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

generalized optimal designs and contingency plans in linear systems abstract to select an optimal linear design means to select the best subset from a set of possible products or opportunities for commitment and to construct the corresponding optimal contingency plans for coping with the changes of decision parameters based on lee shi and yu this paper discusses a method for generating generalized good designs from known potentially good designs we describe how to use the multi criteria and multi constraint level mc 2 simplex method to identify the generalized optimal designs and their related optimal contingency plans a procedure for effectively and systematically solving the problem of selecting linear designs is proposed

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

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

algebraic and proof theoretic characterizations of truth stressers for mtl and its extensions extensions of monoidal t norm logic mtl and related fuzzy logics with truth stresser modalities such as globalization and very true are presented here both algebraically in the framework of residuated lattices and proof theoretically as hypersequent calculi completeness with respect to standard algebras based on t norms embeddings between logics decidability and the finite embedding property are then investigated for these logics

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

fuzzy potential solutions in multi criteria and multi constraint level linear programming problems abstract given a multi criteria and multi constraint level mc 2 linear programming problem we can use an mc 2 simplex method to find a set of potential solutions each potential solution optimizes the mc 2 problem under a certain range of decision parameters namely the criteria weight vector and the constraint level weight vector in this paper we extend the potential solution to a fuzzy potential solution for a given fuzzy mc 2 problem with a certain range of the decision parameters a membership function of the mc 2 problem is first constructed then for such a parameter range a fuzzy potential solution is determined in terms of the membership function and a primal potential basis based on the theoretical analysis we propose a heuristic algorithm to systematically and effectively locate all fuzzy potential solutions for all possible changes of the decision parameters a numerical example is used to illustrate the algorithm

invariance to ordinal transformations in rank aware databases we study influence of ordinal transformations on results of queries in rank aware databases which derive their operations with ranked relations from totally ordered structures of scores with infima acting as aggregation functions we introduce notions of ordinal containment and equivalence of ranked relations and prove that infima based algebraic operations with ranked relations are invariant to ordinal transformations queries applied to original and transformed data yield results which are equivalent in terms of the order given by scores meaning that top k results of queries remain the same we show this important property is preserved in alternative query systems based of relational calculi developed in context of godel logic we comment on relationship to monotone query evaluation and show that the results can be attained in alternative rank aware approaches

distribution based behavioral distance for nondeterministic fuzzy transition systems modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems in this paper we first present a new notion of bisimulation for nondeterministic fuzzy transition systems which is distribution based and coarser than state based bisimulation appeared in the literature then we define a distribution based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations we also propose an on the fly algorithm for computing the bisimilarity metric moreover we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric interestingly this characterization holds for a class of fuzzy modal logics in addition we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric which makes compositional verification possible

graded properties of unary and binary fuzzy connectives the paper studies basic graded properties of unary and binary fuzzy connectives i e unary and binary operations on the set of truth degrees of a background fuzzy logic extending the logic mtl of left continuous t norms the properties studied in this paper are graded generalizations of monotony lipschitz continuity null and unit elements idempotence commutativity and associativity the paper elaborates the initial study presented in previous papers and focuses mainly on parameterization of graded properties by conjunction multiplicities of subformulae in the defining formulae preservation of graded properties under compositions and slight variations of fuzzy connectives the values of graded properties for basic connectives of the ground logic and the dependence of the values on the ground logic the results are proved in the formal framework of higher order fuzzy logic mtl also known as fuzzy class theory fct general theorems provable in fct are illustrated on several semantic examples

on the continuity of residuals of triangular norms abstract in this work a long standing problem related to the continuity of r implications i e implications obtained as the residuum of t norms has been solved a complete characterization of the class of continuous r implications obtained from any arbitrary t norm is given in particular it is shown that an r implication i t is continuous if and only if t is a nilpotent t norm using this result the exact intersection between the continuous subsets of r implications and s n implications has been determined by showing that the only continuous s n implication that is also an r implication obtained from any t norm not necessarily left continuous is the ukasiewicz implication up to an isomorphism

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

some types of generalized fuzzy filters of bl algebras the aim of this paper is to introduce the notions of interval valued q fuzzy boolean implicative positive implicative and fantastic filters in bl algebras and to investigate some related properties some characterizations of these generalized fuzzy filters are derived finally the relations among these generalized fuzzy filters are discussed it is proved that an interval valued q fuzzy filter in bl algebras is an interval valued q fuzzy boolean implicative filter if and only if it is both an interval valued q fuzzy positive implicative filter and an interval valued q fuzzy fantastic filter

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

generating new designs using union operations abstract in many real world problems we want to generate new designs ideas by taking unions of subsets of a given basic set of potentially good designs primitives this paper proposes a streamlined algorithm of finding distinct unions of subsets of the primitives we show how to use the algorithm to eliminate a number of redundant unions of subsets of the primitives in the process of finding all distinct unions theoretical results are derived to justify the algorithm applications of the algorithm are also discussed

granular variable precision fuzzy rough sets with general fuzzy relations the variable precision fuzzy rough sets were proposed to remedy the defects of preexisting fuzzy rough set models however the variable precision fuzzy rough sets were only defined and investigated on fuzzy similarity relations in this paper the granular variable precision fuzzy rough sets with general fuzzy relations are proposed on arbitrary fuzzy relations the equivalent expressions of the approximation operators are given with fuzzy co implications on arbitrary fuzzy relations which can calculate efficiently the approximation operators the granular variable precision fuzzy rough sets are characterized from the constructive approach which are investigated on different fuzzy relations the conclusions on the variable precision fuzzy rough sets are generalized into the granular variable precision fuzzy rough sets

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

on varieties singly generated by a well connected flew algebra abstract in this short note we show that given a variety v of fl e w algebras generated by a well connected algebra there always exists a subdirectly irreducible algebra generating v this solves an open problem first raised in galatos et al residuated lattices an algebraic glimpse at substructural logics 2007

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

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

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

truth values on generalizations of some commutative fuzzy structures hajek introduced the logic bl v t enriching the logic bl by a unary connective vt which is a formalization of zadeh s fuzzy truth value very true bl v t algebras i e bl algebras with unary operations called vt operators which are among others subdiagonal are an algebraic counterpart of bl v t residuated lattice ordered monoids r monoids are common generalizations of bl algebras and heyting algebras in the paper we study algebraic properties of r v t algebras and consequently of bl v t algebras and of those that are enriched by derived superdiagonal operators which in the case of mv algebras are the duals to vt operators

causal compensation for erasures in frame representations in a variety of signal processing and communications contexts erasures occur inadvertently or can be intentionally introduced as part of a data reduction strategy this paper discusses causal compensation for erasures in frame representations of signals the approach described assumes linear synthesis of the signal using a prespecified frame but no specific generation mechanism for the coefficients under this assumption it is demonstrated that erasures can be compensated for using low complexity causal systems if the transmitter is aware of the occurrence of the erasure an optimal compensation is to project the erasure error to the remaining coefficients it is demonstrated that the same compensation can be executed using a transmitter receiver combination in which the transmitter is not aware of the erasure occurrence the transmitter precompensates using projections as if assuming erasures will occur the receiver undoes the compensation for the coefficients that have not been erased thus maintaining the compensation only of the erased coefficients the stability of the resulting systems is explored and stability conditions are derived it is shown that stability for any erasure pattern can be enforced by optimizing a constrained quadratic program at the system design stage the paper concludes with examples and simulations that verify the theoretical results and illustrate key issues in the algorithms

on expansions of wnm t norm based logics with truth constants this paper focuses on completeness results about generic expansions of propositional weak nilpotent minimum wnm logics with truth constants indeed we consider algebraic semantics for expansions of these logics with a set of truth constants r r c for a suitable countable c 0 1 and provide a full description of completeness results when i the t norm is a weak nilpotent minimum satisfying the finite partition property and ii the set of truth constants covers all the unit interval in the sense that each interval of the partition contains values of c in its interior

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

a fuzzy programming approach for solving a multiple criteria and multiple constraint level linear programming problem abstract this paper presents a solution method to the multiple criteria and multiple constraint level linear program mc2lp using a fuzzy linear programming approach this approach finds a potential solution to the problem by solving a fuzzy linear program which is different than the usual approach of mc2 simplex method

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

cancellativity properties for t norms and t subnorms on the one hand cancellativity properties are mainly used to express to which extend the partial functions of a t subnorm t are injective on the other hand the zooms of t corresponding to its non trivial archimedean components are t subnorms that largely determine t fixing one out of four basic types of cancellativity cancellativity conditional cancellativity weak cancellativity and weak conditional cancellativity we figure out which less restrictive type of cancellativity expresses that all maximal archimedean zooms of t satisfy the given cancellativity property we lay bare the mutual relationships between all these types of cancellativity and solve an open problem posed by klement et al

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

nmł a schematic extension of f esteva and l godo s logic mtl abstract a schematic extension nm of f esteva and l godo s logic mtl is introduced in this paper based on a new left continuous but discontinuous t norm which was proposed by s jenei and can be regarded as a kind of distorted nilpotent minimum the semantics of nm is interpreted and the standard completeness theorem of nm is proved the fact that the maximum and the minimum are definable from the negation and implication in nm and nm is discovered which also leads to a modification of the nm axiom system

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

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

tl filters of integral residuated l monoids in this paper we introduce and discuss the concept of tl filters of integral residuated l monoids first we study some basic properties of tl filters and give the formula for calculating the tl filters generated by l subsets then we discuss some properties of tl filters under homomorphisms and study the relationship between tl filters and t congruence l relations on integral commutative residuated l monoids

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

precompensation for anticipated erasures in lti interpolation systems this paper considers compensation of anticipated erasures in a discrete time dt signal such that the desired interpolation can still be accomplished with minimum error through a linear time invariant lti filter the algorithms presented may potentially be useful in the compensation of a fault in a digital to analog converter where samples are dropped at known locations prior to reconstruction four algorithms are developed the first is a general solution that in the presence of erasures minimizes the squared error for arbitrary lti interpolation filters in certain cases e g oversampling and a sinc interpolating filter this solution is specialized so it perfectly compensates for erasures the second solution is an approximation to the general solution that computes the optimal finite length compensation for arbitrary lti interpolation filters the third is a finite length windowed version of the oversampled sinc interpolating solution using discrete prolate spheroidal sequences the last is an iterative algorithm in the class of projection onto convex sets analysis and results from numerical simulations are presented

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

non existence of convolution sum system representations convolution sum system representations are commonly used in signal processing it is known that the convolution sum treated as the limit of its partial sums can be divergent for certain continuous signals and stable linear time invariant lti systems even when the convergence of the partial sums is treated in a distributional setting in this paper we ask a far more general question is it at all possible to define a generalized convolution sum with natural properties that works for all absolutely integrable continuous signals that vanish at infinity and all stable lti systems we prove that the answer is no further for certain subspaces we give a sufficient and necessary condition for uniform convergence finally we discuss the implications of our results on the effectiveness of window functions in the convolution sum

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

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

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

soft bl algebras based on fuzzy sets by means of soft sets and q soft sets some characterizations of implicative positive implicative and fantastic filteristic soft bl algebras are investigated finally we prove that a soft set is an implicative filteristic soft bl algebra if and only if it is both a positive implicative filteristic soft bl algebra and a fantastic filteristic soft bl algebra

lattice based sum of t norms on bounded lattices abstract the concept of ordinal sums in the sense of clifford have long been blamed for their limitations in constructing new t norms including inability to cope with general bounded lattices motivated by this observation and based on the lattice based sum of lattices that has been recently introduced by el zekey et al we propose a new sum type construction of t norms called a lattice based sum of t norms for building new t norms on bounded lattices from given ones the proposed sum is generalizing the well known ordinal and horizontal sum constructions of t norms by allowing for lattice ordered index sets we demonstrate that like the ordinal sum of t norms the lattice based sum of t norms can be generalized using as summands so called t subnorms still leading to a t norm subsequently we apply the results for constructing several new families of t norms and t subnorms on bounded lattices in the same spirit by the duality we will also introduce lattice based sums of t conorms and t subconorms

fuzzy reasoning as a control problem different from the dominant view of treating fuzzy reasoning as generalization of classical logical inference in this paper fuzzy reasoning is treated as a control problem a new fuzzy reasoning method is proposed that employs an explicit feedback mechanism to improve the robustness of fuzzy reasoning the fuzzy rule base given a priori serves as a controlled object and the fuzzy reasoning method serves as the corresponding controller the fuzzy rule base and the fuzzy reasoning method constitute a control system that may be open loop or closed loop depending on the underlying reasoning goals constraints the fuzzy rule base the fuzzy reasoning method and the corresponding reasoning goals constraints define the three distinct ingredients of fuzzy reasoning while various existing fuzzy reasoning methods are essentially a static mapping from the universe of single fuzzy premises to the universe of single fuzzy consequences the new fuzzy reasoning method maps sequences of fuzzy premises to sequences of fuzzy consequences and is a function of the underlying reasoning goals constraints the monte carlo simulation shows that the new fuzzy reasoning method is much more robust than the optimal fuzzy reasoning method proposed in our previous work the explicit feedback mechanism embedded in the fuzzy reasoning method does significantly improve the robustness of fuzzy reasoning which is concerned with the effects of perturbations associated with given fuzzy rule bases and or fuzzy premises on fuzzy consequences the work presented in this paper sets a new starting point for various principles of feedback control and optimization to be applied in fuzzy reasoning or logical inference and to explore new forms of reasoning including robust reasoning and adaptive reasoning it can be also expected that the new fuzzy reasoning method presented in this paper can be used for modeling and control of complex systems and for decision making under complex environments

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

some kinds of fuzzy ideals of bci algebras the concepts of c c q d fuzzy positive implicative implicative and commutative ideals and c c q d fuzzy positive implicative implicative and commutative ideals in bci algebras are introduced some new characterizations are investigated in particular we prove that a fuzzy set m of a bci algebra x is an c c q d fuzzy implicative ideal of x if and only if it is both an c c q d fuzzy positive implicative ideal and an c c q d fuzzy commutative ideal finally we give some characterizations of three particular classes of bci algebras by these generalized fuzzy ideals

distributional behavior of convolution sum system representations in this paper we study the validity of the usual convolution sum sampling representation of linear time invariant lti systems we consider continuous input signals with finite energy that are absolutely integrable and vanish at infinity even for these benign signals the convolution sum does not always converge there exist lti systems and signals such that the convolution sum diverges even in a distributional sense this result shows that the practice of multiplying a signal with a dirac comb and convolving subsequently with the impulse response of the lti system is not valid for this signal space we further fully characterize the lti systems for which we have convergence for all signals in the space and establish a connection between the pointwise uniform and distributional convergence in particular we show that the convolution sum converges in a distributional sense if and only it converges in a classical pointwise sense hence for this signal space nothing can be gained by treating the convergence in a distributional sense

linear optimal designs and optimal contingency plans in optimal design problems we try to select a subset from the opportunity set for commitment for a period of time as the external parameters can vary with time optimal contingency plans must be constructed to cope with the external conditions we describe the formulation and methods for locating potentially good designs and their corresponding optimal contingency plans using a multiple criteria and multiple constraint level mc2 simplex method to solve the optimal design problems which have been shown to become amenable to the techniques of decision making under uncertainty

fuzzy implicative and boolean filters of r 0 algebras the notions of fuzzy filters fuzzy implicative filters and fuzzy boolean filters are introduced in r0 algebras respectively some of their properties are investigated the relations between fuzzy implicative filters and fuzzy boolean filters are discussed the characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent 1 a fuzzy filter f is implicative 2 f is a fuzzy boolean filter 3 x y z l f x z f x z y f y z 4 x y l f x y f x y y 5 x l n 1 f nx f x

undefinability of min conjunction in mtl firstly a sufficient and necessary condition is given to decide whether the lattice operations of a wnm chain can be definable from its other operations secondly we show that it is indeed necessary to introduce the min conjunction into mtl as a primitive connective by constructing a left continuous t norm such that in the propositional calculus defined by this t norm the min conjunction and max disjunction are not definable from the strong conjunction implication and truth constant email protected

disjunctive elimination rule and its application in mtl firstly the disjunctive elimination rule is proved valid in esteva and godo s mtl and hajek s bl logics secondly from this rule a general method is presented for finitely axiomatizing the intersection of the sets of theorems of two given schematic extensions of mtl or bl thirdly the axiomatic system of nm is simplified by replacing the axiom schemata nm with another which is built up with one variable fourthly the intersection of the sets of tautologies of nm and g nm and p nm and l are finitely axiomatized by our method finally new axiom systems for lg email protected pg email protected are presented by our method and some comments are made on the relations between these systems and those given by cignoli et al

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

characterizations and new subclasses of i filters in residuated lattices abstract filters play an important role in studying logical systems and the related algebraic structures various filters have been proposed in the literature in this paper we aim to develop a unifying definition for some specific filters called i filters which provide us with a meaningful method to study these filters and corresponding logical algebras in particular trivial characterizations of i filters non trivial characterizations of classes of i filters such as implicative fantastic and boolean filters and characterizations of homologous logical algebras are obtained next three new types of i filters named divisible filters strong and n contractive filters in residuated lattices are introduced particularly it is verified that n fold implicative bl algebras and n contractive bl algebras coincide finally we investigate the relationships between these specific i filters it is shown that a filter is a fantastic filter if and only if it is both a divisible filter and a regular filter

generalized consistency degrees of theories w r t formulas in several standard complete logic systems abstract the present paper carries out a deep analysis on the inconsistency of theories by means of deduction theorems completeness theorems and satisfiability degrees of formulas and introduces the concept of the degree of entailment of a contradiction from a theory in classical two valued logic system ukasiewicz fuzzy logic system godel fuzzy logic system product fuzzy logic system and the r 0 fuzzy logic system it is proved that in classical two valued logic system ukasiewicz fuzzy logic system and the r 0 fuzzy logic system respectively the concept of consistency degrees of theories defined by the divergence degrees of theories in x n zhou g j wang consistency degrees of theories in some systems of propositional fuzzy logic fuzzy sets and systems 152 2005 321 331 h j zhou g j wang a new theory index based on deduction theorems in several logic systems fuzzy sets and systems 157 2006 427 443 is reasonable and can accurately measure the consistency degrees of theories the concept of the degree of entailment of a contradiction from a theory is generalized by replacing the contradiction with a general formula and then the generalized consistency degrees of theories w r t general formulas in the above mentioned logic systems is established

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

unified full implication algorithms of fuzzy reasoning this paper discusses the full implication inference of fuzzy reasoning for all residuated implications induced by left continuous t norms unified a triple i algorithms are constructed to generalize the known results as the corollaries of the main results of this paper some special algorithms can be easily derived based on four important residuated implications these algorithms would be beneficial to applications of fuzzy reasoning based on properties of residuated implications the proofs of the many conclusions are greatly simplified

semi divisible t norms on discrete scales semi divisibility of left continuous triangular norms is a weakened version of the divisibility axiom the t norms on l 0 1 n 2 n 1 which fulfil the semi divisibility axiom are studied the only semi divisible t norm with ran n t l is shown to correspond to the lukasiewicz t norm several examples of semi divisible discrete t norms are shown

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

proof theory for locally finite many valued logics semi projective logics we extend the methodology in baaz and fermuller 1999 5 to systematically construct analytic calculi for semi projective logics a large family of propositional locally finite many valued logics our calculi defined in the framework of sequents of relations are proof search oriented and can be used to settle the computational complexity of the formalized logics as a case study we derive sequent calculi of relations for nilpotent minimum logic and for hajek s basic logic extended with the n contraction axiom n 1 the introduced calculi are used to prove that the decidability problem in these logics is co np complete

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

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

rotation invariant t norm solutions of a system of functional equations the generalization of the disjunctive and conjunctive boolean normal forms to fuzzy set theory obtained by interpreting as a t norm as a t conorm and as a negator often provides a kind of standard fuzzification procedure a system of functional equations turns up if some functional independence of the difference between both generalizations is demanded in this paper we explore which de morgan triplets based on a left continuous t norm t solve this system imposing some extra continuity conditions on t these t norm solutions can be obtained by the rotation construction of jenei the cauchy equation plays a key role in the reasoning process

the structure of generalized intermediate syllogisms abstract in this paper we continue development of the formal theory of intermediate quantifiers which are expressions of the natural language most many few etc in the previous paper we demonstrated that 105 generalized syllogisms are valid in our theory we introduce the generalization of all the figures and we show that for the proof of validity of all the generalized syllogisms we need to prove the validity of only few of them so that the validity of the other ones immediately follows

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

results on equality algebras in this paper by considering the notion of equality algebra which is introduced by jenei in 18 as a possible algebraic semantic for fuzzy type theory we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice mtl algebra bl algebra mv algebra hertz algebra heyting algebra boolean algebra eq algebra and hoop algebra the aim of this paper is to find that under which conditions equality algebras are equivalent to these logical algebras

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