JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2019 | Volume:5 | Issue:19 |Papers Count:13

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for this information measure and prove some properties about the entropy of independent fuzzy partitions. Some results of the relationship between the Tsallis entropy and conditional Tsallis entropy of fuzzy partitions are obtained and, by using conditional Tsallis entropy of fuzzy partitions, we show that the subadditivity property for Tsallis entropy of fuzzy partitions is not established in the case that the parameter of this entropy is smaller than one. In general, the Tsallis entropy of fuzzy partitions has similar properties to the shannon entropy, where the parameter of this entropy is larger than one, and therefore can be used in addition to the Shannon entropy, to measure the amount of information to be extracted from a fuzzy experiment.

Nowadays, due to the high expectations of customers in meeting their demand and the competition environment among service providers, employers are working to provide customers with new methods in the shortest possible time and in the best possible way to attract customer’ s satisfaction and maximize profits. In this paper, the orienteering problem with variable profits, fractional objective function and demand on arcs is studied. An appropriate integer programming model is proposed to solve it. In this case, the purpose is to determine a route for a vehicle so that it maximizes the profit, the start and end of its route is at the origin, serving demands of customers, and does not exceed a maximum allowed travel time. In the orinteering problem with variable profits and fractional objective function the customers are located on vertices of the graph corresponding to the problem. Next, a problem is considered in which the service is performed on arcs. The resulting problem is called the orinteering arc routing problem with variable profits and fractional objective function. We solve the problem by bisection method. In the end, the numerical efficiency of the proposed model is examined. The proposed algorithms can solve problems in a reasonable amount of time. We will also see that the time of solving problems depends on their graph structure and not on their size.

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gö del (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gö del logics, for showing that the intuitionistic logic is not finitely (many) valued. Now we know that the propositional intuitionistic logic is infinitely many valued (with a countably many logical values). In this paper we provide another proof for this result of Gö del, from the perspective of Kripke model theory. Š vejadr and Bendova (2000) proved that in Gö del fuzzy logic the conjunction and implication are not definable by the rest of the propositional connectives (while disjunction is definable by conjunction and implication). In this paper, we show that disjunction is not definable by implication and negation in Gö del fuzzy logic; two proofs, one by Kripke models and one by fuzzy semantics, are provided for this new theorem.

Let Γ =(V, E) be a graph and W_( a)=\{w_1, … , w_k \} be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v, w_1), … , a_Γ (v, w_k)) is the adjacency representation of v with respect to W in which a_Γ (v, w_i )=min\{2, d_Γ (v, w_i )\} and d_Γ (v, w_i ) is the distance between v and w_i in Γ . W_a is called as an adjacency resolving set for Γ if distinct vertices of Γ have distinct adjacency representations w. r. t W_a. The size of the smallest adjacency resolving set is the adjacency metric dimension of Γ and is denoted by dim_a (Γ ). In this paper, we prove that dim_a(Γ _E (Z_(P^n ) ))=⌈ (n-2)/2⌉ . Also, we show that Γ _E (Z_(p^2n ) )≅ Γ _E (R/I) in which p is a prime number, n is a natural number and I is a 2-absorbing ideal of the ring R which has a minimal primitive decomposition in the form of the intersection of n primitive ideals. Finally we conclude that dim_a⁡ 〖 (Γ _E (R/I))=n-1〗 .

The main purpose of this paper is to solve an inverse random differential equation problem using evolutionary algorithms. Particle Swarm Algorithm and Genetic Algorithm are two algorithms that are used in this paper. In this paper, we solve the inverse problem by solving the inverse random differential equation using Crank-Nicholson's method. Then, using the particle swarm optimization algorithm and the genetic algorithm, we solve them. The algorithms presented in this article have advantages over other old methods that have been presented so far. Implementing these algorithms is simpler, have less run time and produce better approximation. The numerical results obtained in this paper also show that the solutions obtained for the examples presented in the numerical results section are highly accurate and have less error. All of the algorithms in this paper to obtain the desired numeric results, have been implemented on the Pentium (R) Dual core E5700 processor at 3. 00 GHz.

In this paper we propose a new method for ranking Z-numbers and generalizations. This method is based on the internal structure of the artificial neural network, which suggests that the structure of this network consists of inputs weights and the transfer function linear, nonlinear and sometimes linear and nonlinear. It is shown that the proposed method while possessing the ranking properties for Z-numbers whose components of the limiting part are equal and their confidence interval having the same center of gravity has a more logical ranking than those using the center of gravity. While some of the available methods for Z numbers whose boundaries are equal but not equal to their reliability but have the same focal gravity they rank equally which can not be logical in all cases. Therefore, the proposed method overcomes this problem. In some examples the correctness of the subject is shown. the results are compared with some existing methods.

This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples.

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differential equation will be considered. Because for the numerical solution of these equations we need the simulation of stochastic double integrals, we explain the simulation of these integrals in more details. Also one-step and multi steps methods for the solution of affine random ordinary equations (RODEs) which are an important class of RODEs will be considered. The numerical solution of these equations with Wiener and Compound Poisson processes will be established. Two methods for simulation of the double integrals will be explained, and some numerical examples are provided to confirm the theoretical results numerically.

Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of them presented a characterization for Meir-Keeler condensing operators, which needs L-functions. But, finding an appropriate L-function needs more struggle. In this paper, we give a characterization for Meir-Keeler condensing operators via measure of non-compactness. Current characterization presents a criterion by which we can show that if a given generalization of Darbo's fixed point theorem is Meer-Keeler condensing or not. Ultimately, we give several corollaries and point out several generalizations of Darbo's fixed point theorem and show that all of them are Meir-Keeler condensing operator or a special case of this result.

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dynamics of processes in which sudden, discontinuous jumps occur. For the background, theory and applications of impulsive differential equations. There have been many approaches to study the existence of solutions of impulsive fractional differential equations, such as fixed point theory, topological degree theory, upper and lower solutions methods and monotone iterative method. In this paper, we study the existence of solutions for a new class of p-Laplacian fractional boundary value problem with impulsive effects. By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problem have infinitely many solutions.

In the present note, for a ring endomorphism Alpha, we introduce Alpha-skew J-McCoy rings, which are a generalization of Alpha-skew McCoy and J-McCoy rings rings and investigate their properties. For a ring R, we show that if Alpha(e)=e for each idempotent e and R Alpha-skew J-McCoy then eRe is Alpha-skew J-McCoy. The converse holds if R is an abelian ring. Also, we prove that if Alphat =idR for some positive integer t and R[x] is Alpha-skew J-McCoy, then R is Alpha-skew J-McCoy. The converse holds if J(R)[x] subset of J(R[x]). Moreover, we give an example to show that the Alpha-skew J-McCoy property does not pass Mn(R). But, for any n, Tn(R) is a Alpha-skew J-McCoy ring if R is a Alpha-skew J-McCoy ring. Also, we prove that If R is right (left) quasi-duo ring and Alpha be an endomorphism of a ring R, then R is Alpha-skew J-McCoy, the converse does not hold in general.

The aim of this paper is to provide a new numerical method for solving nonlinear singular differential equations that arise in biology problem. These kind of problems appear in various biology problems like oxygen diffusion in red blood cells, distribution of heat source in human head and cancer tumor growth and etc. In this paper this equations are solved by a new numerical method by using Zernike radial polynomials. In the proposed method for the first time the operational matrix of derivative for Zernike radial polynomials is derived and by using this operational matrices of derivative of Zernike radial functions the differential equation convert to a system of algebraic equations that can be solved easily. The implementation of this proposed method is simple and attractive. Finally some applied models are presented to compare the results by other method results, and they show the accuracy and efficiency of the presented method.