extending fuzzy logics with many hedges abstract fuzzy logic aims at modeling logical reasoning with vague or imprecise statements which may contain linguistic hedges in fact many hedges e g very highly rather and slightly can be used simultaneously to express different levels of emphasis moreover each hedge might have a dual one e g slightly can be seen as a dual hedge of very thus it is necessary to extend systems of fuzzy logic with multiple hedges this work proposes two axiomatizations for multiple hedges as an expansion of a core fuzzy logic in one axiomatization hedges do not have any dual one while in the other each hedge can have its own dual one it is shown that the proposed logics not only cover a large class of hedge functions but also have all completeness properties as the underlying logic w r t the class of their chains as well as distinguished subclasses of their chains including standard completeness the axiomatizations are also extended to the first order level furthermore we present a method to build linguistic fuzzy logics based on the axiomatizations and a hedge algebra whose corresponding algebras use a linguistic truth domain taken from the hedge algebra for representing and reasoning with linguistically expressed human knowledge where truth values of vague sentences are given in linguistic terms

mtl algebras arising from partially ordered groups after dropping the implication like operation and reversing the order an mtl algebra becomes a partially ordered structure l 0 1 based on the single addition like operation furthermore may be restricted to a partial but cancellative addition without loss of information we deal in this paper with the case that the resulting partial algebra l 0 1 is embeddable into the positive cone of a partially ordered group it turns out that most of the examples of mtl algebras known at present can be represented in this way so the systematisation of a considerable class of mtl algebras is achieved and the methods of their construction are brought onto a common line

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

uninorm logic with the n potency axiom this paper investigates a class of extensions c nul of uninorm logic ul which is obtained by adding the n potency axiom to ul the main result of this paper is that by generalizing jenei and montagna style approach for proving standard completeness for monoidal t norm based logic mtl we obtain the standard completeness for c nul in addition we present the suitable analytic hypersequent calculi for c nul

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

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

on tail dependence coefficients of transformed multivariate archimedean copulas this paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients in particular we focus on multivariate archimedean copulas in the first part of this paper we calculate multivariate transformed tail dependence coefficients when the generator of the considered transformed copula exhibits some regular variation properties and we investigate the behaviour of these coefficients in cases that are close to tail independence we obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation these results are also valid for non transformed archimedean copulas in the second part we deal with transformations presented by di bernardino and rulliere 20 we show the utility of using transformed archimedean copulas as they permit to build archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients finally we detail the extreme behaviour of the transformed radial part of archimedean copulas using results in larsson and neslehova 52 and we explain possible applications with transformed markov chains

spectra and variance of quantum random variables abstract we study essentially bounded quantum random variables and show that the gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of the essential range of moreover a notion of operator valued variance is introduced leading to a formulation of the moment problem in the context of quantum probability spaces in terms of operator theoretic properties involving semi invariant subspaces and spectral theory as an application of quantum variance new measures of random and inherent quantum noise are introduced for measurements of quantum systems modifying some recent ideas of polterovich 17

dirac equation in external vector fields separation of variables the method of separation of variables in the dirac equation in the external vector fields is developed through the search for exact solutions the essence of the method consists of the separation of the first order matricial differential operators that define the dependence of the dirac bispinor on the related variables but commutation of such operators with the operator of the equations or between them is not assumed this approach which is perfectly justified in the presence of gravitational fields permits one to prove rigorous theorems about necessary and sufficient conditions on the field functions that allow one to separate variables in the dirac equation in analogous investigations by other authors bagrov et al exact solutions of relativistic wave equations nauka novosibirst 1982 for electromagnetic fields an essential demand related to the operators that define the dependence of the bispinor on the separated variables is the demand for the commutation of a complete set of operators betw

solution of a system of linear equations with fuzzy numbers in this paper the interval nature of fuzzy numbers is revealed by showing that many interesting results from classical interval analysis transfer also into the fuzzy case the paper deals with a solution of a fuzzy interval system of linear equations i e a system in which fuzzy intervals numbers appear instead of crisp numbers

copulas diagonals and tail dependence we present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence moreover we present the tail concentration function which depends on the diagonal section of a copula as a tool to give a description of tail dependence at finite scale the tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space moreover it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior

logical structure of fuzzy if then rules abstract this paper provides a logical basis for manipulation with fuzzy if then rules our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to lotfi a zadeh but also other kinds of approximate reasoning methods e g perception based deduction provided that there exists a possibility to characterize them within a formal logical system in contrast with other approaches employing variants of multiple valued first order logic the approach presented here employs fuzzy type theory of v novak which has sufficient expressive power to present the essential concepts and results in a compact elegant and justifiable form within the effectively formalized representation developed here based on a complete logical system it is possible to reconstruct numerous well known properties of cri related fuzzy inference methods albeit not from the analytic point of view as usually presented but as formal derivations of the logical system employed the authors are confident that eventually all relevant knowledge about fuzzy inference methods based on fuzzy if then rule bases will be represented formalized and backed up by proof within the well founded logical representation presented here an immediate positive consequence of this approach is that suddenly all elements of a fuzzy inference method based on fuzzy if then rules are first class citizens of the representation there are clear logically founded definitions for fuzzy if then rule bases to be consistent complete or independent

independence results for multivariate tail dependence coefficients in this paper we study some properties of multivariate lower and upper tail dependence coefficients and analyze the relationship between pairwise tail independence mutual tail independence and extremal independence

on some questions concerning the axiomatisation of wnm algebras and their subvarieties in a seminal paper esteva and godo introduced monoidal t norm based logic mtl and some of its prominent extensions such as nm and wnm we notice that nm is axiomatisable from imtl and hence mtl with one variable axioms by instantiating the wnm axiom over one variable this observation leads us here to study the logic axiomatised by extending mtl by this one variable axiom we shall refer to its equivalent algebraic semantics as the variety of ghp algebras for those algebras will be shown to form the largest variety of mtl algebras such that the falsum free reducts of the positive cones of their chains are the most general totally ordered godel hoops among other results we obtain a general description of ghp standard algebras and use the latter to characterise those extensions of wnm that can be obtained from ghp via the same set of extending axioms

rotation invariant t norms where triple rotation and rotation annihilation meet generalizing the notion of a zoom of a t norm not only allows to extend the triple rotation method and its corresponding decomposition but also allows to describe the interface between the triple rotation method and the rotation annihilation method an alternative view on the partition behind the rotation annihilation method is required to make both methods compatible besides zooms we also use contour lines and the companion of a t norm to concisely formulate the results

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

characterizations of maximal consistent theories in the formal deductive system l nm logic and cantor space a maximal consistent theory is a maximal theory with respect to its consistency the present paper is divided into two parts the first one is devoted to characterize the maximality of a consistent theory in the formal deductive system l which is a logic system equivalent to the nilpotent minimum logic it is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas hence it follows that there is a one to one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e p 0 12 1 the satisfiability theorem and compactness theorem of l are obtained the second part is to investigate the topological structure of the set of all maximal consistent theories over l and the results show that this topological space is a cantor space

conditional expectation and bayes rule for quantum random variables and positive operator valued measures a quantum probability measure is a function on a algebra of subsets of a locally compact and hausdorff sample space that satisfies the formal requirements for a measure but where the values of are positive operators acting on a complex hilbert space and a quantum random variable is a measurable operator valued function although quantum probability measures and random variables are used extensively in quantum mechanics some of the fundamental probabilistic features of these structures remain to be determined in this paper we take a step toward a better mathematical understanding of quantum random variables and quantum probability measures by introducing a quantum analogue for the expected value e of a quantum random variable relative to a quantum probability measure in so doing we are led to theorems for a change of quantum measure and a change of quantum variables we also introduce a quantum conditional expectation which results in quantum versions of some standard identities for r

topology on bl algebras in this paper by using a special family of filters on a bl algebra l we construct a topology on l show that l is a topological bl algebra find the closure of any subsets of l and obtain some conditions under which that l is a hausdorff space also we prove some theorems about connected components of this topological space and use them to construct a quotient semitopological bl algebras finally we introduce the concept of complete bl algebra and attempt to construct a complete bl algebra from l

discrete dualities for n potent mtl algebras and 2 potent bl algebras abstract discrete dualities are developed for n potent mtl algebras and for 2 potent bl algebras that is classes of frames or relational systems are defined that serve as dual counterparts to these classes of algebras the frames defined here are extensions of the frames that were developed for mtl algebras in 24 and 25 the additional frame conditions required are given here and also the proofs that discrete dualities hold with respect to such frames the duality also provides an embedding from an n potent mtl algebra or 2 potent bl algebra into the complex algebra of its canonical frame which is a complete algebra in the lattice sense

an early approach toward graded identity and graded membership in set theory the paper considers an early approach toward a fuzzy set theory with a graded membership predicate and a graded equality relation which had been developed by the german mathematician klaua in 1965 in the context of the mathematical fuzzy logic mtl of left continuous t norms we discuss some properties of these graded relations we compare the simultaneous recursive definitions of these relations with the very similar approach toward boolean algebra valued interpretations of membership and equality presented in 1967 by scott and r solovay in the context of independence proofs for zf set theory finally we speculate about possible reasons why klaua soon abandoned this approach

efficient estimation of copula based semiparametric markov models this paper considers the efficient estimation of copula based semiparametric strictly stationary markov models these models are characterized by nonparametric invariant one dimensional marginal distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes the markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications we first show that markov processes generated via clayton gumbel and student s t copulas and their survival copulas are all geometrically ergodic we then propose a sieve maximum likelihood estimation mle for the copula parameter the invariant distribution and the conditional quantiles we show that the sieve mles of any smooth functional is root n consistent asymptotically normal and efficient and that their sieve likelihood ratio statistics are asymptotically chi square distributed monte carlo studies indicate that even for markov models generated via tail dependent copulas and fat tailed marginals our sieve mles perform very well

density elimination density elimination a close relative of cut elimination consists of removing applications of the takeuti titani density rule from derivations in gentzen style hypersequent calculi its most important use is as a crucial step in establishing standard completeness for syntactic presentations of fuzzy logics that is completeness with respect to algebras based on the real unit interval 0 1 this paper introduces the method of density elimination by substitutions for general classes of first order hypersequent calculi it is shown that density elimination by substitutions is guaranteed by known sufficient conditions for cut elimination these results provide the basis for uniform characterizations of calculi complete with respect to densely and linearly ordered algebras standard completeness follows for many first order fuzzy logics using a dedekind macneille style completion and embedding

on a class of transformations of copulas and quasi copulas the theory of copulas is by now a very well established one recently larger classes of functions c 0 1 n 0 1 that are increasing in each variable and satisfy some conditions at the boundary like quasi copulas have been the object of fruitful research several authors have considered the action of a class of transformations on some aggregation operators as t norms copulas quasi copulas and so on these simple transformations do not preserve in general all properties of copulas or quasi copulas in particular the fact that only some properties are preserved by these transformations suggested the introduction of semi copulas the purpose of the present contribution is to give a fairly complete picture concerning such action on copulas and quasi copulas in particular we prove results concerning inclusions and strict inclusions among these classes of operators and those of their transforms

exchangeable copulas this paper focuses on exchangeable copulas some necessary and sufficient conditions are provided together with a characterization result in differential form a very flexible model capable to generate a wide range of exchangeable copulas is presented

multivariate archimedean copulas d monotone functions and l1 norm symmetric distributions it is shown that a necessary and sufficient condition for an archimedean copula generator to generate a d dimensional copula is that the generator is a d monotone function the class of d dimensional archimedean copulas is shown to coincide with the class of survival copulas of d dimensional l 1 norm symmetric distributions that place no point mass at the origin the d monotone archimedean copula generators may be characterized using a little known integral transform of williamson duke math j 23 1956 189 207 in an analogous manner to the well known bernstein widder characterization of completely monotone generators in terms of the laplace transform these insights allow the construction of new archimedean copula families and provide a general solution to the problem of sampling multivariate archimedean copulas they also yield useful expressions for the d dimensional kendall function and kendall s rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for archimedean copulas the existence of a sharp lower bound for archimedean copulas with respect to the positive lower orthant dependence ordering is shown

subexponential distributions and characterizations of related classes letl 0 0 denote the class of distributionsf satisfying mathop lim limits x to infty bar f 2 x bar f x 2 mathop smallint limits 0 infty e gamma y df y infty i mathop lim limits x to infty bar f 2 x y bar f x e gamma y forall y in mathbb r ii the classesl for 0 are characterized by means of subexponential densities as an application we derive a result on the asymptotic behaviour of densities of random sums in particular for anm g 1 queue we relate the tail behaviour of the stationary waiting time density to that of the service time distribution

prenex normal form in linguistic quantifiers modeled by sugeno integrals in this paper ying s prenex normal form theorem for linguistic quantifiers is strengthened so that it behaves like the one in the classical logic this result further shows elegant logical properties of ying s framework

maxima and minima in fuzzified linear orderings the paper studies the notions of fuzzy maxima minima suprema and infima in the setting of fuzzified linear orderings the main result shows that in fuzzified linear orders satisfying certain reasonable assumptions the fuzzy maxima and minima of all non empty fuzzy sets are non empty

some types of filters in mtl algebras the aim of this work is to introduce the concepts of imtl filters and strong mtl filters in mtl algebras and show that these filters are related to imtl algebras and strong mtl algebras respectively we also introduce the concepts of eimtl and associative filters in mtl algebras the relationships between these filters and quotient algebras that are constructed via these filters are described we clarify that eimtl imtl and fantastic filters coincide in bl algebras whereas they have different properties in mtl algebras moreover the relations between them are delineated we prove that strong filters include some current filters such as implicative positive implicative and fantastic filters

dirac equation in external fields separation of variables in nondiagonal metrics the algebraic method of separation of variables in the dirac equation proposed in earlier works by one of the present authors theor math phys 70 204 1987 j math phys 30 2132 1989 is developed for the space time with nondiagonal metrics the essence of the method consists of the separation of the first order matricial differential operators that define the dependence of the dirac s bispinor on the related variables in contrast to some other authors the pairs of operators are commuted on each step of separation including the variables mixed by nondiagonal elements of fundamental tensor of space time there are reasons to believe that it must be some local similarity transformation connected these commuted operators with noncommuted corresponding operators of other authors although such transformation in view of mathematical difficulties of problem in general were not successfully found

fuzzy sets and formal logics the paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics our focus is on the historical side of these developments

eigenvalues and eigenfunctions of the dirac operator on spheres and pseudospheres the dirac equation for an electron on a curved space time may be viewed as an eigenvalue problem for the dirac operator on the spinor fields of the space time a general eigenvalue problem for the dirac operator on a metric manifold m in terms of spinor and tangent fields defined via the clifford algebra is derived herein then it is shown how to solve the dirac eigenvalue problem on an imbedded submanifold n of codimension one in m by solving an eigenvalue equation on m this is applied to the case of a sphere or pseudosphere imbedded in flat space eigenvalues and eigenfunctions for the dirac operator on any sphere or pseudosphere are determined in particular when the pseudosphere is a space time the dirac equation for a free lepton in this space time can be solved the resulting mass spectrum is discrete and depends on the curvature of the space time

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

some kinds of c ccq interval valued fuzzy ideals of bci algebras in this paper we first introduce the notions of positive implicative implicative and commutative interval valued fuzzy ideals of bci algebras which are generalizations of positive implicative implicative and commutative fuzzy ideals respectively and investigate some of their related properties the concept of quasi coincidence of an interval valued fuzzy point within an interval valued fuzzy set is introduced in fact the concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we further introduce the notions of positive implicative implicative and commutative q interval valued fuzzy ideals of bci algebras and investigate some of their related properties some characterization theorems of these generalized interval valued fuzzy ideals are derived the relationship among these generalized interval valued fuzzy ideals of bci algebras is also considered

an algebraic approach to linguistic hedges in zadeh s fuzzy logic the paper addresses the mathematical modelling of domains of linguistic variables i e term sets of linguistic variables in order to obtain a suitable algebraic structure for the set of truth values of zadeh s fuzzy logic we shall give a unified algebraic approach to the natural structure of domains of linguistic variables which was proposed by ho and wechler fuzzy sets and systems 35 1990 281 and then by ho and nam proc ncst vietnam 9 1 1997 15 logic algebra and computer science vol 46 banach center publications pwn warsaw 1999 p 63 in this approach every linguistic domain can be considered as an algebraic structure called hedge algebra because properties of its unary operations reflect semantic characteristics of linguistic hedges many fundamental properties of refined hedge algebras rh algebras are examined especially it is shown that every rh algebra of a linguistic variable with a chain of the primary terms is a distributive lattice rh algebras with exactly two distinct primary terms one being an antonym of the other will also be investigated and they will be called symmetrical rh algebras it is shown that a class of finite symmetrical rh algebras has a rich enough algebraic structure

continuous weakly cancellative triangular subnorms i their web geometric properties abstract the paper studies web geometric properties of continuous weakly cancellative t subnorms particularly it studies the reidemeister closure condition which is known from web geometry as a visual characterization of those loops that are associative as a result the paper delimits a subset of the domain of a continuous weakly cancellative t subnorm in which the reidemeister closure condition is necessarily satisfied

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

on the use of aggregation operations in information fusion processes this position paper discusses the role of the existing body of fuzzy set aggregation operations in various kinds of problems where the process of fusion of items coming from several sources is central several kinds of membership functions can be useful according to the nature of the information to be merged numerical vs ordinal inputs preferences vs uncertain data observations vs constraints in each case some aggregation operations look more plausible or feasible than others the aim of this discussion is to suggest directions for putting at work the results of recent mathematical investigations in the structure of aggregation operations

on two distributivity equations for fuzzy implications and continuous archimedean t norms and t conorms recently we have examined the solutions of the following distributivity functional equation i x s 1 y z s 2 i x y i x z when s 1 s 2 are continuous archimedean t conorms and i is an unknown function in particular between these solutions we have shown that implication functions are among its solutions in this paper we continue these investigations for the following distributivity equations i t x y z s i x z i y z i s x y z t i x z i y z when t is a continuous archimedean t norm and s is a continuous archimedean t conorm the first equation has been investigated by trillas and alsina in 2002 31 while the second equation has been investigated by balasubramaniam and rao in 2004 12 for different classes of fuzzy implications like r implications s implications and ql implications obtained results are not only theoretical but it can also be useful for the practical problems since such equations have an important role to play in efficient inferencing in approximate reasoning especially in fuzzy control systems

on deductive interpolation for the weak nilpotent minimum logic the weak nilpotent minimum logic wnm was introduced by esteva and godo in 6 and shown to be the logic of the class of weak nilpotent minimum triangular norms in this article we prove that wnm admits the deductive interpolation property by showing through a model theoretic argument that the corresponding variety of algebras has the amalgamation property

an operator valued lyapunov theorem abstract we generalize lyapunov s convexity theorem for classical scalar valued measures to quantum operator valued measures in particular we show that the range of a nonatomic quantum probability measure is a weak closed convex set of quantum effects positive operators bounded above by the identity operator under a sufficient condition on the non injectivity of integration to prove the operator valued version of lyapunov s theorem we must first define the notions of essentially bounded essential support and essential range for quantum random variables borel measurable functions from a set to the bounded linear operators acting on a hilbert space

adjoint negations more than residuated negations negation operators are useful operators which have extensively been studied and used in different fuzzy settings such as in fuzzy logic this paper introduces a new and flexible kind of negation operator based on adjoint triples and which is called adjoint negation relative to a fixed element besides proving several interesting properties the comparison with weak negations studied by trillas esteva et al and pairs of weak negations introduced by georgescu and popescu is presented furthermore adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor

parameterizing the semantics of fuzzy attribute implications by systems of isotone galois connections we study the semantics of fuzzy if then rules called fuzzy attribute implications parameterized by systems of isotone galois connections the rules express dependences between fuzzy attributes in object attribute incidence data the proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches we formalize the general parameterizations propose bivalent and graded notions of semantic entailment of fuzzy attribute implications show their characterization in terms of least models and complete axiomatization and provide characterization of bases of fuzzy attribute implications derived from data

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

a practical approach for estimating weights of interacting criteria from profile sets aggregating multi criteria data is an important problem with many applications commonly used additive aggregation methods such as the weighted arithmetic mean cannot account for the criteria interactions encountered in many practical multi criteria decision problems the choquet integral is a suitable aggregation operator in the presence of interacting criteria it replaces the weight vector with a fuzzy measure that models the importance of each subset or coalition of criteria rather than just the importance of individual criteria however estimating the fuzzy measures in practice has been problematic conventional approaches are cognitively challenging for decision makers while more recent approaches suffer from prohibitive data requirements in this paper we present a formulation for the weights of the choquet integral that uses principal component analysis to account for criteria interaction this novel unsupervised approach to estimating the required fuzzy measures overcomes the limitations of other methods the approach is applied to two case studies in environmental and sustainability analysis and the results are compared with those of the weighted arithmetic mean the first case is a triple bottom line analysis of 135 australian industry sectors evaluated against 11 criteria while the second case is an environmental life cycle assessment of 8 alternative biosolids management options evaluated against 5 criteria these examples demonstrate the ability of the proposed approach to account for criteria interaction in these and other decision contexts

term satisfiability in flew algebras fl ew algebras form the algebraic semantics of the full lambek calculus with exchange and weakening we investigate two relations called satisfiability and positive satisfiability between fl ew terms and fl ew algebras for each fl ew algebra the sets of its satisfiable and positively satisfiable terms can be viewed as fragments of its existential theory we identify and investigate the complements as fragments of its universal theory we offer characterizations of those algebras that positively satisfy just those terms that are satisfiable in the two element boolean algebra providing its semantics to classical propositional logic in case of positive satisfiability these algebras are just the nontrivial weakly contractive fl ew algebras in case of satisfiability we give a characterization by means of another property of the algebra the existence of a two element congruence further we argue that positive satisfiability problems in fl ew algebras are computationally hard some previous results in the area of term satisfiability in mv algebras or bl algebras are thus brought to a common footing with known facts on satisfiability in heyting algebras

a characterization of truth functions in the nilpotent minimum logic abstract by introducing a new family of partitions into the n cube 0 1 n the problem of characterizing truth tables of formulas in the nilpotent minimum logic is solved and their normal forms are presented so far only this kind of fuzzy truth functions have normal forms among all fuzzy propositional calculi which are based on left continuous but discontinuous t norm

a graded notion of functionality abstract we will introduce the notion of functionality as a graded property of a fuzzy relation we will extend known results relating to functional fuzzy relations to their graded counterparts and provide new properties w r t various kinds of relational compositions as a contribution to the theory of fuzzy control we will moreover provide an example of use of graded properties in establishing implicative models of fuzzy rule bases where the non graded property fails

frank s condition for multivariate archimedean copulas in this paper we study possible multivariate generalizations of construction of n copulas with a given diagonal section in the case of archimedean n copulas we prove that email protected s condition which establishes when an archimedean 2 copula is characterized by its diagonal section can be extended to larger dimensions