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

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

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

discrete time pi nonlinear cal h _ infty estimation in this technical note exact and approximate solutions of the discrete time suboptimal proportional integral h estimation problem for affine nonlinear systems using finite dimensional estimators filters are presented sufficient conditions for the solvability of the problem are given in terms of discrete time hamilton jacobi isaac s equations for linear systems it is shown that these equations reduce to a system of linear matrix inequalities simulation results are also presented to show the benefit of the new approach

a note on left and right distributivity equations for semi t operators and uninorms abstract dryga et al showed that lemma 3 3 i in 5 is false by a counterexample see example 2 in 4 for details the goal of this short note is to indicate that example 2 in 4 is wrong and lemma 3 3 i in 5 is valid

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

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

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

disturbance attenuation using proportional integral observers in this paper we first propose a proportional integral observer design for single output uncertain linear systems which permit us to attenuate either measurement noise or modelling errors we show that when only sensor noise is present in the system an integral observer alone suffices to achieve good convergence and filtering properties on the other hand when modelling errors and sensor noise are present we show that for some classes of linear systems the proportional integral observer allows us to decouple completely the modelling uncertainties while keeping satisfactory convergence properties a comparison of the classical proportional observer to the proposed observers are given via academic simulation examples we next extend the design to the class of single output uniformly observable non linear systems we show through a practical simulation example dealing with a flexible joint robot that the non linear proportional integral has very satisfactory disturbance attenuating properties

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

on the 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

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

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

propositional knowledge base revision and minimal change abstract the semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model theoretic point of view a characterization of all revision schemes that satisfy the gardenfors rationality postulates is given in terms of minimal change with respect to an ordering among interpretations revision methods proposed by various authors are surveyed and analyzed in this framework the correspondences between gardenfors like rationality postulates and minimal changes with respect to other orderings are also investigated

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

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

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

propositional belief base update and minimal change abstract in this paper we examine ten concrete propositional update operations of the literature we start by completely characterizing their relative strength and their computational complexity then we evaluate the competing update operations with respect to the postulates proposed by katsuno and mendelzon it turns out that the majority violates most of the postulates we argue that all violated postulates are undesirable except one after that we evaluate the update operations with respect to another property which has been investigated extensively in the literature viz that disjunctive updates should not be identified with the exclusive disjunction we argue that this is desirable and show that the argument gives further support to the rejection of two of the postulates finally we study how the different approaches accommodate general laws governing the world alias integrity constraints summing up our results we conclude that only two of the update operations are satisfactory

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

on the complexity of propositional knowledge base revision updates and counterfactuals abstract we study the complexity of several recently proposed methods for updating or revising propositional knowledge bases under the principle of minimal change in particular we derive complexity results for the following problem given a knowledge base t an update p and a formula q decide whether q is derivable from t p the updated or revised knowledge base note that this problem includes the evaluation of the counterfactual p q over t that is a conditional statement if p then q where p is known or expected to be false we consider the general case where t is an arbitrary propositional formula or theory as well as restricted versions of this problem in particular where t is a conjunction of horn clauses or where the size of the update p is bounded by a constant

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

on nonlinear h_ infty filtering for discrete time stochastic systems with missing measurements in this paper the h infin filtering problem is investigated for a general class of nonlinear discrete time stochastic systems with missing measurements the system under study is not only corrupted by state dependent white noises but also disturbed by exogenous inputs the measurement output contains randomly missing data that is modeled by a bernoulli distributed white sequence with a known conditional probability a filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies h infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero initial condition the existence conditions of the desired filter are described in terms of a second order nonlinear inequality such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the lyapunov functionals as a consequence a linear time invariant filter design problem is discussed for the benefit of practical applications and some simplified conditions are obtained finally two numerical simulation examples are given to illustrate the main results of this paper

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

ltr design of discrete time proportional integral observers applies the proportional integral pi observer in connection with loop transfer recovery ltr design for discrete time systems both the prediction and the filtering versions of the pi observer are considered we show that a pi observer makes it possible to obtain time recovery i e exact recovery for t spl rarr spl infin under mild conditions two systematic ltr design methods one based on an extension of the linear quadratic gaussian loop transfer recovery lqg ltr and the other based on linear matrix inequality lmi are derived for the discrete time pi observer case explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given

knowledge updates semantics and complexity issues we consider the problem of updating of an agent s knowledge we propose a formal method of knowledge update on the basis of the semantics of modal logic s5 in our method an update is specified according to the minimal change on both the agent s actual world and knowledge we discuss general minimal change properties of knowledge update and show that our knowledge update operator satisfies all the update postulates of katsuno and mendelzon we characterize several specific forms of knowledge update which have important applications in reasoning about change of agents knowledge we also examine the persistence property of knowledge and ignorance associated with knowledge update we then investigate the computational complexity of model checking for knowledge update we first show that in general the model checking for knowledge update is s 2 p complete we then identify a subclass of knowledge update problems that has polynomial time complexity for model checking we point out that some important knowledge update problems belong to this subclass we further address another interesting subclass of knowledge update problems for which the complexity of model checking is np complete

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

remarks on uninorm aggregation operators it is proved that continuous uninorm aggregation operators are only t norms or t conorms some general constructions about uninorm aggregation operators are given

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