فصلنامه مدل سازی پیشرفته ریاضی
سال نهم شماره 2 (پاییز و زمستان 1398)

In this paper, an existing method to estimate coefficients of a fuzzy regression model with non-fuzzy inputs and fuzzy out-puts as well as its method to perform a fuzzy hypothesis test and a fuzzy confidence interval are recalled. Then, the disadvantages and shortcoming of this method are examined and criticized by analyzing several numerical examples. By introducing an appropriate alternative approach to estimating coefficients and applying conventional fuzzy hypotheses in a fuzzy environment, we try to improve the method in the structure and decision making to accept or reject fuzzy hypotheses. For this purpose, employing a common distance measure and Bootstrap technique, the required test statistics are defined as non-fuzzy criteria. Then, by comparing the p-value obtained from the test statistics and a given significance, unlike the existing one, one can easily decide to accept or reject the null hypothesis. Also, using some applied examples, the possible advantageous of the proposed approach in hypothesis testing and confidence interval for fuzzy coefficients are compared and discussed.

In this research article,we estimate the multicomponent stress–strength reliability of a system when strength and stress variates are drawn from an exponentiated Weibull distribution with different shape parameters and , and common scale parameter , respectively. The reliability is estimated using the best single observation percentile method and maximum liklihood method of estimation when samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets we illustrate the procedure. Keywords: Stress–Strength, Reliability, Maximum likelihood estimation, Best single observation percentile estimation, Mean square error, Confidence intervals, Gompertz distribution.

In this paper, we first study the theory of the spatial-temporal half spectral modelling and describe some properties of recently proposed half spectral models. Next, we propose an estimation method for the estimation of spatial-temporal covariance functions in the half-spectral setting. To assess the performance of the proposed half-spectral models, we conduct two simulations. in which we compare the proposed fitting approach with respect to the other classical estimation methods. The proposed methods have great success in fitting parametric space-time covariance functions specifically for massive data sets. Finally, we apply the proposed methods for a real daily wind speed data in Zanjan, Iran.

Honey bee is the insect that mainly pollens agricultural products. In recent decades, colony failure rates as a global concern have increased. Some mathematical models have been proposed. In one of the first models the impact of bee death rates on population dynamics was studied and then the food availability and the rate of broods added to the model. Here we improve the model by considering seasonal changes and death rate of hive bees. Our results show that death rates higher than 0.41 lead to colony collapse. At higher death rates, despite of colony failure, food stored in colony and this is instance of colony collapse. Additionally, the model predicts the minimum food needed for colony in various death rates.

In this paper, we provide conditions on the smooth piecewise dynamical systems that guarantee the existence of Devaney chaos. In fact, we show that if f is a generalized semi-baker map with two branches and its derivative greater than or equal √2, then the dynamical system related to that is chaotic in the sense of Devaney. Such conditions on the dynamical systems with more than one discontinues point essentially does not satisfy this result.

The problem of pipeline planning is one of the most complex problems in the field of applied and industrial problems. Multi product pipeline planning and inventory management in distribution centers has to consider the pipeline limitations as well as the operational restrictions. Another important issue is the customer demands that must be satisfy on time. Providing effective mathematical models, that cover different aspects of this problem, as well as appropriate solving methods helps to planner to achieve the optimal scheduling of pipelines. Many researchers have been working on models to provide efficient models and develop appropriate methods for solving this problem. In this paper, a new mixed integer optimization model (MILP) is proposed for scheduling and planning multiple product pipelines that connect a refinery to a distribution center. The advantage of this model is its formulation method, which attempts to reduce the number of binary variables used in the model and reduce the complexity of the mathematical model. For this purpose, the problem has first been formulated without taking into account some operational constraints and during the model's solving, by applying an iterative algorithm, these restrictions are added to the model step by step. Finally, to validate models and solving methods, by implementing the proposed models and solution methods on real pipeline systems (based on information from Iran Telecom and Oil Pipelines), the outputs in terms of solving time and quality solution and objective function value are evaluated.

The slacks-based measure super-efficiency model is presented for ranking SBM's efficient decision making units. Fuzzy data envelopment analysis models have been introduced to evaluate uncertain inputs and outputs for decision making units (DMUs). In this methods, mostly used α-cut procedure. Also, sample fuzzy decision making units in these methods cannot be assessed. This paper proposes generalized fuzzy super-efficiency model which includes, old fuzzy DEA models, and evaluates the sample decision making units. This scheme embraces evaluation method based on vector. As an empirical example, the proposed method is applied to the flexible manufacturing system data to rank efficient units.

The linear systems are one of the most important tools for modeling real-world phenomena. Because the real-world phenomena are always associated with uncertainty, solving the fuzzy linear system have a great importance. One of the proposed methods to find the exact and approximate solutions of a fuzzy linear system is using the least squares method. In this method, by choosing an arbitrary meter and solving a quadratic programming, they provide an approximate (or exact) solution for the fuzzy linear system. In this paper, at first, we prove that under some conditions and not depending on the selected meter the quadratic programming is convex. Therefore, by considering three different meters and solving several examples, we compare the obtained approximate solutions.

The main purpose of the paper is to generalize the concept of equitable efficiency‎ ‎by introducing the concept of equitable A-efficiency‎, ‎where A is an arbitrary matrix with non-negative‎ ‎entries‎. ‎Two conditions are provided to ensure that the relation of equitable A-dominance is an equitable rational preference relation‎. ‎Furthermore the structure of equitably A-efficient set is investigated and is proved that the set of equitably A-efficient solutions is contained within the set of efficient‎. ‎Hence to reduce Pareto-optimal solutions‎, ‎we can use equitably A-efficient solutions‎.

The dominance graph of the binary words, which is denoted by (Γ_n ) , is a directed graph whose vertex set is the set of all binary words of length n. Setting B_1 (w)={1≤i≤n┤| w_i=1}, for every vertex 〖w_1 w_2…w〗_n, we join two vertices v and w by an arc if B_1 (w) is contained in B_1 (v). In this paper, we study some graphical parameters of this graph. For example, after computing the distance of every two vertices and the eccentricity of any vertex, it is proved that the diameter and the radius of the underlying graph of (Γ_n ) equals 3 and 2, respectively. Also, it is proved that this graph has 〖 3〗^n-3(2^n-1) edges. Then we prove that both of the clique nmber and the chromatic number of the dominance graph of binary words of length n are n-1. Among other results, it is shown that the edge chromatic number and the maximum degree of vertices are equal to 2^(n-1)-2. Finally, by a combinatorial method, the independence number of this graph is determined, too.

Using cyclic permutations, Narayana investigated the relation between the area under north-east paths from the origin to the point (n,n) and the number of the flaws of the paths. His result implies a proof to the Chung-Feller Theorem. In this paper by revising the Narayana's approach, we offer short proofs to the theorems of Narayana and Chung-Feller.

A new class of continuous functions, namely s - R - continuous functions, is introduced. The relations of s - R - continuity with continuity and other variants of continuity are discussed. Basic Properties of s - R - continuous functions are studied. Conditions are established under which every weakly theta_cl -continuous function is s - R - continuous.