generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

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

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

resolution of a system of the max product fuzzy relation equations using lou factorization in this paper the lu factorization is extended to the fuzzy square matrix with respect to the max product composition operator called l u factorization equivalently we will find two fuzzy lower and upper triangular matrices l and u for a fuzzy square matrix a such that a l u where is the max product composition an algorithm is presented to find the matrices l and u furthermore some necessary and sufficient conditions are proposed for the existence and uniqueness of the l u factorization for a given fuzzy square matrix a an algorithm is also proposed to find the solution set of a square system of fuzzy relation equations fre using the l u factorization the algorithm finds the solution set without finding its minimal solutions and maximum solution it is shown that the two algorithms have a polynomial time complexity as o n 3 since the determination of the minimal solutions is an np hard problem the algorithm can be very important from the practical point of view

lipschitzian de morgan triplets of fuzzy connectives after studying lipschitzian strong negations lipschitzian de morgan triplets t s n where t is a triangular norm s a triangular conorm and n a strong negation are investigated the relationships between the best lipschitzian constants of functions t s and n are given several examples are included

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

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

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

on triangular norm based propositional fuzzy logics abstract fuzzy logics based on triangular norms and their corresponding conorms are investigated an affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given tautologies contradictions and contigencies with respect to such fuzzy logics are studied in particular for the important cases of min max and ukasiewicz logics finally fundamental t norm based fuzzy logics are shown to provide a gradual transition between min max and ukasiewicz logics

the pseudo linear semantics of interval valued fuzzy logics triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals which are called interval valued residuated lattices ivrls triangle algebras have been used to construct triangle logic tl a formal fuzzy logic that is sound and complete w r t the class of ivrls in this paper we prove that the so called pseudo prelinear triangle algebras are subdirect products of pseudo linear triangle algebras this can be compared with mtl algebras prelinear residuated lattices being subdirect products of linear residuated lattices as a consequence we are able to prove the pseudo chain completeness of pseudo linear triangle logic ptl an axiomatic extension of tl introduced in this paper this kind of completeness is the analogue of the chain completeness of monoidal t norm based logic mtl this result also provides a better insight in the structure of triangle algebras it enables us amongst others to prove properties of pseudo prelinear triangle algebras more easily it is known that there is a one to one correspondence between triangle algebras and couples l a in which l is a residuated lattice and a an element in that residuated lattice we give a schematic overview of some properties of pseudo prelinear triangle algebras and a number of others that can be imposed on a triangle algebra and the according necessary and sufficient conditions on l and a

quantifiers in the formulation of multiple objective decision functions abstract we discuss the interpretation of linguistically quantified statements using fuzzy sets we indicate that there are two methods of interpreting these statements the algebraic approach and the substitution approach we then use quantified statements to express overall decision functions involving multiple objectives these statements are of the type a solution should satisfy many of the objectives using the algebraic and substitution approach we develop a whole family of forms for combining multiple objectives we show that algebraic approach corresponds to situations in which we are unconcerned about the allocation of satisfaction amongst the objectives but just interested in getting much satisfaction the substitution approach on the other hand leads to forms which are dependent upon the allocation of satisfaction between the objectives

multilinear pseudodifferential operators beyond calderon zygmund theory abstract we consider two types of multilinear pseudodifferential operators first we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in lebesgue spaces these results generalise earlier work of the present authors concerning linear pseudo pseudodifferential operators secondly we investigate the boundedness of bilinear pseudodifferential operators with symbols in the hormander s m classes these results are new in the case 1 that is outwith the scope of multilinear calderon zygmund theory

logical operators on complete lattices abstract in the present paper the logical operators on complete lattices and their relations are investigated in detail a concept of consistency among logical operators is given and it is shown that such a concept is inherent this concept provides us with a criterion to judge if a group of logical operators is suitable for fuzzy reasoning at last the necessary and sufficient condition for a kind of logical operators on 0 1 which are consistent is obtained

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

prioritized measure guided aggregation operators this paper mainly investigates a particular type of multicriteria aggregation imperative called prioritized aggregations in order to handle a class of multicriteria decision making problems in which there are prioritizations among criteria in such problems the satisfaction degrees of higher prioritized criteria cannot be compensated by the lower prioritized criteria to describe the prioritizations among criteria quantitatively yager has introduced a prioritized measure from the viewpoint of fuzzy measure which is validated as an effective method except for some little imperfectness on the basis of detailed analysis with respect to yager s prioritized measure we elaborate the properties of prioritized measures and then propose a generalized form of prioritized measure moreover by using the generalized prioritized measure to convey the prioritized imperative we develop a generalized prioritized measure guided aggregation operator that is based on the choquet integral additionally the prioritized weight aggregation operator introduced by yager is verified to be a special case of the generalized prioritized measure guided aggregation operator at length we develop a concrete prioritized measure and the corresponding prioritized measure guided aggregation operator under the framework of the generalized prioritized measure guided aggregation operator and illustrate their feasibility and effectiveness through several numerical examples

on derivations of lattices in this paper we introduce the notion of derivation for a lattice and discuss some related properties we give some equivalent conditions under which a derivation is isotone for lattices with a greatest element modular lattices and distributive lattices we characterize modular lattices and distributive lattices by isotone derivation moreover we prove that if d is an isotone derivation of a lattice l the fixed set fix d l is an ideal of l finally we prove that d l is isomorphic to l in a distributive lattice l

filters of residuated lattices and triangle algebras an important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic is that of a filter filters can be used amongst others to define congruence relations specific kinds of filters include boolean filters and prime filters in this paper we define several different filters of residuated lattices and triangle algebras and examine their mutual dependencies and connections triangle algebras characterize interval valued residuated lattices

robust h2 performance analysis and synthesis of linear polytopic discrete time periodic systems via lmis a particular class of uncertain linear discrete time periodic systems is considered the problem of robust stabilization of real polytopic linear discrete time periodic systems via a periodic state feedback control law is tackled here along with h2 performance optimization using additional slack variables and the periodic lyapunov lemma an extended sufficient condition of robust h2 stabilization is proposed based on periodic parameter dependent lyapunov functions this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework this is illustrated on a numerical example from the literature

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

the standard completeness of interval valued monoidal t norm based logic in this paper we prove the strong standard completeness of interval valued monoidal t norm based logic ivmtl and some of its extensions for other extensions we show that they are not strong standard complete we also give a local deduction theorem for ivmtl and other extensions of interval valued monoidal logic similar results are obtained for interval valued fuzzy logics expanded with baaz s delta

pseudo bck algebras as partial algebras it is well known that the representation of several classes of residuated lattices involves lattice ordered groups an often applicable method to determine the representing group or groups from a residuated lattice is based on partial algebras the monoidal operation is restricted to those pairs that fulfil a certain extremality condition and else left undefined the subsequent construction applied to the partial algebra is easy transparent and leads directly to the structure needed for representation in this paper we consider subreducts of residuated lattices the monoidal and the meet operation being dropped the resulting algebras are pseudo bck semilattices assuming divisibility we can pass on to partial algebras also in this case to reconstruct the underlying group structure from this partial algebra if applicable is again straightforward we demonstrate the elegance of this method for two classes of pseudo bck semilattices semilinear divisible pseudo bck algebras and cone algebras

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

asa and its application to multi criteria decision making case study aggregation plays an important role in many applications related to the development of intelligent systems in a fuzzy environment the existing aggregation operators are generally the t norm t conorm mean operators yager s operator and operator however these aggregation operators do not properly reflect the situation in the aggregation process that is these types of aggregation operators are independent of the aggregation situation in order to solve these problems we propose a new aggregation method to reflect the situation in the aggregation process it is the aggregation based on situation assessment asa method it consists of the situation assessment model sam and the asa algorithm in this asa method the sam is utilized to reflect the situation in the aggregation process this model generates the parameter which is controlled by decision maker it indicates the current degree of aggregation situation therefore our method can be adapted to certain situations by using the parameter in this paper asa method is applied to the multi criteria decision making environment

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

survey invariant representations of discrete time periodic systems the correspondence between periodic and time invariant systems can take a variety of forms the purpose of this survey paper is to present a complete and clear picture on time invariant representations for discrete time periodic systems the core of the treatment evolves around the concept of periodic transfer function

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

extended neuro fuzzy models of multilayer perceptrons in this paper the famous neural model the multilayer perceptron is extended to a new neural model that is called the additive takagi sugeno type multilayer perceptron the present study proves that this new model can also act as a universal approximator and thus it can be used in many fields such as system modeling and identification the concept of f duality and the fuzzy operator interactive or are used to prove that the proposed neural model is functionally equal to a kind of fuzzy inference system further this paper presents another new neuro fuzzy model that is called the sigmoid adaptive network based fuzzy inference system simulation studies show that our proposed models both have stronger approximation capability than multilayer perceptrons

weighted norm inequalities for strongly singular convolution operators we derive sharp function estimates for convolution operators whose kernels are more singular than calder6n zygmund kernels this leads to weighted norm inequalities weighted weak 1 1 results are also proved all the results obtained are in the context of ap weights 0 introduction we begin by recalling notations relevant to r 7 given a function f x its fourier transform will be denoted by j 0 ff x e x dx throughout this paper v x and w x will denote nonnegative locally integrable functions we let

a characterization of the extension principle abstract we provide an alternative characterization of the extension principle of fuzzy sets this characterization is based upon using relations to represent mappings we apply this new characterization to develop an extension for non deterministic mappings

connectives and quantifiers in fuzzy sets abstract we discuss some of the issues involved in the selection of appropriate operators for implementing the union and intersection of fuzzy subsets we discuss the extension principles used in extending operators to fuzzy subsets we provide a structure for aggregating linguistic variables in the theory of approximate reasoning we look at mean operators on fuzzy subsets as well as the inclusion of importances in aggregation we discuss non monotone set operators we introduce the concept of linguistic quantifiers and look at some applications of these structures we are particularly concerned with their application to linguistic summarizers syllogistic reasoning and multi criteria decision making

brief paper approaches to extended non quadratic stability and stabilization conditions for discrete time takagi sugeno fuzzy systems this paper provides simple and effective linear matrix inequality lmi characterizations for the stability and stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this more general classes of non parallel distributed compensation non pdc control laws and non quadratic lyapunov functions are presented unlike the conventional non quadratic approaches using only current time normalized fuzzy weighting functions we consider not only the current time fuzzy weighting functions but also the l step past l 0 and one step ahead ones when constructing the control laws and lyapunov functions consequently by introducing additional decision variables it can be shown that the proposed conditions include the existing ones found in the literature as particular cases examples are given to demonstrate the effectiveness of the approaches

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

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

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

the ł and ł propositional and predicate logics abstract this paper has two main goals the first goal is to show a different axiomatic system of the and 1 2 propositional logics these propositional logics were introduced in esteva et al arch math logic to appear and they are the combinations of the ukasiewicz and the product logic together with the constant 1 2 in case of the 1 2 logic the second goal is to show an axiomatic system and the completeness theorem of a predicate version of the and 1 2 propositional logics it will be shown that godel product and ukasiewicz predicate logics are contained in the logic

mathematical fuzzy logic as a tool for the treatment of vague information the paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language by a semantics and by a calculus for the derivation of formulas besides this logical approach also a more algebraic approach is discussed and the paper ends with some hints toward applications which are based upon these theoretical considerations

an efficient lyapunov function for discrete t s models observer design this paper deals with the design of a new observer synthesis for discrete takagi sugeno t s fuzzy models it is well established that quadratic synthesis for discrete t s models and or linear parameter varying systems can be outperformed easily via nonquadratic syntheses several lyapunov functions can be used nevertheless this paper shows that with a small change in the initial lyapunov function a better in the sense of solutions to the linear matrix inequality constraints problem lyapunov function can be reached this one can introduce very important improvements

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

avoiding matrix inversion in takagi sugeno based advanced controllers and observers many of the recent advances on control and estimation of systems described by takagi sugeno ts fuzzy models are based on matrix inversion which could be a trouble in the case of real time implementation this paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete time case two different methods are proposed the first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure for the first methodology a new class of controllers and observers are introduced which are called respectively the counterpart of an advanced ts based cats controller and the replica of an advanced ts based rats observer instead of relaxations for the linear matrix inequalities conditions an original use of the membership functions is presented in the second methodology it is proposed the estimation based control law for approximating ts based eclats controller that uses a fuzzy state observer the lyapunov theory is used to ensure stability conditions for either the closed loop system as well as the estimation error numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer finally advantages and drawbacks of the proposed method are discussed

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

weighted sobolev spaces and pseudodifferential operators with smooth symbols absmacr let u i be the fefferman stein sharp function of u and for 1 0 such that the pointwise estimate au x cm u x holds for all x e ri and all schwartz functions u this estimate implies the boundedness of 0 order pseudodifferential operators on weighted lp spaces whenever the weight function belongs to muckenhoupt s class ap having established this we construct weighted sobolev spaces of fractional order in r and on a compact manifold prove a version of sobolev s theorem and exhibit coercive weighted estimates for elliptic pseudodifferential operators

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

mathematical aspects of fuzzy sets and fuzzy logic the paper considers some of the main trends of the development of mathematical fuzzy logic and of formalized fuzzy set theory which came out in the history of fuzzy sets and which aim to give solid theoretical foundations for fuzzy set theory

a new axiomatization for involutive monoidal t norm based logic on the real unit interval the notion of a girard monoid coincides with the notion of a t norm based residuated lattice with strong induced negation a geometrical approach toward these girard monoids based on the notion of rotation invariance is turned in an adequate axiomatization for the involutive monoidal t norm based residuated logic

2 increasing binary aggregation operators abstract in this work we investigate the class of binary aggregation operators agops satisfying the 2 increasing property obtaining some characterizations for agops having other special properties e g quasi arithmetic mean choquet integral based modularity and presenting some construction methods in particular the notion of p increasing function is used in order to characterize the composition of 2 increasing agops the lattice structure with respect to the pointwise order of some subclasses of 2 increasing agops is presented finally a method is given for constructing copulas beginning from 2 increasing and 1 lipschitz agops

the mycin certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons abstract the uninorm operator class as defined by yager unifies the t norm and t conorm operator classes and allows special kind of aggregation that depends on the identity element in the paper the mycin certainty factor handling function f m is proved to belong to the uninorm operator class the shape of function f m is studied and its resemblance to artificial neuron s threshold functions is established the two variable function f m can be seen as an extension of typical neuron threshold functions to the three dimensional space the use of one of the two variables as a parameter gives the neuron tuning capabilities a specific class of artificial neural networks that cope with uncertainty and can use m as threshold function is also proposed

fuzzy class theory the paper introduces a simple yet powerful axiomatization of zadeh s notion of fuzzy set based on formal fuzzy logic the presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics its essence is elementary fuzzy set theory cast as two sorted first order theory over fuzzy logic which is generalized to simple type theory we show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism in this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed however we also demonstrate how to add structure to the universe of discourse within our framework

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

a framework for fuzzy quantification models analysis a framework for description of fuzzy quantification models is presented within this framework the fuzzy quantified statements evaluation problem is described as the compatibility between the fuzzy quantifier and a fuzzy cardinality or a fuzzy aggregation measure a list of desirable properties for quantification models is presented and those models that fit the framework are confronted with it

periodic lyapunov functions for periodic ts systems abstract in this paper we consider stability analysis and controller design for periodic takagi sugeno fuzzy models to develop the conditions we use a switching nonquadratic lyapunov function defined at the time instants when the subsystems switch using the proposed conditions we are able to handle periodic takagi sugeno systems where the local models or even the subsystems are unstable or cannot be stabilized the application of the conditions is illustrated on numerical examples

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

on usual values in commonsense reasoning abstract in many cases commonsense knowledge consists of knowledge of what is usual in this paper we develop a system for reasoning with usual information this system is based upon the fact that these pieces of commonsense information involve both a probabilistic aspect and a granular aspect we implement this system with the aid of probabilistic possibilistic granules

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

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

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

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

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

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

an equivalence relation based on the u partial order abstract in this paper an equivalence relation on the class of uninorms induced by the u partial order is discussed defining the set of all incomparable elements w r t the u partial order this set is deeply investigated and some relations with the sets of all incomparable elements w r t the orders induced by the corresponding underlying t norm and t conorm are presented also the set of all incomparable elements with a fixed element w r t the u partial order is defined and studied in detail

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

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

weighted norm inequalities for pseudo pseudodifferential operators defined by amplitudes abstract we prove weighted norm inequalities for pseudodifferential operators with amplitudes which are only measurable in the spatial variables the result is sharp even for smooth amplitudes nevertheless in the case when the amplitude contains the oscillatory factor e i 1 the result can be substantially improved we extend the l p boundedness of pseudo pseudodifferential operators to certain weights end point results are obtained when the amplitude is either smooth or satisfies a homogeneity condition in the frequency variable our weighted norm inequalities also yield the boundedness of commutators of these pseudodifferential operators with functions of bounded mean oscillation