Weirs are installed on open channels to adjust and measure the flow. Also, discharge coefficient is considered as the most important hydraulic parameter of a weir. In this study, using the Radial Base Neural Networks (RBNN) and M5' methods, the discharge coefficient of Triangular plan form weirs is modeled. At first, the effective parameters in the prediction of the discharge coefficient are identified. Then, by combining the input parameters, for each of the RBNN and M5' methods, six different models are introduced. By analyzing the modeling results for all models, it was shown that the M5' model is capable of modeling the discharge coefficient more accurately. Also, based on the modeling results, a model that considered the impact of all input parameters was introduced as a superior model. The mean absolute percentage error (MAPE) and correlation coefficients (R2) values for the preferred model in the test mode were calculated 2.774 and 0.831, respectively. Also, for each of the M5' models, some relationships were proposed to estimate the Triangular plan form weirs. The evaluation of these relationships showed that the parameters of the ratio of head over the weir to channel width (h/B) and Froude number (Fr) were the most effective parameters in the prediction of the discharge coefficient.

In this paper, some elementary operations on Triangular fuzzy numbers (TFNs) are defined. We also define some operations on Triangular fuzzy matrices (TFMs) such as trace and Triangular fuzzy determinant (TFD). Using elementary operations, some important properties of TFMs are presented. The concept of adjoints on TFM is discussed and some of their properties are. Some special types of TFMs (e.g. pure and fuzzy Triangular, symmetric, pure and fuzzy skew-symmetric, singular, semi-singular, constant) are defined and a number of properties of these TFMs are presented.

In this paper, a fuzzy analog controller circuit is provided for the inverted Pendulum problem which resulted in a simple analog circuit simply does the act of controlling without requiring to any processing structure. In other words, in case of constructing the proposed circuit, a small analog chip controls the inverted pendulum. For this purpose, the first step is the study of the dynamic model of the inverted pendulum and then a fuzzy controller is designed systematically. In the following, the number of membership functions and the formation of them are designed. In addition, the different MFs and different numbers are examined for each variable and the most efficient structure is selected as fuzzy controller. To assess efficiency of designed fuzzy controller, the controller is simulated in Simulink and then this design is implemented at transistor level in TSMC 0. 18µ m CMOS technology. In this work, the MFs, the circuits for realization of the knowledge-based and defuzzification circuits are designed in current mode. The proposed circuits are simulated and evaluated in Advanced Design System software based on CMOS technology. Simulation results show that the inverted pendulum is controlled with high accuracy and high speed, meanwhile the controllers have low power consumption and good robustness to outer large and fast disturbance rather than the previous works.

In this study, new methods to construct Triangular norms and Triangular conorms on appropriate bounded lattices are introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and some other approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by induction to a modified ordinal sum for Triangular norms and Triangular conorms on appropriate bounded lattices. And some illustrative examples are given.

A Triangular tile latching system consists of a set $\Sigma$ of equilateral Triangular tiles with at least one latchable side and an attachment rule which permits two tiles to get latched along a latchable side. In this paper we determine the language generated by a Triangular tile latching system in terms of planar graphs.

A watching system in a graph G=(V, E) is a set W={w1, w2, …,wk}, where wi=(vi, Zi); viÎ V and Zi is a subset of closed neighborhood of vi such that the sets LW(v) ={wi: vÎZi} are non-empty and distinct, for any v ÎV. In this paper, we study the watching systems of line graph Kn which is called Triangular graph and denoted by T (n). The minimum size of a watching system of G is denoted by w (G). We show that w (T(n))= [2n/3].

We survey some recent results on cocharacters of upper Triangular matrices. In particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show different techniques in order to solve similar problems.