quasi and pseudo inverses of monotone functions and the construction of t norms abstract several properties of quasi and pseudo inverses of a non decreasing real function are discussed based on a result of schweizer and sklar for a given triangular norm t and non decreasing function f a construction method leading to a commutative fully ordered semigroup on the unit interval is given a similar construction based on the pseudo inverse implies that the resulting operation will be bounded from above by the minimum but then the associativity may be violated several sufficient conditions for constructing new t norms from a given one and a non decreasing function f based on its quasi inverses and on its pseudo inverse respectively are discussed together with illustrative examples

existence and stability of periodic solutions for parabolic systems with time delays this paper is concerned with the existence and stability time periodic solutions for a class of coupled parabolic equations with time delay and time delays may appear in the nonlinear reaction functions the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement our approach to the problem is by the method of upper and lower solution and using schauder fixed point theorem some methods for proving the stability of the periodic solution are also given the results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system finally a model arising from chemistry is used to illustrate the obtained results

additive generators of border continuous triangular norms the characterization of all additive generators of border continuous triangular norms conorms is introduced it is also shown that the pseudo inverse of the cantor function is an additive generator with a dense set of all points of discontinuity in 0 1 yielding a border continuous triangular conorm

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

asymptotic periodicity in diffusive logistic equations with discrete delays has been the object of intensive analysis by numerous authors l 6 as a model of single species population growth it is known that time delay has a tendency to produce oscillations 2 5 61 in 1 which is nonoscillatory when r 0 in an autonomous delay system modeling two competing species time delays can even lead to chaotic behavior 4 if the diffusion is taken into account in the growth rate as well then time delay may cause random and blow up effects in the parabolic logistic delay equation 7 nonlinear periodic diffusion equations arise naturally in population models s 12 where the birth and death rates rates of diffusion rates of interaction and environmental carrying capacities are periodic on a seasonal scale in this paper we study the following periodicparabolic logistic equation with instantaneous and delay effects duct x 3t au t x u t x a t x m x u t x

further properties of reversible triangular norms in this paper we present some properties of discontinuous reversible triangular norms two of them seem to be important 1 a reversible t norm t which possesses only trivial idempotent elements must be archimedean 2 if t is a discontinuous reversible t norm and has non trivial idempotent elements then t is an ordinal sum of two t noms the one on the lower part of the unit square dominating lukasiewcz t norm the other being reversible and archimedean consequently no left continuous t norm that is not continuous is reversible therefore the question of reversibility of discontinuous t norms is reducible to the case when the t norms in question possess trivial idempotent elements only moreover we have completely characterized the reversibility of t the reverse of a reversible t norm t

a family of strict and discontinuous triangular norms answers to some questions about triangular norms are given precisely a procedure of construction of infinitely many triangular norms is obtained one for each operation n2 n such that n is a strictly ordered commutative semigroup each of them is discontinuous at each point of a dense subset of 0 1 2 and it satisfies the condition t kx y t x ky for infinitely many k 0 1

on triangular norm based propositional fuzzy logics abstract fuzzy logics based on triangular norms and their corresponding conorms are investigated an affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given tautologies contradictions and contigencies with respect to such fuzzy logics are studied in particular for the important cases of min max and ukasiewicz logics finally fundamental t norm based fuzzy logics are shown to provide a gradual transition between min max and ukasiewicz logics

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

a note on the ordinal sum theorem and its consequence for the construction of triangular norms in this paper the well known ordinal sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms t norms among them one can find several new families of left continuous t norms too

triangular norms position paper iii continuous t norms this third and last part of a series of position papers on triangular norms for parts i and ii see e p klement r mesiar e pap triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press e p klement r mesiar e pap triangular norms position paper ii general constructions and parameterized families submitted for publication presents the representation of continuous archimedean t norms by means of additive generators and the representation of continuous t norms by means of ordinal sums with archimedean summands both with full proofs finally some consequences of these representation theorems in the context of comparison and convergence of continuous t norms and of the determination of continuous t norms by their diagonal sections are mentioned

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

accelerated monotone iterative methods for finite difference equations of reaction diffusion this paper is concerned with numerical methods for a finite difference system of reaction diffusion convection equation under nonlinear boundary condition various monotone iterative methods are presented and each of these methods leads to an existence comparison theorem as well as a computational algorithm for numerical solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function application is given to a model problem from chemical engineering and some numerical results including a test problem with known analytical solution are presented to illustrate the various rates of convergence of the iterations

common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces in the first part of this paper we generalize results on common fixed points in ordered cone metric spaces obtained by i altun and g durmaz i altun g durmaz some fixed point theorems on ordered cone metric spaces rend circ mat palermo 58 2009 319 325 and i altun b damnjanovic and d djoric i altun b damnjanovic d djoric fixed point and common fixed point theorems on ordered cone metric spaces appl math lett 2009 doi 10 1016 j aml 2009 09 016 by weakening the respective contractive condition then the notions of quasicontraction and g quasicontraction are introduced in the setting of ordered cone metric spaces and respective common fixed point theorems are proved in such a way known results on quasicontractions and g quasicontractions in metric spaces and cone metric spaces are extended to the setting of ordered cone metric spaces examples show that there are cases when new results can be applied while old ones cannot

a characterization of the hamacher family of t norms abstract starting from a fuzzy conjunction there are two main ways of defining a fuzzy implication operator a functional equation for t norms is obtained and studied which describes the equality of these two implications when the underlying conjunction has a particular form defined from a t norm the solution makes clear that this functional equation together with an additional condition provides a complete characterization of the hamacher family of t norms having positive parameter

periodic solutions of parabolic systems with time delays existence of maximal and minimal periodic solutions of a coupled system of parabolic equations with time delays and with nonlinear boundary conditions is discussed the proof of the existence theorem is based on the method of upper and lower solutions and its associated monotone iterations this method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic parabolic system an application is given to a competitor competitor mutualist model which consists of a coupled system of three reaction diffusion equations with time delays

existence and monotone scheme for time periodic nonquasimonotone reaction diffusion systems application to autocatalytic chemistry abstract the article considers time periodic reaction diffusion systems the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions dirichlet and robin boundary conditions are included the existence of periodic solutions is shown under appropriate conditions monotone approximating sequences closing in on the solutions from above and below are constructed application to autocatalysis in chemistry is given

stability and attractivity of periodic solutions of parabolic systems with time delays abstract this paper is concerned with the existence stability and global attractivity of time periodic solutions for a class of coupled parabolic equations in a bounded domain the problem under consideration includes coupled system of parabolic and ordinary differential equations and time delays may appear in the nonlinear reaction functions our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement using schauder fixed point theorem while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme the results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system applications are also given to three lotka volterra reaction diffusion model problems and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

continuous triangular subnorms triangular subnorms are associative commutative non decreasing operations on the unit interval upper bounded by the minimum continuous triangular subnorms are shown to be ordinal sum of archimedean continuous t subnorms with at most one proper t subnorm summand special attention is paid to generate continuous t subnorms an application of continuous t subnorms to the construction of left continuous t norms is shown several illustrative examples are included

fixed point results for generalized quasicontraction mappings in abstract metric spaces in this paper we introduce the concept of generalized quasicontraction mappings in an abstract metric space by using this concept we construct an iterative process which converges to a unique fixed point of these mappings the result presented in this paper generalizes the banach contraction principle in the setting of metric space and a recent result of huang zhang for contractions we also validate our main result by an example

pictorial representations of fuzzy connectives part i cases of t norms t conorms and averaging operators part i of this paper shows a number of examples of existing t norms and t conorms which are known as good models of fuzzy set theoretic intersection and union and then the pictorial representations of t norms and t conorms are made with the aid of a computer several new examples of t norms and t conorms are also given averaging operators between min and max are summarized and their pictorial representations are also made

control and separating points of modular functions let l be a complemented or sectionally complemented lattice and let x be a locally convex linear space we prove the existence of an x valued control for uniformly exhaustive sequences of x valued modular functions on l moreover if l is cr complete we prove that every countable family of cr o c nonatomic group valued modular functions on l admits separating points

on a family of t norms abstract this paper deals with the study of a certain type of dependence between the values of a t norm and those of its diagonal a family of t norms based on the ukasiewicz t norm is obtained

observations on the monoidal t norm logic the paper is a contribution to the theory of the monoidal t norm based logic mtl and stronger logics analogous to the well known extensions of the basic fuzzy logic lukasiewicz godel and product logic main attention is payed to the logic iimtl mtl plus the characteristic axioms ii1 ii2 of product logic

t sum of bell shaped fuzzy intervals the usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of zadeh s extension principle based on a t norm t a t norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class it is important to know which t norms are consistent with a particular type of fuzzy intervals recently dombi and gyorbiro proved that addition is closed if the dombi t norm is used with two bell shaped fuzzy intervals a result proved by mesiar on a strict t norm based shape preserving additions of lr fuzzy intervals with unbounded support is recalled as applications we define a broader class of bell shaped fuzzy intervals then we study t norms which are consistent with these particular types of fuzzy intervals dombi and gyorbiro s results are special cases of the results described in this paper

a reaction diffusion system of a competitor competitor mutualist model we investigate the homogeneous dirichlet problem and neumann problem to a reactiondiffusion system of a competitor competitor mutualist model the existence uniqueness and boundedness of the solutions are established by means of the comparison principle and the monotonicity method for the dirichlet problem we study the existence of trivial and nontrivial nonnegative equilibrium solutions and their stabilities for the neumann problem we analyze the contant equilibrium solutions and their stabilities the main method used in studying of the stabilities is the spectral analysis to the linearized operators the o d e problem to the same model was proposed and studied by b rai h i freedman and j f addicott

coupled nonlinear parabolic systems with time delays a coupled system of parabolic equations with time delays is investigated by the method of upper lower solutions it is shown by using upper and lower solutions as coupled initial iterations that the corresponding sequences converge monotonically to a unique solution of the system this convergence leads to an existence comparison theorem which is useful for studying the asymptotic behavior of the solution this method is extended to a coupled system of integro differential equations and systems of parabolic ordinary equations applications are given to some model problems in ecology and nuclear engineering including the stability property of a steady state solution

periodic solution and oscillation in a competition model with diffusion and distributed delay effects as experimental results reveal the growth rates diffusion rates and interaction coefficients of biological species are very sensitive dependent variables of external environmental conditions a slight change in those conditions may effect the whole evolution process nonlinear periodic diffusion equations arise naturally in population models l 5 where the birth and death rates rates of diffusion and environmental carrying capacities are periodic on a seasonal scale the following periodic parabolic logistic boundary value problem describes the evolution of a population u subject to diffusion having self limitation in growth with periodically varying environmental parameters

the use of fuzzy outranking relations in preference modelling this paper deals with preference modelling in the context of decision aid in this framework conflicting systems of logic uncertain knowledge ambiguous positions are always present in order to tackle this problem a multiple criteria methodology is proposed mainly based on fuzzy outranking relations introduced both at one dimensional and multi dimensional levels some properties of outranking relations are investigated such relations are then combined using fuzzy logical connectives to generate relational systems of fuzzy preferences that are shown to be very useful to reflect the vagueness of information in the various preference situations that may be considered in the modelling process

periodic solutions of coupled semilinear parabolic boundary value problems the study of periodic solutions to parabolic differential systems goes back to j fourier who investigated the linear heat equation for the determination of temperature oscillation on earth cf 141 in recent years attention has been given to nonlinear parabolic boundary value problems cf l 2 4 6 7 15 16 however most of the discussions in the literature are concerned with a single parabolic equation under dirichlet type boundary condition due to the recent development in the biochemical and biological fields there arise various types of reactiondiffusion systems e g see lo 121 an interesting problem in some of these systems such as the belousov zhabotinskii reaction model is an understanding of the oscillating nature of the solution in this paper we investigate periodic solutions for a coupled system of parabolic boundary value problems in a one dimensional domain under various boundary conditions specifically the equations under consideration are given by

on cone metric spaces a survey abstract using an old m krein s result and a result concerning symmetric spaces from s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces banach j math anal 5 1 2011 38 50 we show in a very short way that all fixed point results in cone metric spaces obtained recently in which the assumption that the underlying cone is normal and solid is present can be reduced to the corresponding results in metric spaces on the other hand when we deal with non normal solid cones this is not possible in the recent paper m a khamsi remarks on cone metric spaces and fixed point theorems of contractive mappings fixed point theory appl 2010 7 pages article id 315398 doi 10 1115 2010 315398 the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant also that underlying banach space and the associated cone subset are not necessary in fact khamsi s approach includes a small class of results and is very limited since it requires only normal cones so that all results with non normal cones which are proper extensions of the corresponding results for metric spaces cannot be dealt with by his approach

periodic solutions of parabolic systems with nonlinear boundary conditions this paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions the approach to the problem is by the method of upper and lower solutions and its associated monotone iterations this method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial boundary value problems a sufficient condition for the stability of a periodic solution is also given these results are applied to three model problems arising from chemical kinetics ecology and population biology

continuity of left continuous triangular norms with strong induced negations and their boundary condition first a characterization is given for the continuity of a class of left continuous triangular norms it is established that a left continuous triangular norm with strong induced negation is continuous if and only if it is strictly increasing on the domain where its value is positive second we show that axioms of a left continuous triangular norm with strong induced negation are not independent namely the boundary condition follows from the other axioms

on reversible triangular norms abstract we completely characterize those continuous triangular norms which are recently called reversible this characterization is a step toward the solution of an open problem raised by kimberling publ math dabrecen 20 1973 21 39 25 years ago

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

the global attractor of a competitor competitor mutualist reaction diffusion system with time delays abstract the aim of this paper is to investigate the asymptotic behavior of time dependent solutions of a three species reaction diffusion system in a bounded domain under a neumann boundary condition the system governs the population densities of a competitor a competitor mutualist and a mutualist and time delays may appear in the reaction mechanism it is shown under a very simple condition on the reaction rates that the reaction diffusion system has a unique constant positive steady state solution and for any nontrivial nonnegative initial function the corresponding time dependent solution converges to the positive steady state solution an immediate consequence of this global attraction property is that the trivial solution and all forms of semitrivial solutions are unstable moreover the state state problem has no nonuniform positive solution despite possible spatial dependence of the reaction and diffusion all the conclusions for the time delayed system are directly applicable to the system without time delays and to the corresponding ordinary differential system with or without time delays

asymptotic behaviour of solutions of periodic competition diffusion system on considere le systeme d equations de reaction diffusion u t k 1 u a bu cv v t k 2 v v d eu fv ou k 1 k 2 a b f sont des fonctions suffisamment lisses definies sur un cylindre ou est un domaine borne lisse de r n

dominance in the family of sugeno weber t norms the dominance relationship between two members of the family of sugeno weber t norms is proven by using a quantifier elimination algorithm further it is shown that dominance is a transitive and therefore also an order relation on this family of t norms

fixed points for generalized contractions and applications to control theory the concepts of weak strong topological contraction and a generalization of banach contraction mappings called p contraction are introduced and used to prove fixed point theorems for self mappings from a topological metric space into itself satisfying topological contraction metric p contraction respectively certain non linear integral equations defined on c a b satisfying generalized lipschitzian conditions can easily be solved by applying these theorems in the sequel we shall study the possibility of optimally controlling the solution of the ordinary differential equation via dynamic programming

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given

numerical analysis of coupled systems of nonlinear parabolic equations this paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method three monotone iteration processes for the finite difference system are presented and the sequences of iterations are shown to converge monotonically to a unique solution of the system including an existence uniqueness comparison theorem a theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary value problem an application to a reaction diffusion model in chemical engineering and combustion theory is given

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

structure of left continuous triangular norms with strong induced negations iii construction and decomposition this paper is the continuation of jenei j appl non classical logics 10 2000 83 92 11 2001 351 366 where the rotation construction and the rotation annihilation construction have been presented respectively both constructions produce left continuous but not continuous triangular norms with strong induced negations here we show that these two constructions allow us to define indecomposability and that each decomposable left continuous triangular norm with strong induced negation can be derived as result of one of the above constructions in this way two general decomposition theorems arise in addition the decomposition of left continuous triangular norms with strong induced negations can be defined in a unique way namely when the decomposition is done by the minimal decomposition point