A New Model of Fuzzy Logic: Monadic Monoidal T-Norm Based Logic

In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.

On Weighted Pál Type (0,2)-interpolation on the Unit Circle

In this paper, we study the explicit representation of weighted Pál-type (0,2)-interpolation on two pairwise disjoint sets of nodes on the unit circle, which are obtained by projecting vertically the zeros of (1−x2)Pn(x) and Pn′′(x) respectively, where Pn(x) stands for nth Legendre polynomial.AMS Classification (2000): 41A05, 30E10.

An efficient technique to solve coupled–time fractional Boussinesq–Burger equation using fractional decomposition method

For this work, a novel numerical approach is proposed to obtain solution for the class of coupled time-fractional Boussinesq–Burger equations which is a nonlinear system. This system under consideration is endowed with Caputo time-fractional derivative. By means of the natural decomposition approach, approximate solutions of the proposed nonlinear fractional system are obtained where the exact solutions are presented in the classical case of fractional order at [Formula: see text]. Some numerical examples are given to support the theoretical framework and to point out the role and the effectiveness of the intended method. Our results clearly show the approximate analytical solutions eventually will converge quickly to the already known exact solutions. AMS Classification: 35A22, 35C05, 35C10, 35R11, 44A30.

Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

Ranked set sampling (RSS) is an efficient technique for estimating parameters and is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this paper, we assume [Formula: see text]to have bivariate Lomax distribution where a study variable [Formula: see text]is difficult and/or expensive to measure and is correlated with an auxiliary variable [Formula: see text] which is readily measurable. The auxiliary variable is used to rank the sampling units. In this article, we propose an estimator for the scale parameter of bivariate Lomax distribution using some of the modified RSS schemes. Efficiency comparison of the proposed estimators is performed numerically as well as graphically. A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, we implement the results to real-life datasets. AMS classification codes: 62D05, 62F07, 62G30

Steiner μ Distance in Fuzzy Graphs with Application

In this article we define Steiner and upper Steiner distances in connected fuzzy graphs by combining the notion of Steiner distance with distance and proved that both are metric. Also based on length, eccentricity, radius, diameter, diametric vertex, eccentric vertex, centre, convexity, self-centred graphs are introduced for both Steiner and upper Steiner distances . Some common characteristic properties are analysed and relation between Steiner and upper Steiner distances are discussed with an application. A model result is given for transport network.2010 AMS Classification: 05C72, 05C12

On Asymptotic Standard Normality of the Two Sample Pivot

The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test statistic being asymptotically standard normal, which is known to happen if the two samples are independent and the ratio of the sample sizes converges to a finite positive number. This restriction on the asymptotic behavior of the ratio of the sample sizes carries the risk of rendering the asymptotic justification of the finite sample approximation invalid. It turns out that neither the restriction on the asymptotic behavior of the ratio of the sample sizes nor the assumption of cross sample independence is necessary for the pivotal convergence in question to take place. If the joint distribution of the standardized sample means converges to a spherically symmetric distribution, then that distribution must be bivariate standard normal (which can happen without the assumption of cross sample independence), and the aforesaid pivotal convergence holds. AMS Classification: 62E20, 62G20

Copula-based Bivariate Cointegration Model

This article focuses on a bivariate cointegrating model with non-normal errors. In particular, we propose a bivariate error distribution constructed using two non-identical marginals through a copula. The model parameters are estimated using the method of inference functions for margins and maximum likelihood. Applications of the proposed model are illustrated through real life examples. AMS classification codes: 62M10

Intransitive Permutation Groups with Bounded Movement Having Maximum Degree

Let G be a permutation group on a set withno fixed points in and let m be a positive integer. If for each subset T of the size |Tg\T| is bounded, for gEG, we define the movement of g as the max|Tg\T| over all subsets T of . In this paper we classified all of permutation groups on set of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25

Certain Class of Meromorphically Multivalent Functions Associated with a Linear Operator

In this paper we have introduced a new subclass ( , , , , , ) ,, T a c A B p m l    of meromorphic p-valent functions in the punctured unit disk U*={z∈C:0 less than |z| less than 1} by sing a linear operator p m l I , , .Coefficients inequalities, Distortion theorems, Closure properties, Radii of starlikeness and convexity are obtained for this class. 2010 AMS CLASSIFICATION: Primary 30C45.

Intransitive Permutation Groups with Bounded Movement Having Maximum Degree

Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If for each subset of the size is bounded, for , we define the movement of g as the max over all subsets of . In this paper we classified all of permutation groups on set of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25