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In [13], an algebraic approach to the natural structure of domains of linguistic variables was introduced. In this approach, every linguistic domain can be interpreted as an algebraic structure called a hedge algebra. In this paper, a refinement structure of hedge algebras based on free distributive lattices generated by linguistic hedge operations will be examined in order to model structure of linguistic domains more properly. In solving this question, we restrict our consideration to the specific...

Let $X_i$, $1\le i\le N$, be $N$ independent random variables (i.r.v.) with distribution functions (d.f.) $F_i(x,\Theta )$, $1\le i\le N$, respectively, where $\Theta$ is a real parameter. Assume furthermore that $F_i(·,0)=F(·)$ for $1\le i\le N$. Let $R=(R_1,...,R_N)$ and $R^{+}=(R_1^{+},...,R_N^{+})$ be the rank vectors of $X=(X_1,...,X_N)$ and $\left|X\right|=\left(\right|X_1|,...,|X_N\left|\right)$, respectively, and let $V=(V_1,...,V_N)$ be the sign vector of $X$. The locally most powerful rank tests (LMPRT) $S=S\left(R\right)$ and the locally most powerful signed rank tests (LMPSRT) $S=S(R^{+},V)$ will be found for testing $\Theta =0$ against $\Theta >0$ or $\Theta <0$ with $F$ being arbitrary and with $F$ symmetric, respectively.

The aim of this paper is to establish theorems on the absolute continuity of translation as well as scale invariant statistics in general, from which the related results by Hodges-Lehmann and Puri-Sen follow. The continuity relations between the joint cdf of a random vector and its marginal cdf's are also considered.

CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7   1. Definition and characterization of generalized Post algebras............................................. 7   2. Post subalgebras...

Dans [8], les auteurs ont construit une résolution injective minimale d’un module instable dans la catégorie des modules instables . A partir de cette résolution, un résultat de type conjecture de Segal a été obtenu pour un certain spectre de Thom. Le but de cet article est de refaire ces résultats pour les . Etant donné un premier impair $p$, on construit dans ce travail un complexe de Koszul dans la catégorie des modules instables sur l’algèbre de Steenrod modulo $p$. Une résolution injective d’un...

Višek [3] and Culpin [1] investigated infinite binary sequence $X=(X_1,X_2,\cdots )$ with $X_i$ taking values $0$ or $1$ at random. They investigated also real mappings $H\left(X\right)$ which have the uniform distribution on $[0;1]$ (notation $𝒰(0;1)$). The problem for $n$-ary sequences is dealt with in this paper.