stability analysis of markovian jump stochastic bam neural networks with impulse control and mixed time delays this paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both markovian jump parameters and mixed time delays the jumping parameters are modeled as a continuous time discrete state markov chain based on a novel lyapunov krasovskii functional the generalized ito s formula mathematical induction and stochastic analysis theory a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point at the same time we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters it should be mentioned that our stability results are delay dependent which depend on not only the upper bounds of time delays but also their lower bounds moreover the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results consequently the results obtained in this paper are not only less conservative but also generalize and improve many earlier results finally two numerical examples and their simulations are provided to show the effectiveness of the theoretical results

ordinal sums of triangular norms on bounded lattices abstract in this paper we deal with the problem of ordinal sum construction for t norms on subintervals of a given bounded lattice l to obtain a t norm on l without any additional requirements some illustrative examples are added to emphasize the difference of our method from some existing methods in the literature finally we generalize our construction method to ensure its applicability for a greater number of t norms on the subintervals

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

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

state estimation for fuzzy cellular neural networks with time delay in the leakage term discrete and unbounded distributed delays this paper deals with the problem of state estimation for fuzzy cellular neural networks fcnns with time delay in the leakage term discrete and unbounded distributed delays in this paper leakage delay in the leakage term is used to unstable the neuron states it is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error state system is globally asymptotically stable by constructing the lyapunov krasovskii functional which contains a triple integral term an improved delay dependent stability criterion is derived in terms of linear matrix inequalities lmis however by using the free weighting matrices method a simple and efficient criterion is derived in terms of lmis for estimation the restriction such as the time varying delay which was required to be differentiable or even its time derivative which was assumed to be smaller than one are removed instead the time varying delay is only assumed to be bounded finally numerical examples and its simulations are given to demonstrate the effectiveness of the derived results

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

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

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

new stability results for delayed neural networks this paper is concerned with the stability for delayed neural networks by more fully making use of the information of the activation function a new lyapunov krasovskii functional lkf is constructed then a new integral inequality is developed and more information of the activation function is taken into account when the derivative of the lkf is estimated by lyapunov stability theory a new stability result is obtained finally three examples are given to illustrate the stability result is less conservative than some recently reported ones

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

stability of markovian jump generalized neural networks with interval time varying delays this paper examines the problem of asymptotic stability for markovian jump generalized neural networks with interval time varying delays markovian jump parameters are modeled as a continuous time and finite state markov chain by constructing a suitable lyapunov krasovskii functional lkf and using the linear matrix inequality lmi formulation new delay dependent stability conditions are established to ascertain the mean square asymptotic stability result of the equilibrium point the reciprocally convex combination technique jensen s inequality and the wirtinger based double integral inequality are used to handle single and double integral terms in the time derivative of the lkf the developed results are represented by the lmi the effectiveness and advantages of the new design method are explained using five numerical examples

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

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

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

statics and kinematics of discrete cosserat type granular materials a theoretical framework is presented for the statics and kinematics of discrete cosserat type granular materials in analogy to the force and moment equilibrium equations for particles compatibility equations for closed loops are formulated in the two dimensional case for relative displacements and relative rotations at contacts by taking moments of the equilibrium equations micromechanical expressions are obtained for the static quantities average cauchy stress tensor and average couple stress tensor in analogy by taking moments of the compatibility equations micromechanical expressions are obtained for the infinitesimal kinematic quantities average rotation gradient tensor and average cosserat strain tensor in the two dimensional case alternatively these expressions for the average cauchy stress tensor and the average couple stress tensor are obtained from considerations of the equivalence of the continuum force and couple traction vectors acting on a plane and the resultant of the discrete forces and couples acting on this plane in analogy the expressions for the average rotation gradient tensor and the average cosserat strain tensor are obtained from considerations of the change of length and change of rotation of a line element in the two dimensional case it is shown that the average particle stress tensor is always symmetrical contrary to the average stress tensor of an equivalent homogenized continuum finally discrete analogues of the virtual work and complementary virtual work principles from continuum mechanics are derived

improved stability criteria for a class of neural networks with variable delays and impulsive perturbations this paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses with the help of m matrix the homeomorphism theory some effective inequalities and analysis techniques certain novel criteria on the existence uniqueness and exponential stability of the equilibrium point have been established moreover these criteria possess adjustable real parameters which extend and improve many existing results in the literature in the end two numerical examples are provided to illustrate the validation of the theoretical results

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

new stability criteria of neural networks with interval time varying delay a piecewise delay method abstract this paper provides improved conditions for the global asymptotic stability of a class of neural networks with interval time varying delays a piecewise delay method is firstly proposed in this method the variation interval of the time delay is divided into two subintervals by introducing its central point then by constructing a new lyapunov krasovskii functional and checking its variation in the two subintervals respectively some new delay dependent stability criteria for the addressed neural networks are derived numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature

non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution abstract this study constructs and investigates the non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution the system not only contains the randomly occurring uncertainties of all parameters rouaps and stochastic disturbances in the system model but also includes randomly gain perturbations in the controller by introducing the stochastic variables a new model structure is built obeying bernoulli distribution to describe the system and the controller moreover a modified lyapunov krasovskii function lkf is constructed combining ito s differential formula and free weighting matrix method less conservative results are presented in terms of the linear matrix inequality lmi furthermore an observer based non fragile asynchronous h controller is designed without any limits on the system parameters finally three numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results

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

triangular norms on partially ordered sets in this paper several methods to construct triangular norms on partially ordered sets are proposed these methods include 1 constructing triangular norms on the poset of closed intervals of a given bounded poset 2 constructing triangular norms via galois connections between bounded posets based on a categorical analysis of the construction of triangular norms on closed intervals via monotone functions and their pseudo inverses 3 constructing triangular norms on function spaces between partially ordered sets

generalized continuous and left continuous t norms arising from algebraic semantics for fuzzy logics this paper focuses on the issue of how generalizations of continuous and left continuous t norms over linearly ordered sets should be from a logical point of view taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation we advocate linearly ordered bl algebras and mtl algebras as adequate generalizations of continuous and left continuous t norms respectively in both cases the underlying basic structure is that of linearly ordered residuated lattices although the residuation property is equivalent to left continuity in t norms continuous t norms have received much more attention due to their simpler structure we review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to bl chains in particular we show the good behavior of bl algebras over a finite or complete chain and discuss the partial knowledge of rational bl chains then we move to the general non continuous case corresponding to left continuous t norms and mtl chains the unsolved problem of describing the structure of left continuous t norms is presented together with a fistful of construction decomposition techniques that apply to some distinguished families of t norms and finally we discuss the situation in the general study of mtl chains as a natural generalization of left continuous t norms

tensorial form definitions of discrete mechanical quantities for granular assemblies this paper explains the necessity of tensorial form definitions of mechanical quantities in the discrete mechanics of granular assemblies and how to make such definitions particles are assumed to be circular in 2d or spheres in 3d first we explain the dirichlet tessellation and some important geometric tools defined from this tessellation i e the contact and dual contact cells and dual branch vectors which become necessary for the tensorial form definition comparing the fundamental quantities in discrete and continuum mechanics and regarding their mechanical properties especially of stress and strain we propose a new tensorial form definition for all of discrete mechanical quantities lastly discussions are made on the properties of these quantities especially on the internal work and the compatibility condition of strain

stability criteria for bam neural networks with leakage delays and probabilistic time varying delays this paper is concerned with the stability criteria for bidirectional associative memory bam neural networks with leakage time delay and probabilistic time varying delays by establishing a stochastic variable with bernoulli distribution the information of probabilistic time varying delay is transformed into the deterministic time varying delay with stochastic parameters based on the lyapunov krasovskii functional and stochastic analysis approach delay probability distribution dependent sufficient conditions are derived to achieve the globally asymptotically mean square stable of the considered bam neural networks the criteria are formulated in terms of a set of linear matrix inequalities lmis which can be checked efficiently by use of some standard numerical packages finally a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results

problems on triangular norms and related operators abstract a number of open problems on triangular norms and related operators was posed during the 24th linz seminar on fuzzy set theory triangular norms and related operators in many valued logics held in february 2003 they are collected here together with some other open problems in this context and with some problems which were posed earlier and have been solved in the meantime

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

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

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

additive generators of fuzzy operations in the form of linear fractional functions abstract this paper is devoted to the analysis of additive generators in the form of linear fractional functions the limitations on the coefficients of increasing and decreasing generators are defined it is shown that the compositions of increasing and or decreasing generators are also generators for each case the corresponding triangular norms or conorms are found it is established that the triangular norms and conorms obtained on the basis of linear fractional functions and which are also dual to them have the same structure in fact a new family of dual triangular norms and conorms is proposed

stability and hopf bifurcation of controlled complex networks model with two delays abstract this paper considers hopf bifurcation of complex network with two independent delays by analyzing the eigenvalue equations the local stability of the system is studied taking delay as parameter the change of system stability with time is studied and the emergence of inherent bifurcation is given by changing the value of the delay the bifurcation of a given system can be controlled numerical simulation results confirm the validity of the results found

algebraic structure of fuzzy signatures abstract fuzzy signatures have been used for various applications including medical diagnosis communication of robots based on intention guessing and residential building evaluation however there exist many questions about this research topic which have not been addressed in the literature one of the most important aims is to formally define a family of fuzzy signatures from which an algebraic structure can be obtained allowing to make computations among fuzzy signatures this paper studies this family and defines suitable meet and join operators satisfying the properties of a lattice as an algebraic structure a partial ordering relation the least and greatest elements are also defined on the family of fuzzy signatures as a consequence fuzzy signatures can be used as truth values of fuzzy sets which provides a great level of representativity completely different from the interval valued and type 2 fuzzy sets among others

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

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

smooth t subnorms on finite scales in this work smooth t subnorms and boundary weak t norms bwt norms defined on a finite chain are studied in the smooth case it is proved that smooth bwt norms reduces to smooth t norms whereas a classification of smooth t subnorms as ordinal sums of a smooth t norm and an archimedean smooth t subnorm is proved in a similar way as in the case of 0 1 with respect to archimedean smooth t subnorms some cases depending on their zero region are considered classifying all of them in some cases and some specific families in others

stress strain relationship for granular materials based on the hypothesis of best fit abstract stress strain relationships of a granular system are derived based on the premise that the mean field of displacement is the best fit of actual particle displacements based on the best fit hypothesis two fundamental relationships are derived 1 the average strain as a function of contact displacements and 2 the mean field of contact force as a function of stress these two relationships lead to a stress strain law without the kinematic constraint of uniform strain for an assembly with isotropic packing structure closed form stress strain relationships are explicitly derived in which the modulus can be determined from the inter particle stiffness the difference between the derived stress strain relationship and that derived from voigt hypothesis is discussed the effect of fabric variation is illustrated in the theory discrete element analyses are also performed and the results are used to compare with the estimated moduli from the proposed theory in the comparison the solution bounds for granular assembly system are illustrated

a note on the continuity of triangular norms abstract it is shown that for an associative function on the unit interval with certain boundary conditions separate continuity implies joint continuity this answers a question on triangular norms raised by alsina frank and schweizer in 2003

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

further results on dissipativity and stability analysis of markov jump generalized neural networks with time varying interval delays abstract this work investigates the dissipativity and stability analysis problems for markov jump generalized neural networks subject to time varying interval delays the aim of the present study is to determine whether the new dissipativity and stability criteria with less conservatism could be established for markov jump generalized delayed neural networks or not in this connection a more general dissipative property index inequality is firstly introduced on basis of fully considering mode dependent matrices in the lyapunov krasovskii functional some advantageous negative terms ignored in some existing works are taken into account by employing some novel integral inequalities and stochastic analysis theory some available less conservative criteria are developed three compared examples are finally shown to explain the reduced conservatism and superiority of the presented criteria for markov jump generalized delayed neural networks

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

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

lattice based sums in this contribution the well known ordinal sum technique of posets is generalized by allowing for a lattice ordered index set instead of a linearly ordered index set and we argue for the merits of this generalization we will call such a proposed sum type construction a lattice based sum our new approach of lattice based sum extends also the horizontal sum we show that the lattice based sum of posets is again a poset subsequently we apply the results for constructing new lattices by investigating lattice based sums when the summand posets are lattices we show that under certain assumptions the lattice based sum of lattices will be a lattice

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

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

analysis of three dimensional micro mechanical strain formulations for granular materials evaluation of accuracy an important objective of recent research on micro mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro mechanical quantities at inter particle contacts although the micro mechanical formulation of the stress tensor is well established the corresponding formulation for the strain tensor has proven to be much more evasive still being the subject of much discussion in this paper we study various micro mechanical strain formulations for three dimensional granular assemblies following the work of bagi in two dimensions bagi 2006 all of these formulations are either based on an equivalent continuum approach or follow the best fit approach their accuracy is evaluated by comparing their results using data from discrete element method simulations on periodic assemblies to the macroscopic deformation it is found that bagi s formulation bagi 1996 which is based on the delaunay tessellation of space is the most accurate furthermore the best fit formulation based on particle displacements only did unexpectedly well in contrast to previously reported results for two dimensional assemblies

on large deformation granular strain measures for generating stress strain relations based upon three dimensional discrete element simulations abstract generating stress strain relations based upon three dimensional discrete element simulations for hierarchical multiscale constitutive modeling of granular materials at finite strain requires measures of stress and strain in the reference and current configurations the cauchy stress tensor calculated from interparticle forces and branch vectors resulting from discrete element simulations is well established but the various finite strain definitions existing in the literature are not as well studied or accepted thus the paper develops seven finite strain measures in three dimensions cartesian coordinates assumed two are calculated in the reference configuration and five are calculated in the current configuration in the process a time integrated deformation gradient is formulated with which the cauchy stress tensor can be mapped to either the kirchhoff stress first piola kirchhoff stress or second piola kirchhoff stress the difficulty in calculating strain measures for granular materials is the discrete particulate nature of the materials in the paper strain measures are motivated by the equivalent continuum method but are extended to finite strain in three dimensions simulations are conducted to test the finite strain measures and it is found that these strain measures are independent of rigid body rotation of a particle assembly granular cauchy stress is also calculated for these discrete element simulations to be able to plot stress strain curves in the current configuration finally two numerical examples with large deformation are simulated 1 cavity expansion and 2 pile penetration and their results are analyzed

uncertainty modeling by bilattice based squares and triangles in this paper ginsberg s fitting s theory of bilattices and in particular the associated constructs of bilattice based squares and triangles is introduced as an attractive framework for the representation of uncertain and potentially conflicting information paralleling goguen s l fuzzy set theory we recall some of the advantages of bilattice based frameworks for handling fuzzy sets and systems provide the related structures with adequately defined graded versions of the basic logical connectives and study their properties and relationships

lmi optimization approach on stability for delayed neural networks of neutral type in this paper the global asymptotic stability of delayed cellular neural networks of neutral type is investigated a novel delay dependent criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented since the condition is dependent on the size of time delay it is usually less conservative than delay independent ones two numerical examples are given to show the effectiveness of proposed method

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

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

fuzzy integrals based on pseudo additions and multiplications on definit un semi groupe ou un groupe qui est isomorphe au semi groupe ou du groupe ou la mesure de lebesque est definie on definit une integrale par pseudo addition et pseudo multiplication qui sont des operations de semi anneaux distributives et associatives

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

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

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

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

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

triangle algebras a formal logic approach to interval valued residuated lattices in this paper we introduce triangle algebras a variety of residuated lattices equipped with approximation operators and with a third angular point u different from 0 and 1 we show that these algebras serve as an equational representation of interval valued residuated lattices ivrls furthermore we present triangle logic tl a system of many valued logic capturing the tautologies of ivrls triangle algebras are used to cast the essence of using closed intervals of l as truth values into a set of appropriate logical axioms our results constitute a crucial first step towards solving an important research challenge the axiomatic formalization of residuated t norm based logics on l i the lattice of closed intervals of 0 1 in a similar way as was done for formal fuzzy logics on the unit interval

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

radicals of tl ideals in this paper we first introduce several different definitions of radicals of tl ideals in a commutative ring with identity and study their basic properties then discuss several kinds of primary tl ideals where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

lmi based stability criteria for neural networks with multiple time varying delays abstract in this paper the stability of neural networks with multiple time varying delays is studied a new class of lyapunov krasovskii functionals is constructed and the s procedure and free weighting matrix method are employed to derive a delay dependent stability criterion from which a delay independent criterion is obtained as a special case moreover the result is also extended to delay dependent and rate independent stability criteria for multiple unknown time varying delays finally numerical examples are given to illustrate the effectiveness of our methods and improvement over the existing ones

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

orthogonal grid constructions of copulas we establish a general framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with nonoverlapping rectangles as patches we derive a family of construction methods that require the choice of a single background copula when this background copula is the greatest copula we retrieve the well known ordinal sum construction while in the case of the smallest copula we obtain a construction method that is dual to the ordinal sum construction also nonsingular background copulas lead to suitable construction methods

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

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

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects this paper focuses on the stability analysis for neural networks of neutral type with leakage delays and impulsive effects the discrete delays are assumed to be time varying and belong to a given interval which means that the lower and upper bounds of interval time varying delays are available by utilizing the lyapunov functional method jensen s integral inequality and introducing some free weighting matrices some new delay derivative dependent stability criteria are established for the neutral type neural network the obtained stability criteria are stated in terms of linear matrix inequalities finally numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones

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

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

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

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