A fractional trapezoidal rule type difference scheme for fractional order integro-differential equation is considered. The equation is discretized in time by means of a method based on the trapezoidal rule: while the time derivative is approximated by the standard trapezoidal rule, the integral term is discretized by means of a fractional quadrature rule constructed again from the trapezoidal r...

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

The purpose of this paper is to present three new methods for finding all simple zeros of polynomials simultaneously. First, we give a new method for finding simultaneously all simple zeros of polynomials constructed by applying the Weierstrass method to the zero in the trapezoidal Newton’s method, and prove the convergence of the method. We also present two modified Newton’s methods combined w...

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and attribute values take the form of the generalized interval-valued trapezoidal fuzzy numbers, a new group decision making analysis method is proposed. Firstly, some operational laws, the distance between two generalized interval-valued trapezoidal fuzzy numbers, and transformation from th...

project selection is considered as an important problem in project management. it is multi-criteria in nature and is based on various quantitative and qualitative factors. the main purpose of this paper is to present a new rank-based method for project selection in outranking relation. according to this approach, decision alternatives were clustered in the concordance matrix and the discordance...

The fuzzy c-means clustering algorithm is a useful tool for clustering; but it is convenient only for crisp complete data. In this article, an enhancement of the algorithm is proposed which is suitable for clustering trapezoidal fuzzy data. A linear ranking function is used to define a distance for trapezoidal fuzzy data. Then, as an application, a method based on the proposed algorithm is pres...

In this paper, considers the usage of intuitionistic fuzzy numbers in decision making. The values and ambiguities of the membership degree and the non-membership degree for trapezoidal intuitionistic fuzzy number are defined as well as the value-index and ambiguity-index. The proposed ranking method is easily implemented and has a natural interpretation. 2010 AMS Classification: 47S20, 03E72

In this paper, we want represented a method for ranking of two exponential trapezoidal fuzzy numbers with TRD distance. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of exponential trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems.

We propose a novel SAS macro to utilize PROC NLMIXED in SAS to estimate the standard error for AUC when the AUC estimator is based on the trapezoidal rule. Our method accounts for the trapezoidal region-by-region correlation structure. An example is provided for the standard error of the AUC under the ROC curve.

To make the analysis more consistent and logical according to real life situations, in thispaper, the concept of trapezoidal vague set is extended by the idea of trapezoidal vaguesets of type-II. Also we have introduced: definition of trapezoidal vague set of type-IIand arithmetic operations between two trapezoidal vague sets of type-II. Further, a newmethod has been developed f...