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

ultradiffusion on the fractal branching koch curves ultradiffusion is defined on a family of fractal branching koch curves by an exact renormalization decimation transformation the anomalous long time behaviour of the autocorrelation function is obtained for the particular hierarchy the authors find a non universal crossover c1 m 1 2m and a universal one c2 1 2 as the effective temperature c is increased where m is the maximum ramification number of the fractal they also find that for large m the dynamic behaviour of ultradiffusion on the fractal is independent of the effective temperature c

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

a unary error correction code for the near capacity joint source and channel coding of symbol values from an infinite set a novel joint source and channel code jscc is proposed which we refer to as the unary error correction uec code unlike existing jsccs our uec facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality conventionally these symbols are conveyed using separate source and channel codes ssccs but we demonstrate that the residual redundancy that is retained following source coding results in capacity loss this loss is found to have a value of 1 11 db in a particular practical scenario where quaternary phase shift keying qpsk modulation is employed for transmission over an uncorrelated narrowband rayleigh fading channel by contrast the proposed uec code can eliminate this capacity loss or reduce it to an infinitesimally small value furthermore the uec code has only a moderate complexity facilitating its employment in practical low complexity applications

fuzzy reasoning and fuzzy relational equations l a zadeh first suggested a method of fuzzy reasoning called compositional rule of inference cri for short instead of sup min composition we use a more general composition called sup t composition in cri according to the criteria gmp and gmt the fuzzy implication r must satisfy the sup t composite fuzzy relational equations email protected r s and email protected r 1 q in this paper we discuss the solution of these equations and point out that email protected composition and the implication r n a used to cri will be more suitable under criteria gmp and gmt

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

near capacity joint source and channel coding of symbol values from an infinite source set using elias gamma error correction codes in this paper we propose a novel low complexity joint source and channel code jscc which we refer to as the elias gamma error correction egec code like the recently proposed unary error correction uec code this facilitates the practical near capacity transmission of symbol values that are randomly selected from a set having an infinite cardinality such as the set of all positive integers however in contrast to the uec code our egec code is a universal code facilitating the transmission of symbol values that are randomly selected using any monotonic probability distribution when the source symbols obey a particular zeta probability distribution our egec scheme is shown to offer a 3 4 db gain over a uec benchmarker when quaternary phase shift keying qpsk modulation is employed for transmission over an uncorrelated narrowband rayleigh fading channel in the case of another zeta probability distribution our egec scheme offers a 1 9 db gain over a separate source and channel coding sscc benchmarker

differently implicational universal triple i method of 1 2 2 type as a generalization of the triple i method differently implicational universal triple i method of 1 2 2 type universal triple i method for short is investigated first the concepts of residual operators and strongly residual operators are given and then related conclusions of residual pairs are provided second the related universal triple i solutions including fmp solutions fmt solutions and so on are strictly defined by the infimum where such solutions are divided into two parts respectively corresponding to the minimum and infimum then we put emphasis on the fmp solutions in which the unified forms of fmp solutions w r t strongly residual operators and a new idea for getting fmp solutions w r t infimum are achieved third as a result of analyzing the logic basis of a sort of cri compositional rule of inference method it is found that their cri solutions can be regarded as special cases of fmp solutions lastly the response functions of fuzzy systems via universal triple i method are discussed which demonstrates that the universal triple i method can provide bigger choosing space and get better fuzzy controllers by contrast with the triple i method and cri method

triple i method of fuzzy reasoning abstract the theory of the triple i method with total inference rules of fuzzy reasoning is investigated by using zadeh s implication operator rz the computational formulae for both fuzzy modus ponens fmp and fuzzy modus tollens fmt are obtained the reversibility properties for fmp and fmt are analyzed and the reversibility criteria are given we also investigated the generalized problem of the triple i method and obtained the formulae for the triple i fmp and the triple i fmt

a note on the unified forms of triple i method wang and fu 1 provided the unified forms of the triple i method for fuzzy modus ponens fmp for short and fuzzy modus tollens fmt for short and found an interesting duality between them in this paper we first answer why there exists the duality and then establish another unified form of the triple i method for fmt under a weaker condition

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

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

on the logic foundation of fuzzy reasoning abstract fuzzy reasoning and fuzzy formal deduction theory are two closely related subjects and each of them has been investigated by many researchers unfortunately it seems that the two branches have not been successfully connected the aim of this paper is to establish a so called quasi propositional deductive system syntactically as well as semantically and then set a logic foundation for developing the theory of fuzzy reasoning therefrom

an algebraic and geometric approach to non bijective quadratic transformations this work is concerned with an extension of the so called levi civita and kustaanheimo stiefel transformations the extension is achieved along two lines firstly the authors examine the latter transformations in other dimensions than the ones originally considered by on the one hand levi civita and on the other hand by kustaanheimo and stiefel secondly they pass from the compact to the non compact case this leads to quadratic non bijective transformations that they refer to as hurwitz or kustaanheimo stiefel like and quasihurwitz or levi civita like transformations the hurwitz and quasihurwitz transformations are introduced and studied in an algebraic framework which relies on the use of eight dimensional cayley dickson algebras an explicit formulation of the hurwitz and quasihurwitz transformations is also given in terms of clifford algebras the hurwitz transformations are investigated from a geometrical viewpoint indeed they are connected to hopf and pseudohopf fibrations finally some differential aspects of the hurwitz and to a lesser extent quasihurwitz transformations are developed in view of future physical applications

multifractal nature of diffusion on hierarchical structures the authors study the moments of the first passage time t of random walks on hierarchical structures using the exact enumeration method they find that the different moments scale with the size of the system with an infinite hierarchy of exponents characterising a multifractal behaviour

unified forms of fully implicational restriction methods for fuzzy reasoning the goal of this paper is to extend the scope of previously proposed fully implicational restriction methods for fuzzy reasoning and provide a unified form of these methods which can employ diverse implications by means of the residual implications generated by left continuous t norms we obtain the supremum of triple i the abbreviation of triple implications restriction solutions for fuzzy modus ponens and the supremum of multiple i restriction solutions for general fuzzy reasoning respectively furthermore we obtain the infimum of triple i restriction solutions and the supremum of triple i restriction solutions for fuzzy modus tolens finally the optimal i e the largest or smallest depending on context restriction solutions of both basic and general reasoning problems are derived for four specific residual implications

three and two valued łukasiewicz theories in the formal deductive system l nm logic in order to offer a logic foundation for fuzzy reasoning and to reduce the gap between fuzzy reasoning and artificial intelligence a new formal deductive system l was introduced in 1996 it was proved that the prominent nilpotent minimum logic is a logic system equivalent to l as is well known in classical propositional logic there is a one to one correspondence between deductively closed theories and topologically closed subsets of the stone space of all maximally consistent theories recently by means of the strong completeness of l we obtained the structural and topological characterizations of maximally consistent theories in this logic it was proved that the set of all maximally consistent theories over l with an induced topology is a cantor space in order to establish a similar connection between theories over l and closed subsets of this topological space to the classical case we introduce in this paper the notion of three valued lukasiewicz theory and the notion of two valued lukasiewicz boolean theory we prove that there is also a one to one correspondence between deductively closed three valued lukasiewicz theories and closed subsets of the space and boolean theories correspond to the closed subsets of the subspace of all maximally consistent boolean theories lastly we give an alternative proof for the structural characterization of the maximality of consistent theories over l by induction on the complexity of formulas which is independent of the strong completeness of l and also independent of the perfectness of the standard r 0 algebra

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

continuity of triple i methods based on several implications this paper focuses on the continuity problem of fully implicational triple i methods for fuzzy reasoning based on the residual implications generated by continuous triangular norms the residual implication generated by nilpotent minimum with the standard negation and the zadeh implication respectively continuity and uniform continuity properties of triple i methods are examined in hamming and uniform metrics we also investigate the continuity of the model of a fuzzy if then rule corresponding to the triple i methods

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

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

genetic algorithm aided design of component codes for irregular variable length coding in this paper we propose a novel real valued free distance metric rv fdm for comparing the error correction capabilities of variable length error correction vlec codebooks that have the same integer valued free distance lower bounds we demonstrate that vlec codebooks having higher rv fdms tend to have extrinsic information transfer exit functions with more pronounced s shapes furthermore we show that higher accuracy exit chart matching can be achieved if the component exit functions of an irregular code exhibit more variety this motivates the employment of our novel genetic algorithm for designing the component vlec codes of irregular variable length coding that have particular exit functions in addition to exhibiting desirable bit entropies and decoding complexities

scaling of the first passage time and the survival probability on exact and quasi exact self similar structures the authors calculate the asymptotic behaviour of the moments of the first passage time and survival probability for random walks on an exactly self similar tree and on a quasi self similar comb by applying an exact decimation approach to the master equations for the hierarchical comb a transition from ordinary to anomalous diffusion occurs at r 2 where r is the ratio of teeth length in successive iterations of the structure in the anomalous regime r 2 the positive integer moments of the first passage time tq scale as ltau q with tau q 1 2q 1 ln r ln 2 where l is the linear distance from input to output the asymptotic behaviour of the survival probability is studied using both scaling theory and by a direct solution of the master equations they find that the characteristic time t in the asymptotic exponential decay of the survival probability exp t t scales as t approximately ltau with tau ln r2 ln 2 i e tau is distinct from tau 1 however substantial corrections to this asymptotic form for tau exist and these are needed to account for the recent simulation data of havlin and matan 1988

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

triple i method based on pointwise sustaining degrees the concept of the pointwise sustaining degrees is first introduced and based on it the triple i principles for fuzzy modus ponens fmp for short and fuzzy modus tollens fmt for short are improved and then for the sake of making more implications can be used under the same way general computing formulas of the triple i method for fmp and fmt are established under weaker conditions thus the existing unified forms of triple i method are generalized to new forms

integrated semantics and logic metric spaces the concept of tautology degree of an abstract proposition is proposed in this paper by means of integral of the corresponding function with respect to certain semantics over 0 1 then a pseudo metric among abstract propositions is introduced and the r logic metric space is proposed where r is a suitable implication operator finally a new theoretical framework for approximate reasoning in the r logic metric space is provided

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

irregular trellis for the near capacity unary error correction coding of symbol values from an infinite set irregular joint source and channel coding jscc scheme is proposed which we refer to as the irregular unary error correction iruec code this code operates on the basis of a single irregular trellis instead of employing a set of separate regular trellises as in previous irregular trellis based codes our irregular trellis is designed with consideration of the uec free distance which we characterize for the first time in this paper we conceive the serial concatenation of the proposed iruec code with an irregular unity rate code irurc code and propose a new extrinsic information transfer exit chart matching algorithm for parametrizing these codes this facilitates the creation of a narrow exit tunnel at a low e text b n 0 value and provides near capacity operation owing to this our scheme is found to offer a low symbol error ratio ser which is within 0 4 db of the discrete input continuous output memoryless channel dcmc capacity bound in a particular practical scenario where gray mapped quaternary phase shift keying qpsk modulation is employed for transmission over an uncorrelated narrowband rayleigh fading channel with an effective throughput of 0 508 text bit text s 1 text hz 1 furthermore the proposed iruec irurc scheme offers a ser performance gain of 0 8 db compared to the best of several regular and irregular separate source and channel coding sscc benchmarkers which is achieved without any increase in transmission energy bandwidth transmit duration or decoding complexity

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

multiple valued extensions of analogical proportions this paper provides a discussion of different multiple valued extensions of logical expressions of analogical proportions that are equivalent in the boolean case it is advocated that these extensions may serve different goals or at least reflect different views boolean expressions of analogical proportions modeling statements of the form a is to b as c is to d are first restated and commented an approach to handling the case of binary attributes that may not apply in the boolean setting is also outlined via a proper encoding

scaling properties of diffusion on comb like structures the authors study the scaling properties of the probability density of random walks on comb like structures they find that in contrast to the first passage time in which several exponents are needed to characterise their distribution the probability density can be described by a single exponent

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

a fuzzy similarity inference method for fuzzy reasoning in this paper fuzzy similarity inference fsi is investigated first the axiomatic definition of the fuzzy similarity measure is introduced it is a generalization of the similarity measure some formulas are given to compute the fuzzy similarity of two fuzzy sets second a novel fuzzy reasoning called fuzzy similarity inference is proposed computational formulas for both fuzzy modus ponens fmp and fuzzy modus tollens fmt are obtained based on the theory of partial valuations fsi method is put under the framework of logic semantically furthermore the generalized problem of fsi is investigated computational formulas for a fsi fmp and a fsi fmt are obtained at last reversibility properties of fsi are proved

the extensions l n of the formal system l n and their completeness in this paper the method of well combined semantics and syntax proposed by pavelka is applied to the research of the propositional calculus formal system l the part of constant values are taken as formulas formulas are fuzzified in two manners semantically and syntactically and inferring processes are fuzzified a sequence of new extensions l n of the system l is proposed and the completeness of l n is proved

non fuzzy versions of fuzzy reasoning in classical logics abstract fuzzy reasoning features fuzzy logic in its narrow sense fln and fuzzy modus ponens fmp is the core of fuzzy reasoning as is well known fmp is far more general and complicated than the conventional rule of modus ponens mp and takes the latter as special case under certain conditions this paper proves that there exist non fuzzy versions of fmp in classical 2 valued logic as well as in conventional multivalued systems and reveals the roots of these seemingly surprising results

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

analysis and design of time variant fuzzy systems based on dynamic fuzzy inference in this paper a class of time variant fuzzy systems is designed and analyzed firstly a novel model of dynamic fuzzy inference dfi is proposed and the corresponding dfi method is obtained then the response abilities of time variant fuzzy systems constructed by the dfi method are analyzed some sufficient conditions for time variant fuzzy systems as step functions fitted functions and interpolation functions are derived furthermore a sufficient and necessary condition for time variant fuzzy systems as interpolation functions is also deduced in addition the approximation problem of time variant fuzzy systems is discussed it is proved that time variant fuzzy systems constructed by the dfi method are universal approximators to a class of nonlinear systems in addition the approximation accuracy of the corresponding time variant fuzzy systems is investigated finally a simulation experiment is provided to demonstrate how to design a time variant fuzzy system in order to approximate a given nonlinear system to a desired accuracy

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

scaling of the first passage time of biased diffusion on hierarchical comb structures biased diffusion on hierarchical comb structures is studied within an exact renormalisation group scheme the scaling exponents of the moments of the first passage time for random walks are obtained it is found that the scaling properties of the diffusion depend only on the direction of bias in a particular case the presence of bias may give rise to a new multifractality

unified forms of triple i method first the present paper provides unified forms of triple i method for fuzzy modus ponens and fuzzy modus tollens of which diverse implication operators can be employed second it is clarified that in a sense zadeh s cri method for fuzzy modus ponens can be brought into line with the unified form of the triple i method lastly a unified form of a triple i method is established as well and a duality result concerning a triple i solutions of fuzzy modus ponens and fuzzy modus tollens is obtained

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

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

fuzzy conditional inference under max composition abstract this paper shows that the majority of fuzzy inference methods for a fuzzy conditional proposition if x is a then y is b with a and b fuzzy concepts can infer very reasonable consequences which fit our intuition with respect to several criteria such as modus ponens and modus tollens if a new composition called max composition is used in the compositional rule of inference though reasonable consequences cannot always be obtained when using the max min composition which is used usually in the compositional rule of inference furthermore it is shown that a syllogism holds for the majority of the methods under the max composition though they do not always satisfy the syllogism under the max min composition

the r0 type fuzzy logic metric space and an algorithm for solving fuzzy modus ponens fuzzy modus ponens briefly fmp is the most fundamental form of fuzzy reasoning and has been extensively discussed by diverse researchers the aim of the present paper is to propose a formalized form of fmp called generalized modus ponens in the fuzzy logic system l and solve it in l and then provide its numerical version as a new algorithm for solving fmp as a preparation some related questions such as what is a fuzzy logic metric space why is r 0 implication operator selected and what kind of merits does the fuzzy pseudo metric logic space f s r possess etc are analyzed

stone like representation theorems and three valued filters in r0 algebras nilpotent minimum algebras nilpotent minimum algebras nm algebras are algebraic counterpart of a formal deductive system where conjunction is modeled by the nilpotent minimum t norm a logic also independently introduced by guo jun wang in the mid 1990s such algebras are to this logic just what boolean algebras are to the classical propositional logic in this paper by introducing respectively the stone topology and a three valued fuzzy stone topology on the set of all maximal filters in an nm algebra we first establish two analogues for an nm algebra of the well known stone representation theorem for a boolean algebra which state that the boolean skeleton of an nm algebra is isomorphic to the algebra of all clopen subsets of its stone space and the three valued skeleton is isomorphic to the algebra of all clopen fuzzy subsets of its three valued fuzzy stone space respectively then we introduce the notions of boolean filter and of three valued filter in an nm algebra and finally we prove that three valued filters and closed subsets of the stone space of an nm algebra are in one to one correspondence and boolean filters uniquely correspond to closed subsets of the subspace consisting of all ultrafilters

some properties of fuzzy reasoning in propositional fuzzy logic systems in order to analyze the logical foundation of fuzzy reasoning this paper first introduces the concept of generalized roots of theories in lukasiewicz propositional fuzzy logic luk godel propositional fuzzy logic god product propositional fuzzy logic p and nilpotent minimum logic nm the r 0 propositional fuzzy logic l next it is proved that all consequences of a theory c named d c are completely determined by its generalized root whenever c has a generalized root moreover it is proved that every finite theory c has a generalized root which can be expressed by a specific formula finally we demonstrate the existence of a non fuzzy version of fuzzy modus ponens fmp in luk god p and nm l and we provide its numerical version as a new algorithm for solving fmp

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

structure of left continuous triangular norms with strong induced negations iii construction and decomposition this paper is the continuation of jenei j appl non classical logics 10 2000 83 92 11 2001 351 366 where the rotation construction and the rotation annihilation construction have been presented respectively both constructions produce left continuous but not continuous triangular norms with strong induced negations here we show that these two constructions allow us to define indecomposability and that each decomposable left continuous triangular norm with strong induced negation can be derived as result of one of the above constructions in this way two general decomposition theorems arise in addition the decomposition of left continuous triangular norms with strong induced negations can be defined in a unique way namely when the decomposition is done by the minimal decomposition point