مجله پژوهش های نوین در ریاضی
پیاپی 25 (امرداد و شهریور 1399)

Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy automata on the basis of Myhill-Nerode. To do so, we first define general fuzzy automata induced by fuzzy right congruence using the concept of fuzzy right congruences on a free monoid. Further, using the concept of language identified by an automaton we will show that in this induced automaton there exists an identifiable language if and only if there is an extension from fuzzy right congruence on a free monoid. As a result, this identified language is equivalent to the crisp language of the very automaton. We also define Nerode fuzzy right congruence and Myhill fuzzy congruence with max-min general fuzzy automata showing that the language identified by general fuzzy automata max-min is equivalent to the language identified by max-min general fuzzy automata induced by Nerode fuzzy right congruence. Finally, we elaborate the concepts through examples.

The main objective of this study was to investigate the impact of service quality on customer satisfaction rate private banks Fars Province. Private Banking in the Fars Province, including banks, Pasargad, Parsian, Sinai, Ansar, Ghavamin, Iran zamin, Eghtesad novin, Shahr , Sarmayeh. The study period is the first half of 1396. For ranking of SERVQUAL dimensions including quality of service based on customer satisfaction, Fuzzy AHP technique is used. First, customer satisfaction criteria were compared with each other. Then the quality of service based on customer parameters (Schacht core services, the human factor index, the index system and social responsibility index) were compared. For this purpose, the information you need from the experts (professors and bankers) were collected. Boucher techniques used to test pairwise comparison matrix is incompatible. The ranking was determined that the dimensions of service quality responsiveness, reliability, assurance, tangibles and empathy impact on customer satisfaction. Conclusions are provided at the end of the article.

The purpose of the current research is to provide a performance appraisal system capable of considering the value chain network structure of research and development (R&D) projects for Complex products and systems (CoPS) under uncertainty of data. Therefore, in order to achieve this goal, a network data envelopment analysis (NDEA) approach and the possibilistic programming to provide a new fuzzy network data envelopment analysis (FNDEA) approach have been utilized. It is worth noting that the value chain structure is considered in three phases: research and development, manufacturing and testing and finally operations. Finally, the proposed research approach was implemented using data from 10 Research and Development projects for complex systems and products in Iran and the results indicate the capability and applicability of the proposed approach of fuzzy three-stage data envelopment analysis.Keywords: Research and Development (R&D) Project, Complex Products and Systems (CoPS), Network Data Envelopment Analysis (NDEA), Value-Chain, Uncertainty.

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined. It is shown that the fractional method based on the shifted Grunwald formula is unconditionally stable. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. A numerical example is presented and compared with exact solution for its order of convergence./////////Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined. It is shown that the fractional method based on the shifted Grunwald formula is unconditionally stable. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. A numerical example is presented and compared with exact solution for its order of convergence.

The main purpose of this research is to extend some fixed point results in orthogonal metric spaces. For this purpose, first, we investigate new mappings in this spaces. We introduce the new notions of functions. Then by using it, we define contractive mappings and then we establish and prove some fixed point theorems for such mappings in orthogonal metric spaces. Then by utilizing examples of the function we deduce some new consequences for these fixed point theorems. Also in this research paper we will give applications. As first application, we will show that many fixed point results in metric spaces endowed with a graph G can be deduced easily from fixed point theorems in orthogonal metric spaces. As another application, we will show that many fixed point results in partially ordered metric spaces can be deduced easily from fixed point theorems in orthogonal metric spaces. Indeed, in this paper in addition to extend some fixed point results in orthogonal metric spaces, we will show that our obtained results unify many fixed point results.

In this paper, we obtain the solution of linear and nonlinear delay differential equations in reproducing kernel space. For this purpose, regarding the equation and conditions governing it, a linear operator is defined and subsequently an orthonormal complete system for reproducing kernel space is obtained by using the adjoint operator and reproducing kernel function. Then, the solution of these equations is obtained in the form of a series of the basic functions. Indeed, the analytical solution is represented by infinite series, and the approximate solution is obtained by using an iterative method. As one of the main aims, the convergence analysis and error behavior are discussed for the proposed method. Finally, some numerical examples are studied to demonstrate the validity and applicability of the proposed method. The obtained results of the proposed method are compared with the exact solutions and the earlier works. The outcomes from numerical examples illustrate that the proposed method is very effective and convenient.

A new and attractive metric space is a P-metric space which is a generalization of the concept of b-metric spaces. The generalization of the principle of Banach contraction has been carried out by many authors. Generalizations focus on the extension of metric spaces and the extension of contraction conditions. A few metrics, such as partial metrics, G-metrics, 2-metrics and Branciari metrics are some examples of metrics provided in this field. The aim of this paper is to present some common fixed point results for two mappings (one of them is weakly isotone increasing with respect to another) in the framework of ordered $p$-metric spaces. Our results are generalizations of the presented results in [H. K. Nashine, B. Samet and C. Vetro, Math. Comput. Modelling, 54 (2011) 712–720] and [ J.R. Roshana, V. Parvaneh and Z. Kadelburg, J.Nonlinear Sci. Appl., 7 (2014), 229--245]. An example is also provided to support our results.

In this paper, approximate efficient ( -efficient) solutions of multiobjective optimization problems are investigated. One of the most important methods for solving multiobjective optimization problems is to use scalarization techniques. In these methods, a single objective optimization problem corresponding to the multiobjective problem is solved, and the relationship between optimal solutions of the single objective problem and (weakly, properly) efficient solutions of the multiobjective problem is investigated. In this paper, a combination of the modified constrained and elastic constrained scalarization methods is considered, which will provide necessary and sufficient conditions for generating approximate (weakly, properly) efficient solutions. We compare the results with the necessary and sufficient conditions obtained from the modified constrained and the elastic constrained methods. The presented results can be applied for every multiobjective optimization problem without any convexity assumption for the objective functions. ‎Unlike many of the previous methods, the obtained results are also consistent with multiobjective problems with unbounded criterion space.

Trade-off between objective functions in multi-objective optimization is one of the tools for interpreting and studying efficient solutions. Properly efficient solutions are one of the most important theoretical and practical concepts that represent the behavior of the objective functions during a process change. Actually, these solutions are those efficient solutions that filter the anomalies of objective functions at some points, and this will help the manager to decision making to choose more important solutions. One of the most important tools for obtaining solutions with bounded trade-off in multi-objective optimization field is the Sum weighted scalarization method, which many authors have been studying it in interactive optimization field. This paper provides a method for obtaining properly efficient solutions near the ideal point with a theoretical and interactive view and using Sum weighted scalarization method. Since being near to ideal point will be abele to a preference of decision maker; this method examines the preferences of the decision maker without sacrifice the theory. Therefore, this paper presents an approach to finding properly efficient solutions near to the ideal point.

Let A be a Banach algebra, A’’ a Banach A-module. In this paper, we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions,and them investigate those conditions under which the second adjoint of a derivation into a dual Banach algebra module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included. A^(4) is a banach algebra with four Arens products. The bilinear map T is Arens regular when the equality T*** = T^( r***r ) . If T: A × A’’ → A’’ is multiplication left module on A , the following statements are equivalent , i:T is regular ii : T**** = T^(r****r) iii : T****( A’’’, A’’) ⊆ A’’’ iv : the linear map a → T*( a’’’, a) : A → A’’’ is weakly compact for every a’’’ ∈ A’’’. Also If module actions are regular, then every inner derivation D : A → A’’’ is weakly compact; moreover, D** : (A’’, □ ) → A^(5) and D** : (A’’, ⋄ ) → A^(5) are also inner derivation.

The hierarchy analysis process is one of the most comprehensive systems designed for decision making with multiple criteria, since this technique provides the possibility of formulating the problem in a hierarchical manner, as well as the possibility of considering different quantitative and qualitative criteria. The process involves various options in decision making and the ability to analyze the sensitivity of the criteria and sub-criteria. In addition, it is based on a paired comparison that facilitates judgment and computation. This model starts with the identification and prioritization of decision elements. These elements include goals, criteria and possible options, the process of identifying these elements and the relationship between them ultimately leads to the creation of a hierarchical structure. But in many cases, some or all of the data are fuzzy decision making, so it is necessary to consider uncertainty in such a decision model in the decision model. This article tries to take a fresh look at the issue of fuzzy hierarchy analysis. This view is influenced by the flaws in the fuzzy methods and group decision-making methods such as Delphi.

In this paper‎, ‎we will present a new method for solving a class of two-dimensional linear Volterra integral equation of the second kind with weakly singular kernel from Abel type in the reproducing kernel space‎. The reproducing kernel function is discussed in detail. Weak singularity of problem is removed by applying integration by parts. Further, improper integral belongs to L_2 (Ω). ‎In our method the exact solution ϕ(x,t) is represented in the form of series in the reproducing kernel space W(ω), and the approximate solution ϕ_n (x,t) is constructed via truncating the series to n terms. ‎Convergence analysis of the method is proved in detail‎. ‎Some numerical examples are also studied to demonstrate the efficiency and accuracy of the presented method‎. ‎The obtained results show that the error of the approximate solution is monotone decreasing in the sense of the norm of W(ω), when increasing the number of the nodes. Also, that indicate the method is simple and effective. It turns out that this method is valid.

The purpose of this study is to provide a prediction model for the Tehran Stock Exchange Index using Adaptive Neuro-Fuzzy Inference System (ANFIS) and fuzzy regression analysis. The behavior of this index is nonlinear and chaotic that traditional methods do not predict accurately. Hence, using the above two tools and identifying three macroeconomic variables including inflation rate, exchange rate and crude oil price as independent variables, we predicted the index of the total stock index for the next week. Then, the modeling was performed using the above three variables. By comparing the results, ANFIS performance was better than fuzzy regression. The Root Mean Square Error Performance criterion was obtained for the ANFIS output of 0.021248. The prediction of the next week showed an error reduction for both tools and ANFIS again with an error value of 0.007933, yielded superior performance of the study. Also, the model with four inputs was more accurate compared to the model with three inputs. The emphasis on using macroeconomic variables, predicting the next week's index number, using the two tools mentioned, analyzing the sensitivity of the models during the research are the characteristics of this research. This research can be used by all companies in the stock exchange, investors, brokers, and individuals and legal entities dealing in any way with the stock market.

A Roman dominating function on a graph G is a labeling f:V(G)→{0,1,2} such that every vertex with label 0 has a neighbor with label 2. A Roman dominating function on a graph G is a labeling f:V(G)→{0,1,2} such that every vertex with label 0 has a neighbor with label 2. A maximal Roman dominating function on a graph G is a Roman dominating function f such that V_0={w ∈V(G)│f(w)=0} is not a dominating set of G. The weight of maximal Roman dominating function is the value w(f)=f(V(G))=∑_(x∈V(G))▒〖f(x).〗 The maximal Roman dominating number γ_mR (G) of a graph G equals the minimum weight of a maximal Roman dominating function on G. In this paper, we continue the study of maximal Roman domination number. First, we characterize all graphs G of order n with g(G)≥6 for which γ_mR (G) =n-2, and then, we consider this property for some graphs with girth at most 5.

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