Relation between neutral element and annihilator in absorption equation

2013 ◽  
Vol 228 ◽  
pp. 145-151
Author(s):  
Sai Hareesh Anamandra ◽  
Prabhakar Akella
Keyword(s):  
Neutral Element

IDEMPOTENT UNINORMS ON FINITE ORDINAL SCALES

2009 ◽  
Vol 17 (01) ◽  
pp. 1-14 ◽  
Author(s):  
BERNARD DE BAETS ◽  
JÁNOS FODOR ◽  
DANIEL RUIZ-AGUILERA ◽  
JOAN TORRENS
Keyword(s):  
Ordinal Scale ◽  
Neutral Element ◽  
Ordinal Scales ◽  
One To One

In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n.

scholarly journals Generalized entropy in expanded semigroups and in algebras with neutral element

2014 ◽  
Vol 88 (3) ◽  
pp. 702-714 ◽  
Author(s):  
Erkko Lehtonen ◽  
Agata Pilitowska
Keyword(s):  
Neutral Element ◽  
Generalized Entropy

STABLE AND SEMISTABLE PROBABILITY MEASURES ON CONVEX CONE

2014 ◽  
Vol 98 (3) ◽  
pp. 390-406
Author(s):  
NAM BUI QUANG ◽  
PHUC HO DANG
Keyword(s):  
Probability Measure ◽  
Convex Cone ◽  
Closed Subgroup ◽  
Multiplicative Group ◽  
Domain Of Attraction ◽  
Neutral Element ◽  
Probability Measures ◽  
Semistable Probability

The study concerns semistability and stability of probability measures on a convex cone, showing that the set$S(\boldsymbol{{\it\mu}})$of all positive numbers$t>0$such that a given probability measure$\boldsymbol{{\it\mu}}$is$t$-semistable establishes a closed subgroup of the multiplicative group$R^{+}$; semistability and stability exponents of probability measures are positive numbers if and only if the neutral element of the convex cone coincides with the origin; a probability measure is (semi)stable if and only if its domain of (semi-)attraction is not empty; and the domain of attraction of a given stable probability measure coincides with its domain of semi-attraction.

An Extension of Semiuninorms: Weak-Neutral Semiuninorms

2017 ◽  
Vol 25 (02) ◽  
pp. 301-316
Author(s):  
Hua-Wen Liu ◽  
Feng Qin
Keyword(s):  
Functional Equations ◽  
Neutral Element ◽  
Restricted Domain ◽  
Multiplicative Constant ◽  
Additive Generator

By weakening the neutral element condition of semiuninorms, we introduce a new concept called weak-neutral semiuninorms (shortly, wn-semiuninorms). After analyzing their structure, several classes of wn-semiuninorms are presented and discussed. Particularly, based on a kind of monotone unary functions which are not necessarily continuous and strictly monotone, we introduce representable wn-semiuninorms and discuss some of their properties in detail. We show that there is no idempotent proper wn-semiuninorm. Each representable wn-semiuninorm is Archimidean but not strictly monotone, and its additive generator is unique up to a positive multiplicative constant under some conditions. In the discussion about the representable wn-semiuninorms, we also characterize the solutions to a class of Cauchy functional equations on a restricted domain.

Structure of Uninorms

1997 ◽  
Vol 05 (04) ◽  
pp. 411-427 ◽  
Author(s):  
János C. Fodor ◽  
Ronald R. Yager ◽  
Alexander Rybalov
Keyword(s):  
Representation Theorem ◽  
Unit Interval ◽  
Neutral Element ◽  
General Representation ◽  
Exhaustive Study

An exhaustive study of uninorm operators is established. These operators are generalizations of t-norms and t-conorms allowing the neutral element lying anywhere in the unit interval. It is shown that uninorms can be built up from t-norms and t-conorms by a construction similar to ordinal sums. De Morgan classes of uninorms are also described. Representability of uninorms is characterized and a general representation theorem is proved. Finally, pseudo-continuous uninorms are defined and completely classified.

The Relations between Implications and Left (Right) Semi-Uninorms on a Complete Lattice

2015 ◽  
Vol 23 (02) ◽  
pp. 245-261 ◽  
Author(s):  
Xiaoying Hao ◽  
Meixia Niu ◽  
Zhudeng Wang
Keyword(s):  
Complete Lattice ◽  
Unit Interval ◽  
Neutral Element ◽  
Order Property ◽  
Triangular Norms

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we study the relations between implications and left (right) semi-uninorms on a complete lattice. We firstly investigate the left (right) semi-uninorms induced by implications, give some conditions such that the operations induced by implications constitute left or right semi-uninorms, and demonstrate that the operations induced by a right infinitely ∧-distributive implication, which satisfies the order property, are left (right) infinitely ∨-distributive left (right) semi-uninorms. Then, we discuss the residual operations of left (right) semi-uninorms and show that left (right) residual operators of strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms are right infinitely ∧-distributive implications that satisfy the order property. Finally, we reveal the relationships between strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms and right infinitely ∧-distributive implications which satisfy the order property.

scholarly journals Polski sukces sukcesu w świetle opracowań leksykograficznych i literatury popularnopsychologicznej

2019 ◽  
Author(s):  
Katarzyna Skowronek
Keyword(s):  
Narrative Analysis ◽  
Meaning Of Life ◽  
Neutral Element ◽  
Contemporary Culture ◽  
Self Help ◽  
Culture Of Success ◽  
Polish Language

In her article the author discusses “success” – one of most important words defining the contemporary culture and people. She asks about the meaning of the word and compares its use in self-help books with the definition found in dictionaries of the Polish language. How is the contemporary “culture of success” created by those “new” meaning profiles? The first part of the analysis concerns the semantics of “success” in selected historical and modern dictionaries. K. Skowronek points out that the word has undergone the process of amelioration: from a neutral element to a positive one. The second part of the article is a narrative analysis. The author presents the semantics of the word in contemporary self-help books. She highlights its individualistic and self-disciplining character. Nowadays, success is synonymous with happiness and the meaning of life. It predominantly entails an obsessive chase while not necessarily a real achievement.

scholarly journals On uninorms and nullnorms on direct product of bounded lattices

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 321-327 ◽  
Author(s):  
Martin Kalina
Keyword(s):  
Partial Order ◽  
Direct Product ◽  
Natural Partial Order ◽  
Neutral Element ◽  
Unit Square ◽  
Special Case

AbstractWe will study uninorms on the unit square endowed with the natural partial order defined coordinate-wise. We will show that we can choose arbitrary pairs of incomparable elements, (a, e) and construct a uninorm whose neutral element is e and annihilator is a. As a special case we construct uninorms which are at the same time also nullnorms (or, expressed another way, we construct proper nullnorms with neutral element). We will also generalize this result to the direct product of two bounded lattices. I.e., we will show that it is possible to construct nullnorms with a neutral element on the direct product of two bounded lattices.

scholarly journals On Neutrosophic Triplet Groups: Basic Properties, NT-Subgroups, and Some Notes

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 289 ◽  
Author(s):  
Xiaohong Zhang ◽  
Qingqing Hu ◽  
Florentin Smarandache ◽  
Xiaogang An
Keyword(s):  
Theoretical Analysis ◽  
Mathematical Structure ◽  
Structural Features ◽  
Neutrosophic Set ◽  
Neutral Element ◽  
Standard Group ◽  
Basic Properties ◽  
Homomorphism Theorem ◽  
Generalized Symmetry ◽  
Group 3

As a new generalization of the notion of the standard group, the notion of the neutrosophic triplet group (NTG) is derived from the basic idea of the neutrosophic set and can be regarded as a mathematical structure describing generalized symmetry. In this paper, the properties and structural features of NTG are studied in depth by using theoretical analysis and software calculations (in fact, some important examples in the paper are calculated and verified by mathematics software, but the related programs are omitted). The main results are obtained as follows: (1) by constructing counterexamples, some mistakes in the some literatures are pointed out; (2) some new properties of NTGs are obtained, and it is proved that every element has unique neutral element in any neutrosophic triplet group; (3) the notions of NT-subgroups, strong NT-subgroups, and weak commutative neutrosophic triplet groups (WCNTGs) are introduced, the quotient structures are constructed by strong NT-subgroups, and a homomorphism theorem is proved in weak commutative neutrosophic triplet groups.

scholarly journals Archimedean components of triangular norms

2005 ◽  
Vol 78 (2) ◽  
pp. 239-255 ◽  
Author(s):  
Erich Peter Klement ◽  
Radko Mesiar ◽  
Endre Pap
Keyword(s):  
Unit Interval ◽  
Neutral Element ◽  
Ordered Semigroup ◽  
Triangular Norms ◽  
Construction Methods

AbstractThe Archimedean components of triangular norms (which turn the closed unit interval into anabelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

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