migrative uninorms and nullnorms over t norms and t conorms in this paper the notions of migrative uninorms and nullnorms over a fixed t norm t and over a fixed t conorm s are introduced and studied all cases when the uninorm u lies in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations of u and t and for all possible combinations of u and s a similar study is done for nullnorms

distributivity equation in the class of 2 uninorms this paper is mainly devoted to solving the functional equation of distributivity between aggregation operators with 2 neutral element our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e g triangular norms conorms uninorms nullnorms and implications one of the recent generalizations covering both uninorms and nullnorms are 2 uninorms which form a class of commutative associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements in this work the distributivity of two binary operators from the class of 2 uninorms is considered in particular all possible solutions of the distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized

on the critical schrodinger bopp podolsky system with general nonlinearities abstract this paper deals with the following nonlinear schrodinger bopp podolsky system u v x u u f u u 5 2 a 2 2 4 u 2 in r 3 where a 0 v c r 3 0 with v lim y v y sup x r 3 v x 0 and f c r r satisfying 0 t f s d s t p with p 2 6 for all t 0 by using some new analytic techniques and new inequalities we prove that the above system admits ground state solutions for all 0 if p 4 6 for all 0 if p 2 4 where 0 is a positive constant determined by a v and p our results extend and complement the existence results in d avenia and g siciliano 2019 which only dealt with the subcritical case

distributivity equations in the class of semi t operators recently the distributivity equations have been discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this study we present the solutions to distributivity between semi t operators previous results related to the distributivity between nullnorms and between semi t operators and semi nullnorms can be obtained as simple corollaries

semiclassical ground state solutions for critical schrodinger poisson systems with lower perturbations abstract in this paper we study the following singularly perturbed schrodinger poisson system e 2 u v x u u f u u 5 x r 3 e 2 u 2 x r 3 where e is a small positive parameter v c r 3 r and f c r r satisfies neither the usual ambrosetti rabinowitz type condition nor any monotonicity condition on f u u 3 by using some new techniques and subtle analysis we prove that there exists a constant e 0 0 determined by v and f such that for e 0 e 0 the above system admits a semiclassical ground state solution v e with exponential decay at infinity we also study the asymptotic behavior of v e as e 0 in particular our results can be applied to the nonlinearity f u u q 2 u for q 3 4 and extend the previous work that only deals with the case in which f u u q 2 u for q 4 6

migrative t norms with respect to continuous ordinal sums abstract in this paper we study and characterize continuous migrative t norms t with respect to a continuous t norm t0 depending on whether is an idempotent element of t0 or not the t0 migrative property restricts the ordinal sum structure of t especially locally i e at or around it outside this well defined neighbourhood of the t norm t can be arbitrary under the only condition of keeping it continuous the investigation exploits the ordinal sum structure of continuous t norms and our former results related to the migrative property

on the migrativity of triangular subnorms the a t migrative triangular subnorms where t stands for the three prototype triangular norms namely the product the lukasiewicz t norm and the minimum are investigated in detail the paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous additive generator is a t migrative with respect to any of the three prototype triangular norms

on the structure of special classes of uninorms in this paper the concept of the reidemeister closure condition is adopted in order to characterize associativity of uninorms with a special attention paid to the class of representable uninorms thus conditions replacing the associativity requirement for such uninorms are given further the attention is focused on the uninorms where the underlying t norm and t conorm are idempotent or induce an involutive negator based on the aforementioned results the structure of these classes of uninorms is fully described

the distributive equations for idempotent uninorms and nullnorms the distributive equations only involving idempotent uninorms and nullnorms are investigated the following two cases are proved i as for a nullnorm with an idempotent uninorm having distributivity the necessary and sufficient conditions are given ii as for an idempotent uninorm with a nullnorm having distributivity the necessary and sufficient conditions are given also

the migrativity equation for uninorms revisited abstract the migrativity equation with interesting applications in decision making and image processing has been extensively discussed involving different kinds of aggregation functions from t norms and t conorms to uninorms nullnorms and some generalizations of them in recent papers the already known results concerning the migrativity of two uninorms are based on the assumption that both uninorms belong to one of the most studied classes of uninorms in this paper we will explore the migrativity equation involving uninorms in a most general setting specifically we will study the migrativity between two uninorms in the cases when the second uninorm lies in any of the most studied classes of uninorms but the first one is any uninorm with no further assumptions we will show along the paper that many new solutions appear from this new point of view that were not included in the previous approaches

migrativity property for uninorms the migrative uninorms over a fixed uninorm with different neutral elements are presented all cases when both uninorms lay in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations the solutions obtained generalize the results where both uninorms have the same neutral elements

on the distributivity of uninorms over nullnorms this paper investigates the functional equation of distributivity of uninorms over nullnorms we consider the case where the uninorm is continuous in 0 1 2 or is representable it has been proved that the absorbing element of the nullnorm is an idempotent element of the uninorm if the distributive equation holds and then combining the structures of the uninorm and the nullnorm we give the characterization of the pair of the functions of the uninorm and the nullnorm moreover when the nullnorm is continuous we obtain the sufficient and necessary conditions under which the distributive equation holds

on continuous triangular norms that are migrative in this paper we completely describe all continuous migrative triangular norms since the migrative property excludes both idempotent and nilpotent classes the characterization and construction is carried out by solving a functional equation for additive generators of strict t norms we also study cases when the construction results in a smooth generator

a generalization of the migrativity property of aggregation functions this paper brings a generalization of the migrativity property of aggregation functions suggested in earlier work of some of the present authors by imposing the a migrativity property of durante and sarkoci for all values of a instead of a single one replacing the algebraic product by an arbitrary aggregation function b naturally leads to the properties of a b migrativity and b migrativity this generalization establishes a link between migrativity and a particular case of aczel s general associativity equation already considered by cutello and montero as a recursive formula for aggregation following a basic investigation emphasis is put on aggregation functions that can be represented in terms of an additive generator more specifically strict t norms strict t conorms and representable uninorms

on migrativity property for uninorms recently u 0 migrative uninorms u were introduced and discussed where u and u 0 are two uninorms with neutral element e in this paper we will further study u 2 migrative uninorms u 1 where u 1 and u 2 are two uninorms with different neutral elements e 1 and e 2 respectively all cases when the uninorm u 1 and u 2 are in different families out of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations of u 1 and u 2

self focusing with fourth order dispersion we analyze self focusing and singularity formation in the nonlinear schrodinger equation nls with high order dispersion i psi t pm delta q psi psi 2 sigma psi 0 in the isotropic mixed dispersion nls i psi t delta psi epsilon delta 2 psi psi 2 sigma psi 0 and in nonisotropic mixed dispersion nls equations which model propagation in fiber arrays

on properties of uninorms with underlying t norm and t conorm given as ordinal sums uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory this paper presents some properties of uninorm like operations for which the underlying operations are given by ordinal sums if the underlying operations of a uninorm are given by ordinal sums then the cartesian product of the union of two arbitrary intervals one in 0 e and the other in e 1 where e is the neutral element of the uninorm is a set closed under the uninorm when transposing such a cartesian product to the unit square one obtains a uninorm like operation as a result we have described the uninorm like operations for which the underlying operations are basic pseudo t norms and pseudo t conorms and one of them is idempotent

positive solutions for schrodinger poisson equations with a critical exponent abstract in this paper we establish the existence of a positive solution of the schrodinger poisson equations with a critical sobolev exponent the methods used here are based on the concentration compactness principle of p l lions and methods of brezis and nirenberg

on the planar schrodinger poisson system with the axially symmetric potential abstract in this paper we develop some new variational and analytic techniques to prove that the following planar schrodinger poisson system u v x u u f u x r 2 u 2 x r 2 admits a nontrivial solution and a ground state solution possessing the least energy in the axially symmetric functions space where v x is axially symmetric our results improve and extend the ones in the case v 1 and f u u p 2 u with 2 p 6 in particular we use the assumption that 2 v x v x x is bounded from below instead of the usually one that lim x v x 1 moreover v x is even admitted to be unbounded

ground state solutions of nehari pankov type for schrodinger equations with local super quadratic conditions abstract consider the semilinear schrodinger equation u v x u f x u x r n u h 1 r n where both v x and f x u are periodic in x 0 belongs to a spectral gap of v and f x u is subcritical and allowed to be super linear at some x r n and asymptotically linear at the other x r n in the existing works in the literature it is commonly assumed that lim u 0 u f x s d s u 2 uniformly in x r n to obtain the existence of ground state solutions or infinitely many geometrically distinct solutions in this paper for the first time we prove the existence of ground state solutions and infinitely many geometrically distinct solutions under the weaker super quadratic condition lim u 0 u f x s d s u 2 a e x g just for some domain g r n

heegaard surfaces and measured laminations i the waldhausen conjecture we give a proof of the so called generalized waldhausen conjecture which says that an orientable irreducible atoroidal 3 manifold has only finitely many heegaard splittings in each genus up to isotopy jaco and rubinstein have announced a proof of this conjecture using different methods

on locally internal monotonic operations this paper deals with monotonic binary operations f 0 1 2 0 1 with the property called locally internal property that the value at any point x y is always one of its arguments x y after stating a theorem that characterizes this kind of operations some special cases are studied in detail by considering additional properties of the operation commutativity existence of a neutral element and associativity in case of locally internal associative monotonic operations with neutral element a characterization theorem gives an improvement of a well known theorem of czogala and drewniak on idempotent associative and increasing operations with neutral element as well as an improvement of a characterization theorem for left and right continuous idempotent uninorms

on distributivity equations for uninorms over semi t operators recently dryga generalized nullnorms and t operators and introduced semi t operators by eliminating commutativity from the axioms of t operators distributivity equations were investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we give out the solutions of distributivity equations for uninorms over semi t operators previous results about distributivity equations for uninorms over nullnorms can be obtained as corollaries

generalizing the migrativity of continuous t norms this paper generalizes the migrativity of triangular norms t norms for short precisely we find those continuous t norms t which satisfy t l 1x l 2y email protected 3t x y where l email protected 0 1 i 1 2 3 are given it is worth pointing out that this paper provides a new characterization of the product t norm

an addendum to migrative uninorms and nullnorms over t norms and t conorms the aim of this paper is to complete some results in the paper migrative uninorms and nullnorms over t norms and t conorms 1 that paper studied the alpha migrativity of uninorms over t norms here migrativity in the other direction is investigated

supermigrative semi copulas and triangular norms a semi copula s 0 1 2 0 1 is called supermigrative if it is commutative and satisfies s ax y s x ay for all email protected 0 1 and for all x email protected 0 1 such that y

a characterization of a class of uninorms with continuous underlying operators in this paper all uninorms locally internal in the region a e given by the complement in 0 1 2 of 0 e 2 e 1 2 where e is the neutral element of the uninorm having continuous underlying operators are studied and characterized by distinguishing some cases when the underlying t norm and t conorm are not given by ordinal sums it is proved that uninorms locally internal in a e are in fact all possible uninorms with these underlying operators except when both the t norm and the t conorm are strict in which case there is also the class of representable uninorms leading to a finite number of possibilities when at least one of the continuous underlying operators is given by an ordinal sum again there are other possible uninorms than those that are locally internal in a e but all uninorms with this property are also characterized in this case infinitely many possibilities can appear depending on the set of idempotent elements of the uninorm

a new structure for uninorms on bounded lattices abstract this article investigates the construction of uninorms on bounded lattices first by using the fact that triangular norms t norms and triangular conorms t conorms on an arbitrary bounded lattice always exist we introduce a new construction of uninorms on arbitrary bounded lattices with the neutral element then we illustrate how our new construction method is different from some existing methods for the construction of uninorms on bounded lattices some illustrative examples for the construction of uninorms on bounded lattices are provided

the modularity condition for uninorms and t operators in this work we study the functional equation given by the modularity condition f x g y z g f x y z for all z x where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

migrativity equation for uninorms with continuous underlying operators abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theorem as a kind of restricted general associative equation the migrativity equation has been proven to be useful in a wide range of fields like decision making aggregation of information image processing and so on in the literature the already existing results concerning the migrativity equation for two uninorms are based on the assumption that one of the uninorms belongs to one of the most studied classes of uninorms or that they have the same neutral element in this study we will explore the migrativity equation involving uninorms in a most general setting to be specific we investigate the migrativity between two uninorms with only continuous underlying operators then many new solutions of the equation are fully characterized from this new point of view

bimigrativity of binary aggregation functions we introduce the notions of bimigrativity and total bimigrativity of an aggregation function w r t another aggregation function as a natural generalization of the notions of migrativity and bisymmetry we investigate the role of the presence of neutral or absorbing elements we also pay attention to the class of weighted quasi arithmetic means a well known class of bisymmetric aggregation functions

heegaard structure respects complicated jsj decompositions let m be a 3 manifold with torus boundary components t 1 and t 2 let phi t 1 rightarrow t 2 be a homeomorphism m phi the manifold obtained from m by gluing t 1 to t 2 via the map phi and t the image of t 1 in m phi we show that if phi is sufficiently complicated then any incompressible or strongly irreducible surface in m phi can be isotoped to be disjoint from t it follows that every heegaard splitting of a 3 manifold admitting a sufficiently complicated jsj decomposition is an amalgamation of heegaard splittings of the components of the jsj decomposition

equivariant minimax and minimal surfaces in geometric three manifolds minimal surfaces in riemannian three dimensional manifolds have played a major role in recent studies of the geometry and topology of 3 manifolds in particular stable and least area minimal surfaces have been used extensively sy msy hs on the other hand explicit examples of unstable minimal surfaces have rarely been given for the 3 sphere s with the standard metric of constant sectional curvature there is the classical paper of lawson lh showing that closed orientable surfaces of every genus occur as unstable minimal surfaces embedded in 5 3 more recently karcher pinkall and sterling kps have constructed several new examples in s we have discovered new infinite families of minimal surfaces in s more generally we announce a number of new finite and infinite families of embedded minimal surfaces in geometric 3 manifolds using the minimax procedure described below geometric structures on 3 manifolds were introduced by thurston tw see also the excellent survey by scott sp1 there are eight geometries r s s x r nil h 2 x r s l r solv and h a geometric structure on a 3 manifold s is a representation of e as a quotient of one of the above eight spaces divided out by a covering transformation group acting isometrically equivalently e is locally isometric to one of these spaces with its natural homogeneous space structure the first six of these geometries give seifert fiber spaces and we are mainly interested in such examples the so 2 isometry actions associated with most seifert fiber spaces yield infinite classes of embedded minimal surfaces note that interesting examples can also be obtained in the other two geometries e g in hyperbolic geometry h 3 pr3 2 the minimax procedure has proved to be a versatile and powerful means of constructing unstable minimal surfaces in 3 manifolds for basic details of this technique see pj ss p r l and pr2 suppose that g is a finite group of isometries acting on a closed oriented riemannian 3 manifold e assume that a is a heegaard surface in e i e the closures of the components of e a are handlebodies k and k assume furthermore that a is g equivariant i e ga a for all g e g we consider one parameter smooth families at t 0 1 sweeping out e and having the following properties ao and ai are graphs at is isotopic to a for all 0 t 1 at is g equivariant for all t the handlebody kt is chosen so that the orientation on at is induced from that on

the distributivity equation for uninorms revisited abstract the distributivity equation has been widely studied involving different classes of aggregation functions from t norms and t conorms to uninorms nullnorms and generalizations of them it is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing since uninorms have been used in these topics the study of the distributivity between two uninorms becomes specially interesting in a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone in this paper we want to achieve this study by focusing on the reverse direction that is for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm we show along the paper that this new point of view leads to many new solutions

corrigendum corrigendum to the distributivity condition for uninorms and t operators fuzzy sets and systems 128 2002 209 225 in this paper the study of the distributivity equation involving uninorms in u given in fuzzy sets and systems 128 2002 209 225 is revised two wrong propositions in the mentioned reference are corrected and their right versions are proved

hamilton jacobi formalism for podolsky s electromagnetic theory on the null plane we develop the hamilton jacobi formalism for podolsky s electromagnetic theory on the null plane the main goal is to build the complete set of hamiltonian generators of the system as well as to study the canonical and gauge transformations of the theory

an extension of the migrative property for uninorms in this paper the notion of a migrative uninorms over a fixed uninorm u 0 with the same neutral element is introduced all uninorms u that are a migrative over a uninorm u 0 are studied all cases when u and u 0 have continuous underlying operations and belong to any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations

0 efficient triangulations of 3 manifolds efficient triangulations of 3 manifolds are defined and studied it is shown that any triangulation of a closed orientable irreducible 3 manifold m can be modified to a 0 efficient triangulation orm can be shown to be one of the manifolds s 3 rp 3 or l 3 1 similarly any triangulation of a com pact orientable irreducible irreducible 3 manifold can be modified to a 0 efficient triangulation the notion of a 0 efficient ideal tr is de fined it is shown if m is a compact orientable irreducible irreducible 3 manifold having no essential annuli and distinct from the 3 cell then m admits an ideal triangulation furthermore it is shown that any ideal trian gulation of such a 3 manifold can be modified to a 0 efficient ideal triangula tion a 0 efficient triangulation of a closed manifold has only one vertex or the manifold is s 3 and the triangulation has precisely two vertices 0 efficient tri angulations of 3 manifolds with boundary and distinct from the 3 cell have all their vertices in the boundary and then just one vertex in each bound ary component as tools we introduce the concepts of barrier surface and shrinking as well as the notion of crushing a triangulation along a normal sur face a number of applications are given including an algorithm to construct an irreducible decomposition of a closed orientable 3 manifold an algorithm to construct a maximal collection of pairwise disjoint normal 2 spheres in a closed 3 manifold an alternate algorithm for the 3 sphere recognition prob lem results on edges of low valence in minimal triangulations of 3 manifolds and a construction of irreducible knots in closed 3 manifolds

on the α migrativity of semicopulas quasi copulas and copulas in this paper we address the problem of a migrativity for a fixed a for semicopulas copulas and quasi copulas we introduce the concept of an a sum of semicopulas this new concept allows us to completely characterize a migrative semicopulas and copulas moreover a sums also provide a means to obtain a partial characterization of a migrative quasi copulas

embeddability in the 3 sphere is decidable we show that the following algorithmic problem is decidable given a 2 dimensional simplicial complex can it be embedded topologically or equivalently piecewise linearly in r3 by a known reduction it suffices to decide the embeddability of a given triangulated 3 manifold x into the 3 sphere s3 the main step which allows us to simplify x and recurse is in proving that if x can be embedded in s3 then there is also an embedding in which x has a short meridian that is an essential curve in the boundary of x bounding a disk in s3 b x with length bounded by a computable function of the number of tetrahedra of x

the distributivity equations for semi t operators over uninorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we describe the solutions of distributivity for semi t operators over uninorms previous results about distributivity for nullnorms over uninorms can be obtained as a corollary

distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t conorm this paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms in particular the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict from the obtained results it is deduced that distributivity and conditional distributivity are equivalent moreover we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict

nonlinear schrodinger equation in the bopp podolsky electrodynamics solutions in the electrostatic case abstract we study the following nonlinear schrodinger bopp podolsky system u u q 2 u u p 2 u a 2 2 4 u 2 in r 3 with a 0 we prove existence and nonexistence results depending on the parameters q p moreover we also show that in the radial case the solutions we find tend to solutions of the classical schrodinger poisson system as a 0

heegaard splittings the virtually haken conjecture and property τ the behaviour of finite covers of 3 manifolds is a very important but poorly understood topic there are three increasingly strong conjectures in the field that have remained open for over twenty years the virtually haken conjecture the positive virtual b1 conjecture and the virtually fibred conjecture any of these would have profound ramifications for 3 manifold theory in this paper we explore the interaction of these conjectures with the following seemingly unrelated areas eigenvalues of the laplacian and heegaard splittings

on distributive laws of uninorms over overlap and grouping functions overlap and grouping functions as two new classes of special binary aggregation functions have been investigated by several authors for applications in image processing decision making classification and fuzzy community detection problems on the other hand after aczel studied the distributive law between two operations the distributive laws among particular binary aggregation functions become an interesting and natural research area in this paper we continue to discuss this topic for uninorms and overlap and grouping functions first we give some basic properties for the distributive law of uninorms over overlap functions second we study this distributive law when the uninorms belong to one of the usual classes e g mathcal u min mathcal u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 finally we investigate the distributive law of uninorms over grouping functions by an analogous way

on the conditional distributivity of continuous semi t operators over uninorms abstract the issue of conditional distributivity or how it is also called restricted distributivity which is a form of relaxed distributivity on the restricted domain is crucial for many different areas such as utility theory and integration theory the focus of this paper is on this specific form of distributivity for a continuous semi t operator with respect to a continuous t conorm and for a continuous semi t operator with respect to a uninorm of the form u min or u max with continuous underlying t norm and t conorm

the distributivity condition for uninorms and t operators in this work we study the functional equation given by the distributivity condition f x g y z g f x y f x z for all x y z 0 1 where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

distributivity and conditional distributivity for t uninorms abstract aggregation operators play an important role in many theoretical and practical aspects of applied mathematics recently the focus is on operators with an annihilator therefore the topic of this paper is distributivity both conditional and regular for certain classes of aggregation operators with this property the characterization of all pairs f g of aggregation operators that are satisfying distributivity law on both whole and restricted domain where f is a t uninorm in u max and g is a t conorm or a uninorm from u min or u max is given

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

migrativity property for uninorms and semi t operators in this paper the notions of migrative uninorms over semi t operators and migrative semi t operators over uninorms are introduced and investigated all solutions of the migrativity equations for all possible combinations of semi t operators and uninorms are characterized

effective finiteness of irreducible heegaard splittings of non haken 3 manifolds the main result is a short effective proof of tao li s theorem that a closed non haken hyperbolic 3 manifold n has at most finitely many irreducible heegaard splittings along the way we show that n has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index 1 minimal surfaces this effective result together with the sequel with daniel ketover solves the classification problem for heegaard splittings of non haken hyperbolic 3 manifolds

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

distributivity and conditional distributivity of semi uninorms over continuous t conorms and t norms the distributivity and conditional distributivity of a uninorm and a continuous t conorm present an open problem recalled by klement in the linz2000 closing session in 2006 ruiz and torrens 14 solved this problem for the most usual known classes of uninorms recently rak 13 solved the same problem for several classes of semi uninorms i e a special class of conjunctive semi uninorms a special class of disjunctive semi uninorms and the class of idempotent semi uninorms in this work we continue to investigate the same topic as the above by focusing on two other classes of semi uninorms i e representable semi uninorms and continuous semi uninorms the obtained results are different from the case of representable uninorms and also different from the cases of other known classes of semi uninorms moreover the dual case of distributivity and conditional distributivity of the above two classes of semi uninorms over continuous t norms is also investigated and similar results are obtained

on the distributivity property for uninorms abstract distributivity between two operations is a property that was already posed many years ago and that is especially interesting in the framework of logical connectives for this reason the distributivity property has been extensively studied for several families of operations like triangular norms and conorms some kinds of uninorms and nullnorms also called t operators and even for some generalizations of them in this paper we investigate the distributivity equation involving two uninorms lying in any one of the most studied classes of uninorms leading to many new solutions

the modularity law in some classes of aggregation operators abstract in this study we consider the functional equation of modularity in a special class of aggregation operators with an absorbing element first we focus on the modularity between commutative binary operators and their duals and then we examine the modularity for operators from the class of 2 uninorms which generalize nullnorms by extending their certain conditions in particular for these operators depending on the positions of their neutral elements and possessing the same absorbing element we obtain positive and negative results which are analogous to the results in the general case for operators with different absorbing elements

a note on an extension of the migrative property for uninorms this paper shows by an example that proposition 15 iv c in mas et al 2013 about migrative property for uninorms in u c o s m i n is false and corrects these propositions

a single point characterization of representable uninorms we study uninorms of which both the underlying t norm and underlying t conorm are strict such uninorms are the only candidates for being representable by an additive generator we prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the remaining open part of the unit square more explicitly such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments if this single value coincides with one of these bounds then the value of the uninorm at any point in the remaining open part is determined by the same bound

an extension of the migrative property for triangular norms in this paper we extend the migrative property of triangular norms by allowing an arbitrary fixed t norm t 0 in the defining equation instead of the originally used product equivalent forms of this extended migrativity are also provided and proved two particular cases when t 0 is either the minimum or the lukasiewicz t norm are studied in these cases all continuous extended migrative t norms are characterized and represented the proofs are constructive which helps the reader to build up various families of extended migrative t norms

distributivity between uninorms and nullnorms recently the distributivity equation was investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms generally the assumption of associativity is not necessary in consideration of distributivity equation moreover if we omit commutativity assumption consideration of the left and right distributivity conditions is reasonable previous results about distributivity between uninorms and nullnorms can be obtained as simple corollaries

distributivity between semi t operators and semi nullnorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this paper we describe the solutions of distributivity between semi t operators and semi nullnorms previous results about distributivity between nullnorms can be obtained as simple corollaries