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

truth depressing hedges and bl logic abstract we show a complete axiomatization of unary connectives interpreted by monotone and superdiagonal truth functions so called truth depressing hedges these connectives formalize linguistic hedges like slightly true and more or less we follow ideas of p hajek on very true fuzzy sets and systems 124 2001 329 333 and show that bl vt logic can be enriched by a unary connective for which we can establish strong completeness with respect to the desired interpretation

the number of reidemeister moves for splitting a link we give an explicit upper bound for the number of reidemeister moves for deforming a link diagram of a split link to be disconnected

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

p ary unified sequences p ary extended d form sequences with the ideal autocorrelation property in this paper for a prime number p a construction method to generate p ary d form sequences with the ideal autocorrelation property is proposed and using the ternary sequences found by helleseth kumar and martinsen 2000 ternary d form sequences with the ideal autocorrelation property are constructed by combining the methods for generating p ary extended sequences a special case of geometric sequences and p ary d form sequences a construction method of p ary unified extended d form sequences which also have the ideal autocorrelation property is proposed this is a very general class of p ary sequences including the binary and nonbinary extended sequences and the d form sequences from the ternary sequences by helleseth kumar and martinsen ternary unified sequences with the ideal autocorrelation property are also generated

character sum factorizations yield sequences with ideal two level autocorrelation we give a new existence criterion for p ary sequences which have ideal two level autocorrelation and we use it to obtain four general families of such sequences one for p 2 one for general odd primes p and two special ones for p 3 the binary family turns out to be equivalent to that discovered by dillon and dobbertin and published in 2004 the general p ary family is equivalent to that discovered by gong and helleseth by dillon and when p 3 by helleseth kumar and martinsen all of these p ary results were published in 2001 and 2002 the special ternary families are new and give as special cases the sequences conjectured by alfred lin in his 1998 ph d thesis as well as most of those conjectured in 2001 by ludkovski and gong our sequences may also be used to construct relative difference sets their corresponding block designs and generalized weighing matrices

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

on v filters and normal v filters of a residuated lattice with a weak vt operator in this paper we study further the filter theory of residuated lattices first we discuss the concepts of filters and normal filters of residuated lattices and propose some equivalent conditions for them then we introduce and investigate the notions of v filter and normal v filter of a residuated lattice with a weak vt operator and lay bare the formulas for calculating the v filters and the normal v filters generated by subsets finally we show that the lattices of v filters and normal v filters of a residuated lattice with a vt operator are both complete brouwerian lattices

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

new families of codebooks achieving the levenstein bound in this paper a construction of codebooks based on a set of bent functions satisfying certain conditions is introduced it includes some earlier constructions of codebooks meeting the levenstein bound as special cases with this construction two new families of codebooks achieving the levenstein bound are obtained the codebooks constructed in this paper could have a very small alphabet size

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 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

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

on the linear complexity of some new q ary sequences some new q ary sequences with period q 3 e k 1 q p m p an odd prime m e k integers are first constructed and then inspired by antweiler s method their linear complexity is examined the exact value of linear complexity k 6e w is determined when email protected i 1 wp e i furthermore an upper bound of the linear complexity is given for the other values of r our results show that this sequence has larger linear span than gmw sequence with the same parameters finally the results of a maple program are included to illustrate the validity of the results

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

effective algebraic degeneracy we show that for every smooth projective hypersurface x n 1 of degree d and of arbitrary dimension n 2 if x is generic then there exists a proper algebraic subvariety y x such that every nonconstant entire holomorphic curve f x has image f which lies in y as soon as its degree satisfies the effective lower bound d geqslant 2 n 5

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

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

a new family of nonbinary sequences with three level correlation property and large linear span in this correspondence we present a new family of nonbinary sequences with three level nontrivial correlations and large linear complexity the sequences may be considered as nonlinear analogues of the well known sequences by trachtenberg and helleseth it is shown that the family is optimal with respect to the welch bound in terms of root mean square of all nontrivial correlations we also determine the correlation distribution of the new family

functional completeness of bounded structures of fuzzy logic with wvt operators a simple criterion for a functional completeness of partially ordered commutative integral monoids with a weak very true operator is presented

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

binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation generated by the polynomial z sup d z 1 sup d we present a construction for binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation property using the polynomial z sup d z 1 sup d we show that the sequence obtained from the polynomial becomes an m sequence for certain values of d we also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k spl plusmn 1 where k is a positive integer these new sequences are represented using a trace function and the results are tabulated

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

divisible difference sets relative difference sets and sequences with ideal autocorrelation abstract in this correspondence we consider the equivalent condition that a sequence possesses ideal autocorrelation function as we know for a binary sequence the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets this paper proves that for a p ary sequence with d form property the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p 1 relative difference sets moreover a new way to construct cyclic divisible difference sets is presented

some new classes of zero difference balanced functions zero difference balanced zdb functions were introduced recently by ding for the construction of optimal constant composition codes and optimal and perfect difference systems of sets they are closely related to partitioned difference families in this paper we present generic constructions of zdb functions from functions with difference balanced property in particular two classes of zdb functions with new and flexible parameters are reported employing these new zdb functions we obtain at the same time optimal 1 constant composition codes 2 constant weight codes and 3 perfect difference systems of sets all with new and flexible parameters

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

bounding codimension one subvarieties and a general inequality between chern numbers we extend the miyaoka yau inequality for a surface to an arbitrary nonuniruled normal complex projective variety eliminating the hypothesis that the variety must be minimal the in equality is sharp in dimension three and is also sharp among minimal varieties for nonminimal varieties in dimension four or higher an error term is picked up which can be controlled as a consequence we bound codimension one subvarieties in a variety of general type linearly in terms of their chern numbers in particular we show that there are only a finite number of smooth fano abelian and calabi yau subvarieties of codimension one in any variety of general type

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

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

new nonbinary sequences with ideal two level autocorrelation we find new families of nonbinary sequences of period p sup n 1 with symbols from a finite field f sub p for any prime p spl ges 3 the sequences have two level ideal autocorrelation and are generalizations of previously found ternary sequences with ideal autocorrelation difference sets with parameters p sup n 1 p 1 p sup n 1 1 p 1 p sup n 2 1 p 1 can also be derived from these sequences in a natural way

almost etale resolution of foliations in the general this article addresses the nature of and relation between canonical and log canonical singularities of foliations by curves the case of equivariance under a finite group action has several peculiarities amongst which are examples from dimension 3 onward where no birational modification can be both gorenstein and log canonical the article in the specific i e a functorial resolution algorithm for foliated 3 folds in the 2 category of deligne mumford champs is thus not only optimal but natural

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

new cyclic relative difference sets constructed from d homogeneous functions with difference balanced property for a prime power q we show that a cyclic relative difference set with parameters q sup n 1 q 1 q 1 q sup n 1 q sup n 2 can be constructed from a d homogeneous function from f sub q sup n spl bsol 0 onto f sub q with difference balanced property where f sub q sup n is the finite field with q sup n elements this construction method enables us to construct several new cyclic relative difference sets with parameters p sup n 1 p sup l 1 p sup l 1 p sup n l p sup n 2l from p ary sequences of period p sup n 1 with ideal autocorrelation property introduced by helleseth and gong using a lifting idea other new cyclic relative difference sets can be constructed from the helleseth gong hg sequences also the 3 ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary hg sequences and ternary lin sequences are derived

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

the proof of lin s conjecture via the decimation hadamard transform in 1998 lin presented a conjecture on a class of ternary sequences with ideal two level autocorrelation those sequences have a very simple structure i e their trace representation has two trace monomial terms in this paper we present a proof for the conjecture the mathematical tools employed are the second order multiplexing decimation hadamard transform stickelberger s theorem the teichmuller character and combinatorial techniques for enumerating the hamming weights of ternary numbers as a by product we also prove that the ternary sequences conjectured by lin are hadamard equivalent to ternary m sequences

new constructions for optimal sets of frequency hopping sequences in this paper two generic constructions of optimal frequency hopping sequence fhs sets employing d form functions with difference balanced property are presented they generalize the previous constructions of optimal fhs sets using m sequences and produce new optimal fhs sets that cannot be produced by the earlier constructions by choosing appropriate d form functions with difference balanced property both constructions lead to fhss with large linear complexity in addition one of the proposed constructions gives new optimal parameters of fhs sets

a three valued walsh transform from decimations of helleseth gong sequences the walsh transform of two level autocorrelation sequences has played an important role in the construction of the set of sequences in which any two sequences are orthogonal for p ary sequences there are only two basic classes of two level autocorrelation sequences with no subfield structures for an arbitrary odd prime p one is the class of p ary m sequences and the other is the class of p ary helleseth gong sequences in this paper the walsh transform of a subclass of p ary helleseth gong sequences and the walsh transform of their particular decimations are completely determined and are shown to be three valued

higher dimensional tautological inequalities and applications we study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds using ahlfors currents in higher dimension we obtain several strong degeneracy statements such as the proof of a generalized green griffiths lang conjecture for threefolds with holomorphic foliations of codimension one

some results on cross correlation distribution between a p ary m sequence and its decimated sequences for an odd prime p and two positive integers m k such that m gcd k m 3 is odd let d be a positive integer satisfying d p k 1 2 mod p m 1 i n this paper the cross correlation between a p ary m sequence and its d decimated sequences is investigated and the cross correlation distribution is completely determined the relationship between the decimations d considered in this paper and some known ones is also studied this paper generalizes some previous results and also gives new decimations which lead to low cross correlation