order equivalent triangular norms in this paper an equivalence relation on the class of t norms induced by a t partial order is provided and discussed the equivalence classes linked to some special t norms are characterized as well as some properties preserved by the introduced equivalence defining the set of incomparable elements with respect to the t partial order this set is deeply investigated finally we give an answer to a recently posed open problem

scale invariant solutions to partial differential equations of fractional order with a moving boundary condition in this paper we give similarity solutions of partial differential equations of fractional order with a moving boundary condition the solutions are given in terms of a generalized wright function the time fractional caputo derivative and two types of space fractional derivatives are considered the scale invariant variable and the form of the solution of the moving boundary are obtained by the lie group analysis a comparison between the solutions corresponding to two types of fractional derivative is also given

on ordinal sums of triangular norms on bounded lattices ordinal sums have been introduced in many different contexts e g for posets semigroups t norms copulas aggregation operators or quite recently for hoops in this contribution we focus on ordinal sums of t norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets necessary and sufficient conditions are provided for an ordinal sum operation yielding again a t norm on some bounded lattice whereas the operation is determined by an arbitrary selection of subintervals as carriers for arbitrary summand t norms by such also the structure of the underlying bounded lattice is investigated further it is shown that up to trivial cases there are no ordinal sum t norms on product lattices in general

stabilization of the lattice boltzmann method using the ehrenfests coarse graining idea the lattice boltzmann method lbm and its variants have emerged as promising computationally efficient and increasingly popular numerical methods for modeling complex fluid flow however it is acknowledged that the method can demonstrate numerical instabilities e g in the vicinity of shocks we propose a simple technique to stabilize the lbm by monitoring the difference between microscopic and macroscopic entropy populations are returned to their equilibrium states if a threshold value is exceeded we coin the name ehrenfests steps for this procedure in homage to the vehicle that we use to introduce the procedure namely the ehrenfests coarse graining idea

characterizing when an ordinal sum of t norms is a t norm on bounded lattices one of the most important operators in soft computing are the triangular norms t norms as well as the combination among them the ordinal sum of triangular norms on 0 1 has been used to construct other triangular norms however on a bounded lattice an ordinal sum of t norms may not be a t norm several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t norms is in fact a t norm moreover we show that a large set of ordinal sums verify these conditions hence they are very interesting in order to verify whether an ordinal sum on a bounded lattice is a t norm for a particular family of t norms

medians and nullnorms on bounded lattices nullnorms are generalizations of triangular norms and triangular conorms with a zero element in the interior of the unit interval in this paper we work on nullnorms which are defined on an arbitrary bounded lattice we introduce a general median based method for constructing nullnorms by means of triangular norms and triangular conorms furthermore we highlight a significant difference between the existence and representation of idempotent nullnorms on chains distributive bounded lattices and general bounded lattices

distributive n ary semicopulas on lattices in the present paper definitions of an n ary semicopula on a bounded lattice l a distributive n ary semicopula on l and an infinite distributive n ary semicopula on l are introduced a relation between the set of all bounded lattices l with a distributive n ary semicopula on l and the set of all bounded lattices l with a distributive m ary semicopula on l where 2 n 2 m n m is obtained the method is given for investigation of the following questions a description of all bounded lattices l such that every n ary semicopula on l is distributive and a description of all complete lattices l such that every n ary semicopula on l is infinite distributive

a general method for constructing left continuous t norms a new method for constructing left continuous t norms is introduced and analyzed in this paper we shall construct via embedding a left continuous t norm from any countable residuated totally and densely ordered commutative integral monoid moreover we can construct a left continuous t norm from any countable totally ordered commutative integral monoid which is not necessarily densely ordered and residuated a special case the embedding of such monoids on lexicographic product spaces is investigated in detail and several examples are demonstrated the results shed some light to chang s mv algebra to a recently proposed extraordinary t norm and to the standard semantics of the recently introduced logic ii mtl of hajek

an order induced by nullnorms and its properties abstract in this paper an order induced by nullnorms on bounded lattices is given and discussed we define the set of incomparable elements with respect to the order induced by a nullnorm also by defining such an order an equivalence relation on the class of nullnorms is defined and this equivalence is deeply investigated

semi t operators on bounded lattices abstract we study semi t operators on bounded lattices and show the existence of semi t operators using the fact that there exist some pseudo t norms and pseudo t conorms on the arbitrary fixed bounded lattice l as a by product some constructive approaches to semi t operators are discussed using these approaches we obtain the least semi t operators and the greatest semi t operators on bounded lattices a partial order relation is also defined based on the semi t operator and some properties of this relation are examined

on the direct decomposability of pseudo t norms t norms and implication operators on product lattices in this paper we discuss the direct decomposability of pseudo t norms and t norms on a product lattice characterize the implication operator on a product lattice that is a direct product of two implication operators and study the direct decomposability of s implications r implications n reciprocal r implications and n reciprocal ql implications on a product lattice

on the direct decomposability of strong negations and s implication operators on product lattices in this paper we discuss the direct product of strong negations we characterize strong negations on product lattices that are direct products of strong negations furthermore we present a method for constructing t norms on product lattices which are not direct products this method is quite general and useful to generate a wide class of such t norms and solves an open problem posed in 2003 by jenei and de baets finally we study direct decompositions of s implication operators on product lattices

non negativity and stability analyses of lattice boltzmann method for advection diffusion equation stability is one of the main concerns in the lattice boltzmann method lbm the objectives of this study are to investigate the linear stability of the lattice boltzmann equation with the bhatnagar gross krook collision operator lbgk for the advection diffusion equation ade and to understand the relationship between the stability of the lbgk and non negativity of the equilibrium distribution functions edfs this study conducted linear stability analysis on the lbgk whose stability depends on the lattice peclet number the courant number the single relaxation time and the flow direction the von neumann analysis was applied to delineate the stability domains by systematically varying these parameters moreover the dimensionless edfs were analyzed to identify the non negative domains of the dimensionless edfs as a result this study obtained linear stability and non negativity domains for three different lattices with linear and second order edfs it was found that the second order edfs have larger stability and non negativity domains than the linear edfs and outperform linear edfs in terms of stability and numerical dispersion furthermore the non negativity of the edfs is a sufficient condition for linear stability and becomes a necessary condition when the relaxation time is very close to 0 5 the stability and non negativity domains provide useful information to guide the selection of dimensionless parameters to obtain stable lbm solutions we use mass transport problems to demonstrate the consistency between the theoretical findings and lbm solutions

on the t partial order and properties for a t norm t on 0 1 a partial order t was recently defined and studied in this study for any fixed email protected 0 1 we define the set of incomparable elements according to t and this set is deeply investigated by means of the equivalence relation defined in 14 it is shown the set 0 1 denoting the set of all equivalence classes on t norms on 0 1 is uncountably infinite finally with the help of any t norm t on 0 1 it is obtained that the family t l l 0 1 of t norms on 0 1 if t is a divisible t norm then it is obtained that 0 1 t l is a lattice thus we give an answer to an open problem in 10

internal direct product of integral ν distributive binary aggregation functions and the classification of all integral ν distributive binary aggregation functions of length 3 we present some relations between an external direct product and an internal direct product of a family of integral distributive binary aggregation functions relations between a direct decomposition of the unit and a family of pairwise comaximal elements in a lattice with an integral distributive binary aggregation function are investigated using these results the classification of all integral distributive binary aggregation functions on a lattice of length 3 and a description of all lattices of length 3 with an integral distributive binary aggregation function are given

stability and stabilization of the lattice boltzmann method we revisit the classical stability versus accuracy dilemma for the lattice boltzmann methods lbm our goal is a stable method of second order accuracy for fluid dynamics based on the lattice bhatnager gross krook method lbgk the lbgk scheme can be recognized as a discrete dynamical system generated by free flight and entropic involution in this framework the stability and accuracy analysis are more natural we find the necessary and sufficient conditions for second order accurate fluid dynamics modeling in particular it is proven that in order to guarantee second order accuracy the distribution should belong to a distinguished surface the invariant film up to second order in the time step this surface is the trajectory of the quasi equilibrium distribution surface under free flight the main instability mechanisms are identified the simplest recipes for stabilization add no artificial dissipation up to second order and provide second order accuracy of the method two other prescriptions add some artificial dissipation locally and prevent the system from loss of positivity and local blowup demonstration of the proposed stable lbgk schemes are provided by the numerical simulation of a one dimensional 1d shock tube and the unsteady 2d flow around a square cylinder up to reynolds number mathrm re ensuremath sim 20 phantom rule 0 2em 0ex 000

characterization of uninorms on bounded lattices in this paper we propose a characterization of uninorms on a general bounded lattice l by means of a sextuple of a triangular norm a triangular conorm and four aggregation functions on l observe that in the case when l is a chain it is enough to consider a triple consisting of a t norm a t conorm and an averaging aggregation function an example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown note that this cannot happen if we consider uninorms acting on a chain two general constructions of uninorms on l are added letting a t norm a t conorm linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions

distributive and infinitely distributive t norms on complete lattices abstract a relation between the direct decomposability of an infinitely distributive t norm on a complete lattice l and direct decompositions of the neutral element 1 of l is obtained some useful applications of this relation are given in particularly the description of all t 1 lattices without infinitely distributive t norms on complete lattices and the description of all distributive t norms on lattices of length 2 are given the paper also contains the solutions of two open problems

pseudo t norms and implication operators direct products and direct product decompositions in this paper we further study the pseudo t norms and implication operators on a complete brouwerian lattice and discuss their direct products and direct product decompositions

on the direct decomposability of t norms on product lattices in this paper a method is presented for constructing t norms on product lattices in other words commutative partially ordered integral monoids over product lattices which are not direct products the method is fairly general and allows to generate a broad class of such t norms this solves an open problem posed in 1999 by de baets and mesiar

pairwise comaximal elements and the classification of all ν distributive triangular norms of length 3 for a lattice with a distributive t norm one useful inequality is obtained theorems on relations between a family of pairwise comaximal elements and a direct decomposition of the unit in a lattice with a distributive t norm have given using these results the description of all distributive triangular norms of length 3 and all lattices of length 3 with a distributive t norm have obtained

nullnorms on bounded lattices nullnorms are generalization of triangular norms and triangular conorms with a zero element in the interior of the unit interval in this paper we generalize nullnorms to an arbitrary bounded lattices we show the existence of nullnorms with zero element a for arbitrary element a l 0 1 using the fact that some t norms and t conorms on an arbitrary fixed bounded lattice l always exist as a by product we give a method of constructing nullnorms using this method we obtain also the smallest nullnorm and the greatest nullnorm with given zero element a some other construction methods for nullnorms are also added

infinitely distributive t norms on complete lattices and pseudo complements in this paper we have introduced the concepts of t prime element t prime radical element and t semi prime element and have studied their properties we have investigated the construction methods of new infinitely distributive t norms from given infinitely distributive t norms by means of t prime elements and pseudo complements if every element of l is t prime radical element then we show that l is a complete brouwerian lattice and email protected if l is an algebraic lattice t is a t norm on l and every compact element of l is idempotent then we obtain that email protected we show that l r is a complete lattice and that the restriction of t to l r is an infinitely distributive t norm on l r when t is an infinitely distributive t norm on l and 0 is a t prime we present infinitely distributive t norms on a complete sublattice l and study their properties