monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem the choquet sugeno and shilkret integrals with respect to monotone measures as well as their generalization the universal integral stand for a useful tool in decision support systems in this paper we propose a general construction method for aggregation operators that may be used in assessing output of scientists we show that the most often currently used indices of bibliometric impact like hirsch s h woeginger s w egghe s g kosmulski s maxprod and similar constructions may be obtained by means of our framework moreover the model easily leads to some new very interesting functions

on lattices with a smallest set of aggregation functions given a bounded lattice l with bounds 0 and 1 it is well known that the set pol 0 1 l of all 0 1 preserving polynomials of l forms a natural subclass of the set c l of aggregation functions on l the main aim of this paper is to characterize all finite lattices l for which these two classes coincide i e when the set c l is as small as possible these lattices are shown to be completely determined by their tolerances also several sufficient purely lattice theoretical conditions are presented in particular all simple relatively complemented lattices or simple lattices for which the join meet of atoms coatoms is 1 0 are of this kind

extension of the concept of mappings using fuzzy sets abstract in this paper we develop a new method of extending the concept of ordinary mappings from ordinary sets to ordinary sets to mapping from sets to fuzzy sets by constructing corresponding mappings from original ordinary mappings we also compare this method with other similar methods including zadeh s extension

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

fixed points and generators of fuzzy relations abstract the fixed points of a t indistinguishability operator are characterized as its generators in the sense of the representation theorem of valverde the geometric description of the set of fixed points of a reflexive and symmetric fuzzy relation based on this characterization gives a way to explicitly calculate it

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

aggregation on boolean multi polar space three types of aggregation operators defined on a boolean multi polar space 0 1 m are compared three different monotonicity conditions that yield different types of aggregation operators are discussed and the structure of these aggregation operators on 0 1 m with additional properties of associativity and commutativity is studied for any m n the commutative associative boolean multi polar aggregation operators are shown to coincide with boolean multi polar uninorms the structure of commutative associative sl aggregation operators is shown to be dependent on the structure of the class of abelian idempotent semigroups based on m 1 elements with an annihilator we show that each commutative associative sl aggregation operator with annihilator 0 corresponds to a lower semi lattice with bottom element 0 for m 2 the class of commutative associative c aggregation operators is proved to be equal to the intersection of the class of commutative associative boolean multi polar aggregation operators and the class of commutative associative sl aggregation operators examples of the three types of commutative associative aggregation operators are shown and discussed for m 1 2 3

the tame infinitesimal groups of odd characteristic abstract given an infinitesimal group g over an algebraically closed field k of characteristic p 3 we provide criteria for the principal block b 0 g of its algebra of distributions to be of tame representation type these are employed in conjunction with galois coverings to determine the structure of g modulo its multiplicative center as well as the quiver and the relations of the algebra b 0 g

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

on finding common subtrees abstract let t and r be two arbitrary ordered trees t r whose nodes are labelled over an alphabet a we devise a simple solution for detecting all the common subtrees in o t time and space if the size of a is finite and o t log min a t time otherwise we solve the problem of finding in t and r all occurrences if any of any given tree b in either o t b or o b t b time this requires to set up a simple data structure in o t time that allows to find all maximal subtrees of b in o b time and to solve other related problems

representations of non splittable extension algebras let a be an algebra over a field k and d a self duality d mod a 2 mod aop where aop is the opposite algebra of a and mod a the category of finitely generated left a modules by an extension for short we understand an extension algebra t over a with kernel da in the sense of cartan eilenberg 3 0 da t p a 0 where p is an algebra epimorphism in the case where a is hereditary by means of the heller function qaxda the auslander reiten quiver rawda of the trivial extension a k da is completely determined by ra lo moreover for any extension t tr is isomorphic to rawda it seems that this fact suggests the existence of a closer connection between some categories of modules over t and over a 1x da though mod t is not in general equivalent to mod a k da in this paper we are concerned with categorical relations between non splittable extensions and the trivial extensions and we shall establish some relation between them for some class of algebras to which hereditary algebras belong we prove the following where mod a denotes the category of finitely generated left a modules without projective summands

a characterization of selfinjective algebras of strictly canonical type abstract we prove that the class of selfinjective algebras of strictly canonical type investigated in kwiecien and skowronski 2009 27 kwiecien and skowronski 2009 28 coincides with the class of selfinjective algebras having triangular galois coverings with infinite cyclic group and the auslander reiten quiver with quasi tubes maximally saturated by simple and projective modules satisfying natural conditions

description of sup and inf preserving aggregation functions via families of clusters in data tables abstract connection between the theory of aggregation functions and formal concept analysis is discussed and studied thus filling a gap in the literature by building a bridge between these two theories one of them living in the world of data fusion the second one in the area of data mining we show how galois connections can be used to describe an important class of aggregation functions preserving suprema and by duality to describe aggregation functions preserving infima our discovered method gives an elegant and complete description of these classes also possible applications of our results within certain biclustering fuzzy fca based methods are discussed

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

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

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

positive galois coverings of self injective algebras abstract in the article we study the structure of galois coverings of self injective artin algebras with infinite cyclic galois groups in particular we characterize all basic connected self injective artin algebras having galois coverings by the repetitive algebras of basic connected artin algebras and with the galois groups generated by positive automorphisms of the repetitive algebras

enumeration of bc subtrees of trees a bc tree block cutpoint tree is a tree with at least two vertices where the distance between any two leaves is even motivated from the study of the core of a graph bc trees form an interes

congruences and the discrete sugeno integrals on bounded distributive lattices we study compatible aggregation functions on a general bounded distributive lattice l where the compatibility is related to the congruences on l as a by product a new proof of an earlier result of g gratzer is obtained moreover our results yield a new characterization of discrete sugeno integrals on bounded distributive lattices

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

automorphisms of repetitive algebras abstract let b be the repetitive algebra of a finite dimensional algebra b over a field k by the b bimodule db hom b k and let be the nakayama automorphism of b we determine the positive automorphisms of b such that the orbit algebra b is isomorphic to a splittable extension algebra of b by the b bimodule db for an automorphism of b and we characterize weakly symmetric algebras and symmetric algebras of the form b with a positive automorphism of b as an application we characterize some class of weakly symmetric algebras with non periodic generalized standard auslander reiten components

selfinjective algebras with hereditary stable slice abstract we determine the structure of all finite dimensional selfinjective algebras over a field whose auslander reiten quiver admits a hereditary stable slice

binary generating set of the clone of idempotent aggregation functions on bounded lattices abstract in a recent paper botur et al 2018 we have presented a generating set of the clone of idempotent aggregation functions on bounded lattices as the main result we have shown that this clone is generated by certain ternary idempotent functions from which all idempotent aggregation functions of l can be obtained by usual term composition the aim of this paper is to present an essential improvement of the result above by presenting a new generating set of this clone a bit artificial ternary functions are substituted here by natural binary lattice a medians and certain binary characteristic functions consequently the clone is generated by its binary part and the result strengthens the essential role of medians within all idempotent aggregation functions moreover we will show that for an n element lattice l the upper bound of binary generators is 2 n 1

on the decomposability of aggregation functions on direct products of posets abstract based on results concerning equivalences on direct products of sets a representation of aggregation functions acting on products of ordered structures by means of aggregation functions acting component wise is obtained and discussed in particular t norms and t conorms on direct products of bounded lattices are considered generalizing some earlier results of de baets and mesiar

on the properties of the f partial order and the equivalence of nullnorms in this study we investigate a partial order induced by a nullnorm f on a bounded lattice l called the f partial order which was recently introduced by asici we consider the case where l 0 1 l 0 1 first we define and comprehensively study the set of all incomparable elements with arbitrary but fixed x 0 1 x 0 1 according to the f partial order we then define and discuss the equivalence relation on the class of nullnorms according to the partial orders that they generate by defining this relation the equivalence relations defined on the class of t norms and t conorms are extended to a more general form finally we provide an answer to an open problem regarding the relation between the lattice order and the f partial order on 0 1 0 1

selfinjective algebras having a generalized standard family of quasi tubes maximally saturated by simple and projective modules abstract we give a complete description of finite dimensional selfinjective algebras over an algebraically closed field whose auslander reiten quiver admits a generalized standard family of quasi tubes maximally saturated by simple and projective modules in particular we show that these algebras are selfinjective algebras of strictly canonical type

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

on auslander reiten components of blocks and self injective biserial algebras we investigate the existence of auslander reiten components of euclidean type for special biserial self injective algebras and for blocks of group algebras in particular we obtain a complete description of stable auslander reiten quivers for the tame self injective algebras considered here

on generating sets of the clone of aggregation functions on finite lattices abstract in a recent paper 12 we have shown that aggregation functions on a bounded lattice l form a clone i e the set of functions closed under projections and composition of functions moreover for any finite lattice l we gave a finite set of unary and binary aggregation functions on l from which the aggregation clone is generated in this paper a general method for constructing generating sets of the aggregation clone on l is presented our approach is based on extending of l valued capacities leading to so called full systems of aggregation functions several full systems on l are presented including singleton ones and their arities are discussed

on selfinjective algebras of finite representation type with maximal almost split sequences abstract we investigate the structure of finite dimensional selfinjective algebras of finite representation type over an arbitrary field having almost split sequences of modules whose middle term admits the maximal possible number of indecomposable direct summands

enumeration of bc subtrees of trees a bc tree block cutpoint tree is a tree with at least two vertices where the distance between any two leaves is even motivated from the study of the core of a graph bc trees form an interesting class of trees we provide a comprehensive study of questions related to bc trees as the analogue of the study of extremal questions on subtrees of trees we first characterize the general extremal trees that maximize or minimize the number of bc subtrees or leaf containing bc subtrees we further discuss the middle part of a tree with respect to the number of bc subtrees namely the bc subtree core that behaves in a rather different way than all previously known middle parts of a tree last but not least fast algorithms are proposed following similar ideas as those of the enumeration of subtrees for enumerating various classes of bc subtrees of a tree

multi distance granularity structural α subtree index of generalized bethe trees abstract in graph theory and its applications trees bc trees subtrees and bc subtrees have been extensively studied we introduce a generalization of the bc tree called the multi granular tree which is a tree of order at least 1 where any two leaves are at a distance that is a multiple of we study the number of subtrees through subtree generating functions for generalized bethe trees bethe trees and dendrimers hyper branched structures in molecular topology our results can also be used to examine the asymptotic behavior of the average order of subtrees in dendrimers

isomorphisms between de morgan triplets abstract this paper deals with the characterization of the isomorphisms of the structures related to de morgan triplets as is well known the de morgan triplets are used in order to define the basic connectives meet join and negation in the setting of the multiple valued logic underlying fuzzy set theory therefore such triplets will induce isomorphisms on the structures defined in 0 1 x by these connectives a classification of the de morgan triplets is given for which the de morgan triplets of the type min max n and therefore the corresponding de morgan algebras constitute a class the main resulting equivalence classes of de morgan triplets are studied

on generating of idempotent aggregation functions on finite lattices abstract in a recent paper 9 we proposed the study of aggregation functions on lattices via clone theory approach observing that aggregation functions on lattices just correspond to 0 1 monotone clones as the main result of 9 we have shown that all aggregation functions on a finite lattice l can be obtained as usual composition of lattice operations and certain unary and binary aggregation functions the aim of this paper is to present a generating set for the class of intermediate or equivalently idempotent aggregation functions this set consists of lattice operations and certain ternary idempotent aggregation functions

subtrees of spiro and polyphenyl hexagonal chains the number of subtrees of a graph and its variations are among popular topological indices that have been vigorously studied we investigate the subtree numbers of spiro and polyphenyl hexagonal chains molecular graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons we first present the generating functions for subtrees through which explicit formulas for computing the subtree number of spiro and polyphenyl hexagonal chains are obtained we then establish a relation between the subtree numbers of a spiro hexagonal chain and its corresponding polyphenyl hexagonal chain this allows us to show that the spiro and polyphenyl hexagonal chains with the minimum resp second minimum third minimum subtree numbers coincide with the ones that attain the maximum resp second maximum third maximum wiener indices and vice versa the subtree densities of these hexagonal chains are also briefly discussed

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

on mixed de morgan triplets abstract in this paper we find the general solution of the functional equation t f x y f x n y h x where t is a t norm or t conorm f is an aggregation function n is a strong negation on the unit interval and h is an increasing function

constructions of triangular norms on lattices by means of irreducible elements constructions and characterizations of triangular norms t norms have been discussed in many different contexts in this paper we present two methods to construct t norms on lattices from given partial information since the idea is to follow from part to whole we especially consider the lattices with decompositions firstly we investigate the structure of the partially ordered set of irreducible elements then for a given t norm t on the complete distributive lattice 0 1 2 we study the restriction of t to the poset of irreducible elements of 0 1 2 furthermore we give a method for generating t norms on a finite distributive lattice l by means of irreducible elements in l we show that a t norm on a finite distributive lattice is idempotent if and only if it is idempotent on the set of irreducible elements finally we introduce a formula to obtain t norms on l n from given t norms on irreducible elements of l n we present the dual statements for t conorms

generators of aggregation functions and fuzzy connectives we show that the class of all aggregation functions on 0 1 can be generated as a composition of infinitary sup operation bigvee acting on sets with cardinality not exceeding mathfrak c b medians mathsf med b b in 0 1 and unary aggregation functions 1 0 1 and 1 a 1 a in 0 1 moreover we show that we cannot relax the cardinality of argument sets for suprema to be countable thus showing a kind of minimality of the introduced generating set as a by product generating sets for fuzzy connectives such as fuzzy unions fuzzy intersections and fuzzy implications are obtained too

generators of copulas and aggregation the most applied class of copulas for fitting purposes is undoubtedly the class of archimedean copulas due to their representation by means of single functions of one variable i e by means of additive generators or the corresponding pseudo inverses in this paper we characterize aggregation functions preserving additive generators pseudo inverses of additive generators of archimedean copulas as a by product we obtain an efficient method to construct new additive generators from some given ones

structure of n uninorms in this paper we study binary operators on 0 1 which are associative monotone non decreasing in both variables and commutative amc with neutral element in this work we generalize the concept of neutral element and this generalization gives rise to a new class of amc binary operators on 0 1 called n uninorms n uninorms are denoted as u n where n comes from the generalization of the neutral element we study the structure of n uninorms the structure resembles an ordinal sum structure made up of n uninorms we characterize some special cases of them based on some continuity considerations and show that t norms t conorms uninorms and nullnorms t operators are special cases of n uninorms we also show that given n there are n 1 classes of operators in u n and each of them has many subclasses we also study the frank equation involving n uninorms and show that we need to consider only n uninorms for the study finally we show that the total number of subclasses of operators in u n follows the famous series called catalan numbers

a new way to extend t norms t conorms and negations this work presents a method of extending t norms t conorms and fuzzy negations to a lattice valued setting by preserving the largest possible number of properties of these fuzzy connectives which are invariants under homomorphisms further we also apply this method to extend de morgan triples automorphisms and n dimensional t norms

on linear approximations of sugeno integrals on bounded distributive lattices this paper aims at extending the study of sugeno integrals on bounded distributive lattices also including several linguistic scales we introduce study and discuss linear approximations of such sugeno integrals the best linear approximations keeping as much information as possible are also characterized our approach significantly reduces the computational complexity which is illustrated by an example too

stack and queue layouts of directed acyclic graphs part i stack layouts and queue layouts of undirected graphs have been used to model problems in fault tolerant computing and in parallel process scheduling however problems in parallel process scheduling are more accurately modeled by stack and queue layouts of directed acyclic graphs dags a stack layout of a dag is similar to a stack layout of an undirected graph with the additional requirement that the nodes of the dag be in some topological order a queue layout is defined in an analogous manner the stacknumber queuenumber of a dag is the smallest number of stacks queues required for its stack layout queue layout in this paper bounds are established on the stacknumber and queuenumber of two classes of dags tree dags and unicyclic dags in particular any tree dag can be laid out in 1 stack and in at most 2 queues and any unicyclic dag can be laid out in at most 2 stacks and in at most 2 queues forbidden subgraph characterizations of 1 queue tree dags and 1 queue cycle dags are also presented part ii of this paper presents algorithmic results in particular linear time algorithms for recognizing 1 stack dags and 1 queue dags and proof of np completeness for the problem of recognizing a 4 queue dag and the problem of recognizing a 9 stack dag

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