ranking, alsois feasiblein any circumstances of return to scale.

Resource allocation has always been one of the main challenges in the design of wireless cellular networks. Suitable resource allocation, more specifically that includes suitable base station selection and bandwidth allocation can play an effective role in interference mitigation and users’ quality of service requirement satisfaction. In this paper, a game theoretic approach is proposed to solve the BS selection problem in two-tier wireless femtocell networks. We formulate the competitive behavior of users as evolutionary game theory. We calculate the probability of a user choosing a BS, compute the cell load of each BS, and analyze the demand rejection probability of the user associated with the BS. The proposed approach maximizes network throughput as well as meeting the QoS requirements of the users. Finally, we propose a decentralized learning algorithm based on EXP3 algorithm to achieve the evolutionary equilibrium as the solution of the game. Simulation results show that the proposed approach achieves a desirable performance and guarantees users’ QoS requirements.