Theory of Approximation and Applications
Volume:14 Issue: 2, Summer and Autumn 2020

In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matrix. This linear system determines $r$-level of fuzzy solution at mesh points. By combining of this solutions, we obtain fuzzy solution of main problem at mesh points, approximately. Its applicabilityis illustrated by someexamples

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Health-medical facilities are among the applications that, if incorrectly located, in addition to the economic and financial necessities that come with it, may lead to irreparable loss of life. Geographical location is a critical component of access to medical services. Therefore, the significance of the optimal and convenient location of this type of usage is multiplied. This study aimed to determine the hospital’s optimal locations and provide easy access, better service, customer and patient satisfaction, and public welfare to all segments of society in Iran, the Markazi province, and Arak city. For this purpose, a combination of Geographic Information System (GIS) output and integrated Analytic Network Process-Weighted Aggregated Sum Product Assessment (ANP-WASPAS) model in a fuzzy environment was used. First, effective criteria for locating the hospital were selected based on the literature, national standards and regulations, expert opinion, and the location and geographical conditions of the area. The criteria were then weighted by experts using the Fuzzy ANP (F-ANP) method. Then, according to the criteria and final weights, the desired maps were created in the ArcGIS software environment. The results were then combined using fie fuzzy operators. As a result, optimal and suitable locations for the hospital were introduced. Finally, using the Fuzzy WASPAS (F-WASPAS) method, the identified locations were prioritized.

The uncertain functional differential equations are animportant tool to deal with dynamic systems including thepast states in uncertain environments. The contribution ofthis paper to the uncertain functional differential equationtheory is to provide an existence and uniqueness theoremunder the weak Lipschitz condition and the linear growthcondition.

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to compute the moments for the solution of logistic stochastic differential equation.

In this note, we define the expansive map on S-metric space, also we study behavior of expansive map defined on a complete S-metric space and offer some new ways to proving fixed point type theorems and survey it by some illustrative examples.

where m is the number of edges, μ is the cyclomatic number of G, d(u) is thesum of distances between vertex u and all of the vertices of G, and the summationgoes over all edges from the edge set E(G). In this paper we obtain amethod for calculating the Balaban index of nanotubes which have square andoctagon structure and denoted by C4C8(S) nanotubes.

One of the most essential pieces of information given by DEA models is the cost efficiency of decision-making units (DMUs). Cost efficiency (CE) is defined as the ratio of minimum costs to current costs and in fact, evaluates the ability to produce current outputs at a minimal cost. While the traditional cost efficiency models require the values for all data to be known exactly, in real-world problems the exact values of input prices are unknown, and only the maximum and minimum bounds of input prices can be estimated for each DMU. Hence, the main aim of the current paper is to develop a pair of two-level mathematical programming problems, whose optimal values represent the optimistic and pessimistic cost efficiency measures. The two-level nonlinear program for the optimistic cost efficiency measure is then transformed into a one-level linear program. In this regard, we provide an explicit formula for measuring the pessimistic CE measure.

Ranking DMUs based on individual preferences is an interesting and useful part of decision-making problems. Comparing the weighted sum of the selected number of rank votes, after determining the weights in a selected rank, can be regarded as a common approach to compute the total ranking of alternatives. In actual applications, making the weight of a certain rank zero means that we throw away the corresponding part of the obtained rank voting data. This paper proposes a new model to assess the non-zero weights for each position.

M. S. Knebelman [1] has developed conformal geometry of generalised metricspaces. The decomposability of curvature tensor in a Finsler manifold was studiedby P. N. Pandey [4]. The purpose of the present paper is to decompose the Projectivecurvature tensor and study the identities satisfied by projective curvature tensor inconformal Finsler space.

In this paper, we introduce a new iterative process for two nonexpansive mapsatisfying the condition (II) in CAT(0) space and establish Delta-convergence theoremfor the proposed process under condition.

Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introduced. Some properties of these polynomials are consideredto implement a collocation method in order to approximate the solution of Fuzzy Volterra integral equations ofthe second kind. The existence and uniqueness of the solution also convergence and error analysis of proposedmethod are proved thoroughly. The results showed the calculations of the method are simple and low cost.