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

on the existence of states on mtl algebras the aim of this paper is to investigate the existence of bosbach states and riecan states on mtl algebras we prove that an mtl algebra l has bosbach states if and only if l has an mv filter we also establish that l has a state morphism if and only if l has a maximal mv filter furthermore we obtain the necessary and sufficient condition for an mtl chain having riecan states

traveling wavefronts for time delayed reaction diffusion equation ii nonlocal nonlinearity abstract in this paper we study a class of time delayed reaction diffusion equation with local nonlinearity for the birth rate for all wavefronts with the speed c c where c 0 is the critical wave speed we prove that these wavefronts are asymptotically stable when the initial perturbation around the traveling waves decays exponentially as x but the initial perturbation can be arbitrarily large in other locations this essentially improves the stability results obtained by mei so li and shen m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 for the speed c 2 d m e p d m with small initial perturbation and by lin and mei c k lin m mei on travelling wavefronts of the nicholson s blowflies equations with diffusion submitted for publication for c c with sufficiently small delay time r 0 the approach adopted in this paper is the technical weighted energy method used in m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 but inspired by gourley s a gourley linear stability of travelling fronts in an age structured reaction diffusion population model quart j mech appl math 58 2005 257 268 and based on the property of the critical wavefronts the weight function is carefully selected and it plays a key role in proving the stability for any c c and for an arbitrary time delay r 0

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

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

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

the radical of a perfect residuated structure in this paper we extend some properties of the radical of an mtl algebra to the non commutative case of a more general residuated structure namely the fl w algebra for the particular case of pseudo mtl algebras some specific results are presented we introduce the notion of a local additive measure on a perfect pseudo mtl algebra and we prove that with some additional conditions every local additive measure can be extended to a riecan state a necessary and sufficient condition is given for such an extension to be a bosbach state

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

rough approximation operators on r0 algebras nilpotent minimum algebras with an application in formal logic l an abstract axiomatization to pawlak rough set theory in the context of r0 algebras equivalently nm algebras has been proposed in the present paper more precisely by employing the conjunction operator and the disjunction operator in r0 algebras the notions of rough upper approximation operator u and rough lower approximation operator l on r0 algebras are proposed respectively owing to the logical properties of and any r0 algebra equipped with l and u forms an abstract approximation space in the sense of g cattaneo a duality relationship between the set of lower crisp elements and the set of upper crisp elements is established and some important properties are examined moreover its connection with tarski closure interior approximation space and halmos closure interior approximation is studied such a pair of rough approximations on r0 algebras can naturally induce a pair of rough upper lower truth degrees for formulae in l some uncertainty measures such as roughness degree and accuracy degree are subsequently presented and two kinds of approximate reasoning methods merging rough approximation and fuzzy logic are eventually established

global asymptotics in some quasimonotone reaction diffusion systems with delays abstract both dichotomy and trichotomy on the global asymptotics of some quasimonotone reaction diffusion systems with delays are established in terms of the principal eigenvalue of linear weakly coupled elliptic systems applications to a class of delayed reaction diffusion models of single species growth and to a reaction diffusion system with delay modelling the spread of bacterial infections are provided

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

stability of non monotone critical traveling waves for reaction diffusion equations with time delay abstract this paper is concerned with the stability of critical traveling waves for a kind of non monotone time delayed reaction diffusion equations including nicholson s blowflies equation which models the population dynamics of a single species with maturation delay such delayed reaction diffusion equations possess monotone or oscillatory traveling waves the latter occurs when the birth rate function is non monotone and the time delay is big it has been shown that such traveling waves x c t exist for all c c and are exponentially stable for all wave speed c c 13 where c is called the critical wave speed in this paper we prove that the critical traveling waves x c t monotone or oscillatory are also time asymptotically stable when the initial perturbations are small in a certain weighted sobolev norm the adopted method is the technical weighted energy method with some new flavors to handle the critical oscillatory waves finally numerical simulations for various cases are carried out to support our theoretical results

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

on filter theory of residuated lattices the aim of this paper is to develop the filter theory of general residuated lattices first we extend some particular types of filters and fuzzy filters in bl algebras and mtl algebras naturally to general residuated lattices and further enumerate some relative results obtained in bl algebras or mtl algebras which still hold in general residuated lattices next we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices which are two new types of filters and fuzzy filters and derive some of their characterizations finally we discuss the relations between fuzzy regular filters and several other special fuzzy filters and also characterize some special classes of residuated lattices by filters or fuzzy filters

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

wavefronts and global stability in a time delayed population model with stage structure we formulate and study a one dimensional single species diffusive delay population model the time delay is the time taken from birth to maturity without diffusion the delay differential model extends the well known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes this delayed model is known to have simple global dynamics similar to that of the logistic equation through the use of a sub supersolution pair method we show that the diffusive delay model continues to generate simple global dynamics this has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics we also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population connecting the zero solution of that equation with the positive steady state our main finding here is that our fronts appear to be all monotone regardless of the size of the delay this is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

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

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

states on finite monoidal t norm based algebras the aim of this paper is to study the existences of bosbach states and riecan states on finite monoidal t norm based algebras mtl algebras for short we give some examples to show that there exist mtl algebras having no bosbach states and riecan states the conditions under which mtl algebras have bosbach states and riecan states are investigated respectively we prove that riecan states on mtl algebras are reduced to states on imtl algebras furthermore the necessary and sufficient conditions for finite linearly ordered locally finite mtl algebras and peculiar mtl algebras having bosbach states and riecan states are obtained respectively in addition the notions of pseudo quasi equivalent and a subalgebra under pseudo quasi equivalent are proposed and some of their properties are investigated

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

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

exponential stability of traveling waves in a nonlocal dispersal epidemic model with delay abstract in this paper we are concerned with the stability of traveling waves of a nonlocal dispersal epidemic model with delay in the quasi monotone case we prove the exponential stability of traveling wavefronts by the weighted energy method and the comparison principle when the initial perturbation around the traveling wavefront decays exponentially as x but can be arbitrarily large in other locations in the non quasi monotone case we investigate the exponential stability of traveling waves when the initial perturbation around the traveling wave is properly small in a weighted norm

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

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

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

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

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

stability of traveling waves of a diffusive susceptible infective removed sir epidemic model this paper is concerned with the stability and uniqueness of traveling waves of a delayed diffusive susceptible infective removed sir epidemic model we first prove the exponential stability of traveling waves by using the weighted energy method where the traveling waves are allowed to be non monotone then we establish the exact asymptotic behavior of traveling waves at by using ikehara s theorem finally the uniqueness of traveling waves is proved by the stability result of traveling waves

on the scope of some formulas defining additive connectives in fuzzy logics in fuzzy sets and systems 149 2005 297 wang et al defined a new fuzzy logic called nmg they also introduced new formulas to define the additive connectives from multiplicative conjunction residuated implication and bottom in nmg however they did not study the scope of these formulas in the general framework of fuzzy logics this is the aim of this paper therefore we add the definability formulas to known fuzzy logics as new axioms following the method used in beyond two theory and applications of multiple valued logic 2003 251 and we obtain some families of logics presented in a simpler language finally we discuss the standard completeness of these new logics

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

traveling waves in a nonlocal dispersal population model with age structure abstract this paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age structure if the birth function is monotone then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness it is proved that the traveling wavefront is strictly increasing and unique up to a translation the asymptotic behavior of traveling wavefronts is also obtained if the birth function is not monotone the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi monotonicity

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

a kahler structure on finsler spaces with nonzero constant flag curvature in this paper we obtain a kahler structure on the tangent bundle of a finsler manifold of positive constant flag curvature we show that there does not exist any finsler metric such that this structure became locally symmetric or einstein manifold similar results are obtained on a tube around zero section in the tangent bundle in the case of a finsler manifold of negative constant flag curvature

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

states on semi divisible generalized residuated lattices reduce to states on mv algebras a semi divisible residuated lattice is a residuated lattice l satisfying an additional condition weaker than that of divisibility such structures are related to mathematical fuzzy logic as well as to extended probability theory by the fact that the subset of complemented elements induces an mv algebra we define generalized residuated lattices by omitting commutativity of the corresponding monoidal operation and study semi divisibility in such structures we show that given a good generalized residuated lattice l the set of complemented elements of l denoted by mv l forms a pseudo mv algebra if and only if l is semi divisible maximal filters on a semi divisible generalized residuated lattice l are in one to one correspondence with maximal filters on mv l we study states on semi divisible generalized residuated lattices riecan states on a semi divisible generalized residuated lattice l are determined by riecan states on mv l the same holds true for bosbach states whenever l is a good divisible generalized residuated lattice extremal riecan states on a semi divisible generalized residuated lattice l are in one to one correspondence with maximal and semi normal filters on l

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