The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups on E

The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on E-inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in E-inversive semigroups. Moreover, we show that the set of group t-fuzzy congruences and the set of normal subsemigroups with tip t in a given E-inversive semigroup form two mutually isomorphic modular lattices for every t∈0,1

Rees coextensions of finite tomonoids and free pomonoids

A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We reconsider in this paper the problem of describing the one-element Rees coextensions of a finite, negative tomonoid S, that is, those tomonoids that are by one element larger than S and whose Rees quotient by the poideal consisting of the two smallest elements is isomorphic to S. We show that any such coextension is a quotient of a pomonoid R(S) , called the free one-element Rees coextension of S. We investigate the structure of R(S) and describe the relevant congruences. We moreover introduce a finite family of finite quotients of R(S) from which the coextensions arise in a particularly simple way.(VLID)331182

The approximation of left-continuous t-norms

Abstract A discrete t-norm is a binary operation on a finite subset of the real unit interval fulfilling the same algebraic conditions as t-norms. We show that any left-continuous t-norm can, in a natural sense, be approximated by a discrete t-norm with an arbitrary precision

On idempotent n-ary semigroups

This thesis, which consists of two parts, focuses on characterizations and descriptions of classes of idempotent n-ary semigroups where n >= 2 is an integer. Part I is devoted to the study of various classes of idempotent semigroups and their link with certain concepts stemming from social choice theory. In Part II, we provide constructive descriptions of various classes of idempotent n-ary semigroups. More precisely, after recalling and studying the concepts of single-peakedness and rectangular semigroups in Chapters 1 and 2, respectively, in Chapter 3 we provide characterizations of the classes of idempotent semigroups and totally ordered idempotent semigroups, in which the latter two concepts play a central role. Then in Chapter 4 we particularize the latter characterizations to the classes of quasitrivial semigroups and totally ordered quasitrivial semigroups. We then generalize these results to the class of quasitrivial n-ary semigroups in Chapter 5. Chapter 6 is devoted to characterizations of several classes of idempotent n-ary semigroups satisfying quasitriviality on certain subsets of the domain. Finally, Chapter 7 focuses on characterizations of the class of symmetric idempotent n-ary semigroups. Throughout this thesis, we also provide several enumeration results which led to new integer sequences that are now recorded in The On-Line Encyclopedia of Integer Sequences (OEIS). For instance, one of these enumeration results led to a new definition of the Catalan numbers

Systems of difference equations as a model for the Lorenz system

We consider systems of difference equations as a model for the Lorenz system of differential equations. Using the power series whose coefficients are the solutions of these systems, we define three real functions, that are approximation for the solutions of the Lorenz system

Hyperidentities and Related Concepts, I

This survey article illustrates many important current trends and perspectives for the field including classification of hyperidentities, characterizations of algebras with hyperidentities, functional representations of free algebras, structure results for bigroups, categorical questions and applications. However, the paper contains new results, too