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

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

nonlinear eigenvalue neumann problems with discontinuities in this paper we study nonlinear eigenvalue problems with neumann boundary conditions and discontinuous terms first we consider a nonlinear problem involving the p laplacian and we prove the existence of a solution for the multivalued approximation of it then we pass to semilinear problems and we prove the existence of multiple solutions the approach is based on the critical point theory for nonsmooth locally lipschitz functionals

multivalued elliptic equation with exponential critical growth in r2 abstract in this work we study the existence of nontrivial solutions for the following class of multivalued elliptic problems p u v x u h x t f x u in r 2 where 0 v is a continuous function verifying some conditions h h 1 r 2 and t f x u is the generalized gradient of f x t with respect to t and f x t 0 t f x s d s assuming that f is a discontinuous function with exponential critical growth we have applied variational methods for locally lipschitz functional to get two solutions for p when is small enough

on a new class of t norms and t conorms on bounded lattices abstract the ordinal sum of triangular norms on unit interval has been used to construct other triangular norms but in general ordinal sum construction of triangular norms and triangular conorms may not work on an arbitrary bounded lattice in this study we focus on ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice moreover we show a complete generalization of our ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice and some illustrative examples are added for clarity

a note on uninorms with continuous underlying operators abstract our investigations are motivated by the fact uninorms as mixed aggregation operations on the unit interval have been widely used in fuzzy set theory this paper is mainly to characterize the inner structure of uninorms with continuous underlying operators given by ordinal sums and then presents some of their properties to be specific for a uninorm we describe the relations of its two arbitrary summands and characterize the structure on cartesian products of its underlying intervals corresponding to those two summands mentioned previously one in 0 e and the other in e 1 where e is the neutral element of the uninorm these results bring us a step closer to get the full structure of a uninorm with continuous underlying operators

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

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

three symmetric solutions for a class of elliptic equations involving the p laplacian with discontinuous nonlinearities in rn abstract using a three critical points theorem for a non differentiable functional and a sobolev embedding result we establish the existence of three radially symmetric solutions for a class of elliptic equations involving the p laplacian with discontinuous nonlinearities in the whole space

cell decompositions for rank two quiver grassmannians we prove that all quiver grassmannians for exceptional representations of a generalized kronecker quiver admit a cell decomposition in the process we introduce a class of regular representations which arise as quotients of consecutive preprojective representations cell decompositions for quiver grassmannians of these truncated preprojectives are also established we provide two combinatorial labelings for these cells on the one hand they are naturally labeled by certain subsets of a so called 2 quiver attached to a truncated preprojective representation on the other hand the cells are in bijection with compatible pairs in a maximal dyck path as predicted by the theory of cluster algebras the provided bijection between these two labelings gives a geometric explanation for the appearance of dyck path combinatorics in the theory of quiver grassmannians

new construction of t norms and t conorms on bounded lattices abstract this article studies the construction of ordinal sums of triangular norms t norms and triangular conorms t conorms on bounded lattices first we present a new class of t norms and t conorms on an arbitrary bounded lattice some examples are provided to illustrate that our new construction method is different from some existing methods for the construction of ordinal sums of t norms and t conorms on an arbitrary bounded lattice then we illustrate that our new construction method can be generalized by induction to a modified ordinal sum construction for t norms and t conorms on an arbitrary bounded lattice finally for any bounded sublattice s of a bounded lattice l we provide a sufficient condition that does not need s and l to have the same bottom and top elements such that an ordinal sum function is a t norm on l whereas the function is determined by an arbitrary selection of bounded sublattices as carriers for arbitrary summand t norms in particular we give a necessary and sufficient condition that needs s to have the same bottom element as l such that an ordinal sum function is a t norm on l

a characterization of the classes umin and umax of uninorms on a bounded lattice abstract as generalizations of the classes umin and umax of uninorms on the real unit interval we introduce the classes umin and umax of uninorms on a bounded lattice and lay bare the structure of their members it is shown that uninorms in umin resp umax are characterized by a triangular conorm resp triangular norm and a triangular subnorm resp triangular superconorm the characterization theorems unify all the existing construction methods for these two classes of uninorms known in the literature we also introduce four new related classes of uninorms on a bounded lattice and present dedicated construction methods using triangular subnorms and triangular superconorms finally connections among the introduced classes of uninorms are discussed

uninorms on bounded lattices we study uninorms on bounded lattices we show the existence of uninorms with the neutral element which is different from the top element and the bottom element using the fact that the t norms and t conorms on arbitrary lattice l always exist as a by product we give a method of constructing uninorms using this method we obtain also the smallest uninorm and the greatest uninorm with a given neutral element e

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

construction of nullnorms on bounded lattices and an equivalence relation on nullnorms abstract in this study we present two methods for the construction of nullnorms on bounded lattices based on the existence of t norms as well as t conorms on an arbitrary bounded lattice l we demonstrate that these methods differ from the existing approaches mainly because of their more generalized structures an equivalence relation is also defined based on a class of nullnorms and some properties of this relation are examined

generalized ordinal sums of aggregation operators on bounded lattices abstract in this paper four kinds of generalized ordinal sums of aggregation operators on bounded lattices are provided and discussed firstly necessary and sufficient conditions for lower resp upper generalized ordinal sum of many summands to be an aggregation operator are provided in which case that the smallest resp greatest aggregation operator that coincides with each summand is given meanwhile the idempotent lower resp upper generalized ordinal sum of idempotent aggregation operators is also discussed then the relationships between these four kinds of generalized ordinal sums are given finally the lattice structures of some sets of special aggregation operators are investigated

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

on constructing the largest and smallest uninorms on bounded lattices abstract uninorms on the unit interval are a common extension of triangular norms t norms and triangular conorms t conorms as important aggregation operators uninorms play a very important role in fuzzy logic and expert systems recently several researchers have studied constructions of uninorms on more general bounded lattices in particular cayli 2019 gave two methods for constructing uninorms on a bounded lattice l with e l 0 1 which is based on a t norm t e on 0 e and a t conorms s e on e 1 that satisfy strict boundary conditions in this paper we propose two new methods for constructing uninorms on bounded lattices our constructed uninorms are indeed the largest and the smallest among all uninorms on l that have the same restrictions t e and s e on 0 e and respectively e 1 moreover our constructions does not require the boundary condition and thus completely solved an open problem raised by cayli

idempotent nullnorms on bounded lattices abstract nullnorms are generalizations of triangular norms and triangular conorms with a zero element to be an arbitrary point from a bounded lattice in this paper we study and discuss the existence of idempotent nullnorms on bounded lattices considering an arbitrary distributive bounded lattice l we show that there exists a unique idempotent nullnorm on l we prove that an idempotent nullnorm may not always exist on an arbitrary bounded lattice furthermore we propose a construction method to obtain idempotent nullnorms on a bounded lattice l with an additional constraint on a for the given zero element a l 0 1

critical point theory for nondifferentiable functionals and applications abstract we consider minimization results for locally lipschitzian functionals on a banach space by introducing a compactness condition of the palais smale type which is suggested by the variational principle of ekeland applications are given to some semilinear elliptic problems with discontinuous nonlinearities

on the relationships between the orders induced by uninorms and nullnorms abstract in this paper some relationships between the orders induced by uninorms and nullnorms are discussed some relations between the sets admitting some incomparability w r t those orders are investigated also some relationships between the algebraic structures obtained from those orders are determined

modularity conditions between overlap grouping function and uni nullnorm or null uninorm abstract overlap and grouping functions as two kinds of special continuous commutative aggregation functions have wide applications in image processing and classification modularity conditions between the class of overlap grouping functions satisfying o 1 e e g 0 e e and special classes of uninorms and those of another special class of overlap grouping functions over nullnorms have been studied in 49 in this paper we extend these results to any overlap grouping function moreover we study the modularity conditions between overlap grouping functions and uni nullnorms null uninorms which are the generalization of uninorms nullnorms

general representations of quivers we investigate general representations of a quiver q there are two main questions that we shall address the first which was raised by kac is to find the dimension vectors of the summands of a general representation of dimension vector a the second is to find the dimension vectors of the subrepresentations of a general representation of dimension vector a these two questions are closely related one consequence of our investigation is to find an algorithm to compute the canonical decomposition of an arbitrary dimension vector in terms of the euler form of the quiver

constructing uninorms via closure operators on a bounded lattice abstract in this paper via closure resp interior operators on a bounded lattice l we propose a rather effective method to construct uninorms on l with a given triangular norm t resp triangular conorm s on the subinterval 0 e resp e 1 of l our method encompasses as special cases the construction methods introduced by f karacal and r mesiar 2015 16 as well as by g d cayli et al 2016 5 we also exploit a pair of novel closure and interior operators on complete lattices and utilize this pair of operators to construct uninorms several interesting examples are included to illustrate our method

convex combinations of uninorms and triangular subnorms abstract the problem whether a non trivial convex combination of two continuous triangular norms can be a t norm was extensively studied in the last decades bringing the negative answer in all examined special cases on the other hand in the field of non continuous t norms including left continuous t norms several examples were found including mainly a convex combination of an migrative t norm and the drastic product t norm or a convex combination of ordinal sums of product related t subnorms recently convex combinations of uninorms were discussed in 18 since any uninorm with the neutral element e 0 1 restricted to 0 e 2 is isomorphic to a t norm this investigation extends the original problem of a convex combination of t norms given by alsina frank and schweizer in this work we will study convex combinations of uninorms further covering uninorms with continuous underlying functions uninorms with different neutral elements and representable uninorms we will also show that convex combinations of triangular subnorms play a major role in this investigation

some results on the convex combination of uninorms abstract it is well known that under some conditions a convex combination of the drastic product t d and the strict triangular norm is still a triangular norm uninorms as a special kind of generalization of both triangular norms and triangular conorms have been widely used in fuzzy set theory in this paper the convex combination of uninorms is studied some properties of the class of uninorms with the underlying triangular norm t d are presented firstly then the convex combination of this class of uninorms is discussed and it is shown that only in some trivial cases the convex combination is still a uninorm

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 a class of semilinear schrodinger equations involving critical growth and discontinuous nonlinearities abstract in this paper we deal with a class of schrodinger equation in r n involving critical sobolev exponent and jump discontinuities the basic tool employed here is an approximation technique with periodic functions and variational arguments based on a linking theorem for locally lipschitz functionals

the modularity condition for uninorms revisited abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory the modularity equation is a kind of restricted general associative equations in the literature the already known results concerning the modularity equation for two uninorms are based on the assumption that both uninorms lie in one of the most studied classes of uninorms in this study we explore the modularity equation involving uninorms in a most general setting specifically we investigate the modularity between two uninorms in the cases when one uninorm belongs to any of the most studied classes of uninorms but the other one is any uninorm with no further assumptions further many new solutions appear from this new point of view that were not included in previous approaches

on the structure of uninorms on bounded lattices abstract uninorms are a generalization of triangular norms and triangular conorms with a neutral element in the interior of a bounded lattice in this study we present two methods to construct uninorms from a given triangular norm and triangular conorm on bounded lattices under some constraints as a by product of these methods we obtain new types of idempotent uninorms with a neutral element on bounded lattices in addition some illustrative examples for the constructions of uninorms on bounded lattices are provided

uninorms on bounded lattices constructed by t norms and t subconorms abstract the construction of uninorms on bounded lattices has been a attractive research area in this paper we introduce some new classes of uninorms on bounded lattices via t subnorms and t subconorms with a neutral element e under some constraints we also give some illustrative examples to help understand the structure of these new uninorms moreover we provide an answer to the open problem raised by cayli in 2019 finally the differences between our methods and existing approaches are assessed

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

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

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

a characterization of discrete uninorms having smooth underlying operators in this paper discrete uninorms u such that their underlying t norm t and t conorm s are smooth are characterized the different cases combining when t is the minimum or the ukasiewicz t norm and s is the maximum or the ukasiewicz t conorm are given separately and the number of discrete uninorms with these underlying operators is given the same is done for the general case when t and or s are smooth but ordinal sums

on a new class of uninorms on bounded lattices we study and propose some new construction methods to obtain uninorms on bounded lattices considering an arbitrary bounded lattice l we show the existence of idempotent uninorms on l for any element e l 0 1 playing the role of a neutral element by our construction method we obtain the smallest idempotent uninorm and the greatest idempotent uninorm with the neutral element e l 0 1 we see that the obtained uninorms are conjunctive and disjunctive uninorms respectively on the other hand if l is not a chain we also provide an example of an idempotent uninorm which is neither conjunctive nor disjunctive

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

conditional distributivity equation for uninorms with continuous underlying operators our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory and focused also by klement in the linz seminar 2000 closing session this paper is mainly devoted to solving the functional equations of conditional distributivity of u 1 over u 2 where both u 1 and u 2 are uninorms with continuous underlying operators then the almost complete characterization of such a pair u 1 u 2 of uninorms is given except for only a small fraction of the unit square next we give the complete characterization of the previous pair under some appropriate restriction that is the second operator u 2 in mathbf u max cup mathbf u min finally we also construct a counterexample to illustrate that the obtained results are necessary but not sufficient for general cases with unlimited condition

uninorms continuous on 0 e 2 e 1 2 uninorms continuous on 0 e 2 e 1 2 are discussed archimedean uninorms continuous and cancellative on 0 e 2 e 1 2 are characterized and related non archimedean uninorms are also discussed the problem when is the border continuous projection of a t norm associative i e a t subnorm is also answered

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

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

a local minimax characterization for computing multiple nonsmooth saddle critical points this paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design most characterizations for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax problems thus they are not helpful for numerical algorithm design inspired by the results on computational theory and methods for finding multiple smooth saddle critical points in 14 15 19 21 23 a local minimax characterization for multiple nonsmooth saddle critical points in either a hilbert space or a reflexive banach space is established in this paper to provide a mathematical justification for numerical algorithm design a local minimax algorithm for computing multiple nonsmooth saddle critical points is presented by its flow chart

characterizing set valued functions of uninorms with continuous underlying t norm and t conorm abstract the uninorms with continuous underlying functions were characterized by their set of discontinuity points in the previous work of the author using the characterizing set valued function in this paper properties of this characterizing set valued function are studied it is shown that the type of the monotonicity of such a set valued function is always changed in idempotent points of the corresponding uninorm several additional properties of the characterizing set valued function of a uninorm with continuous underlying functions are shown and an example is included results shown in this paper are used for a complete characterization of uninorms with continuous underlying functions via the ordinal sum construction which is shown in the consecutive paper

exceptional modules are tree modules abstract we consider representations of a quiver over an arbitrary field recall that an indecomposable representation m without self extensions is said to be exceptional we are going to show that exceptional representations can be exhibited using matrices involving as coefficients just 0 and 1 actually if d is the dimension of m there exists such a matrix presentation with precisely d 1 non zero coefficients the corresponding coefficient quiver is a tree

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

on properties of uninorms locally internal on the boundary abstract recently a class of uninorms locally internal on the boundary was proposed by mas et al during the study of the migrativity property for uninorms in this paper some properties of this class of uninorms are presented and the characterizations are obtained for different cases

tl filters of integral residuated l monoids in this paper we introduce and discuss the concept of tl filters of integral residuated l monoids first we study some basic properties of tl filters and give the formula for calculating the tl filters generated by l subsets then we discuss some properties of tl filters under homomorphisms and study the relationship between tl filters and t congruence l relations on integral commutative residuated l monoids

on the structure of semi t operators on bounded lattices abstract in this study we show some construction methods to obtain a semi t operator from a given pseudo t conorm and pseudo t norm on bounded lattices using these methods we prove that the known methods of constructing semi t operators on bounded lattices proposed by fang and hu are incorrect and present the correct forms at the same time furthermore some other construction methods for semi t operators on bounded lattices are also added

properties of uninorms with the underlying operations given as ordinal sums abstract uninorms as mixed aggregation operations on the unit interval have been widely used as logical connectives in fuzzy set theory this paper presents some properties of uninorms for which the underlying operations are given as ordinal sums specially we present the relations between two arbitrary summands and the value on cartesian product of their underlying intervals one in 0 e and the other in e 1 where e is neutral element of the uninorm whose results bring us a step closer to the structure of uninorms that have continuous underlying operations as a byproduct we characterize several special classes of uninorms that are different from the well studied classes of uninorms

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

lattice based sum of t norms on bounded lattices abstract the concept of ordinal sums in the sense of clifford have long been blamed for their limitations in constructing new t norms including inability to cope with general bounded lattices motivated by this observation and based on the lattice based sum of lattices that has been recently introduced by el zekey et al we propose a new sum type construction of t norms called a lattice based sum of t norms for building new t norms on bounded lattices from given ones the proposed sum is generalizing the well known ordinal and horizontal sum constructions of t norms by allowing for lattice ordered index sets we demonstrate that like the ordinal sum of t norms the lattice based sum of t norms can be generalized using as summands so called t subnorms still leading to a t norm subsequently we apply the results for constructing several new families of t norms and t subnorms on bounded lattices in the same spirit by the duality we will also introduce lattice based sums of t conorms and t subconorms

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

nonlinear elliptic eigenvalue problems with discontinuities abstract in this paper we study the existence of solution for two different eigenvalue problems the first is nonlinear and the second is semilinear our approach is based on results from the nonsmooth critical point theory in the first theorem we prove the existence of at least two nontrivial solutions when is in a half axis in the second theorem based on a nonsmooth variant of the generalized mountain pass theorem we prove the existence of at least one nontrivial solution for every r

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

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

on a class of schrodinger systems with discontinuous nonlinearities using a non smooth critical point theory for locally lipschitz functionals we investigate a class of stationary schrodinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow up at infinity the existence of nontrivial solution is obtained

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

characterization of uninorms with continuous underlying t norm and t conorm by their set of discontinuity points uninorms with continuous underlying t norm and t conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown this set is proved to be a subset of the graph of a special symmetric u surjective nonincreasing set valued function which gives us a necessary condition for a uninorm to have continuous underlying functions a sufficient condition for a uninorm to have continuous underlying operations is also given several examples are included

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

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

multiplicity result for a discrete eigenvalue problem with discontinuous nonlinearities using a three critical points theorem for nondifferentiable functionals we investigate a class of second order difference equation with discontinuous nonlinearities a new multiplicity result is obtained

some notes on the partial orders induced by a uninorm and a nullnorm in a bounded lattice abstract in this paper an equivalence on the class of nullnorms on a bounded lattice is discussed some relationships between the u and v partial orders are investigated a necessary and sufficient condition making a bounded lattice also a lattice w r t the v partial order is given moreover the relation between the algebraic structures related to the u and v partial orders is studied

different interpretations of triangular norms and related operations triangular norms and triangular conorms and uni norms can be treated as semigroup two place function also as commutative semiring multiplications it can also be derived from the difference operation in a difference poset we discuss here these different interpretations and their consequences

uni nullnorms on bounded lattices abstract in this paper we study uni nullnorms with both neutral elements and zero elements on bounded lattices in order to illustrate the existence of uni nullnorms on bounded lattices we present two construction methods for obtaining such a uni nullnorm also we show two additional methods for the construction of idempotent nullnorms on bounded lattices which are generalizations of the one proposed by cayli and karacal furthermore we discuss the presence of idempotent uni nullnorms on bounded lattices and propose two construction methods to obtain an idempotent uni nullnorm on any bounded lattice

construction methods for idempotent nullnorms on bounded lattices abstract in this paper we discuss the presence of idempotent nullnorms on bounded lattices and investigate some properties of these operators we introduce two new methods for constructing idempotent nullnorms on bounded lattices for a zero element under a constraint that all elements incomparable with the zero element are comparable with each other in order to stress the role of this constraint satisfying that our constructions yield an idempotent nullnorm some illustrative examples are added

some properties of idempotent uninorms on a special class of bounded lattices abstract binary operations have many applications in fuzzy set theory one of them is uninorms in this paper we study some properties of idempotent uninorms on bounded lattices it is shown that idempotent uninorms on an arbitrary bounded lattice need not always be internal with the extended definition of the term internal we give a sufficient condition for the bounded lattice to any idempotent uninorm be internal in addition that it is given many properties of idempotent uninorms in this case

non differentiable functionals and applications to elliptic problems with discontinuous nonlinearities abstract multiple critical points theorems for non differentiable functionals are established applications both to elliptic variational hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

an eigenvalue dirichlet problem involving the p laplacian with discontinuous nonlinearities a multiplicity result for an eigenvalue dirichlet problem involving the p laplacian with discontinuous nonlinearities is obtained the proof is based on a three critical points theorem for nondifferentiable functionals

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

on a certain class of aggregative operators abstract here our starting point is a study of connection with dombi aggregative operators uninorms strict t norms and t conorms we present a new representation theorem of strong negations that explicitly contains the neutral value then the relationships for aggregative operators and strong negations are verified as well as those for the t norm and t conorm using the pan operator concept we introduce the multiplicative pliant concept and give the necessary and sufficient conditions for it we study a certain class of weighted aggregative operators representable uninorms which build a self demorgan class with infinitely many negations we provide the necessary and sufficient conditions for these operators

new construction of an ordinal sum of t norms and t conorms on bounded lattices abstract this paper introduces a new ordinal sum construction of t norms and t conorms on bounded lattices based on interior and closure operators the proposed method generalizes several known constructions and provides a simple tool to introduce new classes of t norms and t conorms

uninorms on bounded lattices with the underlying t norms and t conorms abstract uninorms are a generalization of the concepts of triangular norms t norms and triangular conorms t conorms that admit a neutral element as any element in a bounded lattice in this study we discuss the characterization of uninorms on bounded lattices we introduce some new constructions for uninorms on bounded lattices which are derived from both t norms and t conorms in particular two idempotent uninorms on bounded lattices are obtained we also provide some corresponding examples to help understand the structure of these new classes of uninorms in addition we provide an answer to the open problem proposed by cayli 2019 14