dual fuzzy neighbourhood spaces i abstract a fuzzy neighbourhood space fns is determined by means of a system of fuzzy neighbourhoods of the ordinary points of that space we provide a general method for constructing bases for all fuzzy neighbourhood systems in a natural way from the fuzzy topologies of a special type of fuzzy topological spaces fts s which we call the fuzzy neighbourhood base spaces this construction is shown to be functorial of those new fts s the full subcategory of dual fuzzy neighbourhood spaces is shown to be isomorphic to the category of fns s and a fns will coincide with its dual fts iff it is topologically generated

fuzzy sets and residuated logic abstract the properties of a set theory rzf defined in a logic weaker than intuitionistic logic are investigated using natural models rzf is intended to act as a framework for fuzzy set theory more general and applicable than heyting valued structures such as topoi the theory rzf contains an interpretation of classical set theory and is consistent relative to this theory it is also a suitable theory for the expression of attributes of uncertainty and vagueness since a certain subclass of the sets definable in this theory are crisp or two valued and behave classically whereas sets in general obey only residuated logic of which the ukasiewicz semantics on 0 1 the real interval is a particular realisation

algorithms for a multi level network optimization problem in this paper we work on a multi level network optimization problem that integrates into the same model important aspects of i discrete facility location ii topological network design and iii network dimensioning potential applications for the model are discussed stressing its growing importance the multi level network optimization problem treated is defined and a mathematical programming formulation is presented we make use of a branch and bound algorithm based on lagrangean relaxation lower bounds to introduce some new powerful auxiliary algorithms to exactly solve the problem we conduct a set of computational experiments that indicate the quality of the proposed approach

a comparative study of adjoint triples adjoint triples are helpful as basic operators used in several domains for example adjoint triples play an important role in two important frameworks multi adjoint logic programming and multi adjoint concept lattices this paper shows that adjoint triples are an interesting generalization of t norms and their residuated implications since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework furthermore these operators will be related to other important general triples specifically implication triples and the definition of these latter operators will be improved

convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing abstract this paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form x k 2 x k r y k k 1 2 k where x k and y k denote fuzzy sets r and 2 fuzzy relations the sup min compositional operator the inf max one and a fuzzy convex combinator whose complement is furthermore we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations focusing our attention on the modeling of fuzzy input output systems normality of fuzzy sets characterizing fuzzy input fuzzy logical aspects of systems and association between fuzzy information finally it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems

on generalized modus ponens with multiple rules and a residuated implication we consider a multiple rule generalized modus ponens inference scheme with an interpretation based on compositional rule of inference cri and a residuated implication we show that such a system is equivalent as far as cri is concerned to a system that satisfies the basic requirement for fuzzy reasoning proposed by turksen and tian fuzzy sets and systems 58 1993 3 40 we establish an analogous conclusion for an alternative interpretation due to magrez and smets of generalized modus ponens which we call consequent dilation rule cdr this method is computationally faster than cri but it produces less specific inference results

fuzzy relational equations with generalized connectives and their applications the idea of fuzzy relational equation with generalized connectives is introduced and algorithms of resolution of this class equations are presented in details it is clearly shown that some types of well known fuzzy relational equations sup min inf max can be treated as special cases of a wise class of equations under discussion applicational aspects are carefully investigated presenting the advantages of the proposed approach

associatively tied implications we say that an implication operator a on a complete lattice l is associatively tied if there is a binary operation t on l that ties a that is the identity a a gamma a t holds for all in l this property extends to multiple valued logic the following equivalence in classical logic x y z x y z we show that in this case there exists an associative binary operation ta that ties a hence the nomenclature we study properties of that ta when a is associatively tied we then seek a characterization for the validity of associative tiedness for an implication a phrased in terms of a and two adjoints of it

enhanced formulations and branch and cut for the two level network design problem with transition facilities abstract we consider a new combinatorial optimization problem that combines network design and facility location aspects given a graph with two types of customers and two technologies that can be installed on the edges the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree in addition besides fixed link installation costs facility opening costs associated to each node where primary and secondary subtree connect have to be paid the problem is called the two level network design problem with transition facilities tlndf we first model the problem on an extended graph where an additional set of arcs corresponds to the installation of node facilities and propose a cut set based model for the tlndf that is defined on this extended graph we present several theoretical results relating families of cut set inequalities on the extended graph with subfamilies of cut set inequalities on the original graph we then show how a standard multi commodity flow model defined on the original graph can be strengthened using disaggregation by technology we prove that the disaggregated compact formulation on the original graph provides the same lower bound as the cut set formulation on the extended graph we develop a branch and cut algorithm for solving the tlndf the performance of this algorithm is improved by separating subfamilies of cut set inequalities on the original graph our computational study confirms the efficiency and applicability of the new approach

perturbation lda learning the difference between the class empirical mean and its expectation fisher s linear discriminant analysis lda is popular for dimension reduction and extraction of discriminant features in many pattern recognition applications especially biometric learning in deriving the fisher s lda formulation there is an assumption that the class empirical mean is equal to its expectation however this assumption may not be valid in practice in this paper from the perturbation perspective we develop a new algorithm called perturbation lda p lda in which perturbation random vectors are introduced to learn the effect of the difference between the class empirical mean and its expectation in fisher criterion this perturbation learning in fisher criterion would yield new forms of within class and between class covariance matrices integrated with some perturbation factors moreover a method is proposed for estimation of the covariance matrices of perturbation random vectors for practical implementation the proposed p lda is evaluated on both synthetic data sets and real face image data sets experimental results show that p lda outperforms the popular fisher s lda based algorithms in the undersampled case

a global optimization algorithm for reliable network design in this paper we consider the problem of designing reliable networks that satisfy supply demand flow balance and capacity constraints while simultaneously allocating certain resources to mitigate the arc failure probabilities in such a manner as to minimize the total cost of network design and resource allocation the resulting model formulation is a nonconvex mixed integer 0 1 program for which a tight linear programming relaxation is derived using rlt based variable substitution strategies and a polyhedral outer approximation technique this lp relaxation is subsequently embedded within a specialized branch and bound procedure and the proposed approach is proven to converge to a global optimum various alternative partitioning strategies that could potentially be employed in the context of this branch and bound framework while preserving the theoretical convergence property are also explored computational results are reported for a hypothetical scenario based on different parameter inputs and alternative branching strategies related optimization models that conform to the same class of problems are also briefly presented

fuzzy equations max with conditionally cancellative operations fuzzy systems of equations email protected x b are studied where email protected 0 1 m x n email protected 0 1 m and stands for max product in the case of continuous strictly increasing triangular norm b s shieh information sciences 177 19 2007 4208 4215 showed that non zero coordinates of minimal solutions are coordinates of the greatest solution the goal of this paper is a presentation of the weakest assumptions about the operation which guarantee such result thus the fuzzy system of equations is considered for a left continuous increasing conditionally cancellative operation such that 1 0 0 minimal solutions of the system are described as orthogonal projections of the greatest solution and the number of minimal solutions of email protected x b is estimated moreover an efficient method is presented for the determination of the family of all minimal solutions

a new kind of fuzzy relation equations based on inner transformation this paper mainly deals with a new kind of fuzzy relation equations based on inner transformation first the inner projection of a fuzzy relation and the inner transformation by a fuzzy relation are introduced and also what is a fuzzy relation equation based on inner transformation is described second the discriminative matrix and the discriminative vector are defined on the basis of them an approach of discriminating whether such a fuzzy relation equation has nonzero solution is obtained at last a procedure of solving such fuzzy relation equations is presented the solution set of a fuzzy relation equation based on inner transformation is not closed with respect to join and meet operations in general this shows that the traditional methods being used for solving email protected composite fuzzy relation equations cannot be applied into the study of this kind of fuzzy relation equations based on inner transformation

on good eq algebras a special algebra called eq algebra has been recently introduced by vilem novak its original motivation comes from fuzzy type theory in which the main connective is fuzzy equality eq algebras have three binary operations meet multiplication and fuzzy equality and a unit element they open the door to an alternative development of fuzzy many valued logic with the basic connective being a fuzzy equality instead of an implication this direction is justified by the idea presented by g w leibniz that a fully satisfactory logical calculus must be an equational one in this paper we continue the study of eq algebras and their special cases we introduce and study the prefilters and filters of separated eq algebras we give great importance to the study of good eq algebras as we shall see in this paper the goodness property and thus separateness is necessary for reasonably behaving algebras we enrich good eq algebras with a unary operation d the so called baaz delta fulfilling some additional assumptions that are heavily used in fuzzy logic literature we show that the characterization theorem obtained until now for representable good eq algebras also hold for the enriched algebra

increasing continuous operations in fuzzy max equations and inequalities abstract in this paper solutions of fuzzy systems of equations a x b and systems of inequalities a x b a x b are considered where a 0 1 m n b 0 1 m stands for max product and x 0 1 n is an unknown vector in this paper the families of all solutions are described during the last thirty years this problem was considered by many authors our goal is to achieve the most general assumptions for which sets of solutions systems of equations and inequalities are the union of lattice intervals especially a method of determination of all minimal solutions in such systems is indicated as a result the families of all solutions of fuzzy systems of inequalities a x b and a x b are described as the main part of these results the method of determination of the family of all minimal solutions in max system of equations with an increasing operation continuous on the second argument is presented

a dynamic programming algorithm for the local access telecommunication network expansion problem abstract in this paper we consider the local access telecommunication network expansion problem in which growing demand can be satisfied by expanding cable capacities and or installing concentrators in the network the problem is known to be np hard we prove that the problem is weakly np hard and present a pseudo polynomial dynamic programming algorithm for the problem with time complexity o nb 2 and storage requirements o nb where n refers to the size of the network and b to an upper bound on concentrator capacity the cost structure in the network is assumed to be decomposable but may be non convex non concave and node and edge dependent otherwise this allows for incorporation of many aspects occurring in practical planning problems computational results indicate that the algorithm is very efficient and can solve medium to large scale problems to optimality within fractions of seconds to minutes

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

reducing the hierarchical network design problem abstract the hierarchical network design problem hndp can be seen as a minimum spanning tree problem involving two weight functions it is shown that the hndp is a special case of the directed steiner tree problem theorems are given to obtain optimal arcs that are used in a lagrangean relaxation of the linear programming model reduction tests reducing the size of the problem graph and or eliminating variables from this program are specialized and developed for the hndp the presented techniques are illustrated on example problems from the literature and computational results for the reduction tests are given

connectivity upgrade models for survivable network design disruptions in infrastructure networks to transport material energy and information can have serious economic and even catastrophic consequences since these networks require enormous investments network service providers emphasize both survivability and cost effectiveness in their topological design decisions this paper addresses the survivable network design problem a core model incorporating the cost and redundancy trade offs facing network planners using a novel connectivity upgrade strategy we develop several families of inequalities to strengthen a multicommodity flow based formulation for the problem and show that some of these inequalities are facet defining by increasing the linear programming lower bound the valid inequalities not only lead to better performance guarantees for heuristic solutions but also accelerate exact and approximate solution methods we also consider a heuristic strategy that sequentially rounds the fractional values starting with the linear programming solution to our strong model extensive computational tests confirm that the valid inequalities added via a cutting plane algorithm and the heuristic procedure are very effective and their performance is robust to changes in the network dimensions and connectivity structure our solution approach generates tight lower and upper bounds with average gaps that are less than 1 2 for various problem sizes and connectivity requirements

a dual ascent procedure for large scale uncapacitated network design the fixed charge network design problem arises in a variety of problem contexts including transportation communication and production scheduling we develop a family of dual ascent algorithms for this problem this approach generalizes known ascent procedures for solving shortest path plant location steiner network and directed spanning tree problems our computational results for several classes of test problems with up to 500 integer and 1 98 million continuous variables and constraints show that the dual ascent procedure and an associated drop add heuristic generate solutions that in almost all cases are guaranteed to be within 1 to 4 of optimality moreover the procedure requires no more than 150 seconds on an ibm 3083 computer the test problems correspond to dense and sparse networks including some models that arise in freight transport

fuzzy t locality spaces abstract a lowen fuzzy topological space is said to be localizable at points if it is completely determined in some prescribed manner by a system of fuzzy neighbourhoods called here fuzzy localities of its ordinary points we introduce for each lower semicontinuous triangular norm t a new type of those spaces which we call fuzzy t locality spaces the particularity of a fuzzy t locality space is that its fuzzy interior operator is obtained from its t locality system through a definition of fuzzy containment of fuzzy sets that employs the t residuated implication operator the origins of this new theory lie in the theory of probabilistic metric spaces indeed fuzzy t locality spaces provide a fuzzy topological framework for a naturally defined notion of metric t continuity of functions between probabilistic t metric spaces in a manner described in the last two sections of this article before that we establish characterizations and aspects of good behaviour for fuzzy t locality spaces including that every t locality system has an open basis we briefly study their level topologies and we show that all topologically generated spaces are fuzzy t locality spaces we prove that the category t fls of fuzzy t locality spaces and continuous functions between them is a topological category we show that it is closed in fts under the formation of optimal lifts of sources we provide a condition on t under which t fls becomes closed in fts also under the formation of co optimal lifts of sinks

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

general fuzzy acceptors for syntactic pattern recognition abstract in this paper the behavior of general fuzzy acceptor over a commutative cl semigroup l is considered and the properties of equivalence relation are investigated from these results we can apply for pattern recognition of deformed images or for enhancement of distorted patterns

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

fuzzy real numbers as dedekind cuts with respect to a multiple valued logic abstract viewing fuzzy set theory as a model of set with respect to a given multiple valued logic we establish the dedekind macneille completion of a partially ordered l valued set contrary to other constructions in fuzzy set theory the completion is unique up to an order isomorphism specializing this situation to the set of all crisp rational numbers we obtain in a unique way the fuzzy dedekind real numbers

a rank one update method for least squares linear discriminant analysis with concept drift linear discriminant analysis lda is a popular supervised dimension reduction algorithm which projects the data into an effective low dimensional linear subspace while the separation between the projected data from different classes is improved while this subspace is typically determined by solving a generalized eigenvalue decomposition problem its high computation costs prohibit the use of lda especially when the scale and the dimensionality of the data are large based on the recent success of least squares lda lslda we propose a novel rank one update method with a simplified class indicator matrix using the proposed algorithm we are able to derive the lslda model efficiently moreover our lslda model can be extended to address the learning task of concept drift in which the recently received data exhibit with gradual or abrupt changes in distribution in other words our lslda is able to observe and model the data distribution changes while the dependency on outdated data will be suppressed this proposed lslda will benefit applications of streaming data classification or mining and it can recognize data with newly added class labels during the learning process experimental results on both synthetic and real datasets with and without concept drift confirm the effectiveness of our propose lslda

a dual based algorithm for multi level network design given an undirected network with l possible facility types for each edge and a partition of the nodes into l levels or grades the multi level network design mlnd problem seeks a fixed cost minimizing design that spans all the nodes and connects the nodes at each level by facilities of the corresponding or higher grade this problem generalizes the well known steiner network problem and the hierarchical network design problem and has applications in telecommunication transportation and electric power distribution network design in a companion paper we studied alternative model formulations for a two level version of this problem and analyzed the worst case performance of several heuristics based on steiner network and spanning tree solutions this paper develops a dual based algorithm for the mlnd problem the method first performs problem preprocessing to fix certain design variables and then applies a dual ascent procedure to generate upper and lower bounds on the optimal value we report extensive computational results on large random two level test problems containing up to 500 nodes and 5 000 edges with varying cost structures the integer programming formulation of the largest of these problems has 20 000 integer variables and over 5 million constraints our tests indicate that the dual based algorithm is very effective producing solutions that are within 0 9 of optimality

a general method for constructing left continuous t norms a new method for constructing left continuous t norms is introduced and analyzed in this paper we shall construct via embedding a left continuous t norm from any countable residuated totally and densely ordered commutative integral monoid moreover we can construct a left continuous t norm from any countable totally ordered commutative integral monoid which is not necessarily densely ordered and residuated a special case the embedding of such monoids on lexicographic product spaces is investigated in detail and several examples are demonstrated the results shed some light to chang s mv algebra to a recently proposed extraordinary t norm and to the standard semantics of the recently introduced logic ii mtl of hajek

iterative improvement methods for a multiperiod network design problem we address an important problem in telecommunications planning the multiperiod network expansion problem our aim is to show that it can be efficiently solved using a new local search approach to achieve our goal we first show how to adapt the problem s formulation to meet our local search program s requirements we then describe glit generic local improvement template a new generic auto calibrating local search algorithm the different neighbouring strategies that we designed specifically for this problem as well as a genetic algorithm for this problem we compare and discuss the performance of these algorithms using extensive computational tests on a large range of instances with up to 7500 arcs these experiments show that glit clearly outperforms competitive approaches especially when it is coupled with genetic algorithms we also show that the hybrid algorithms genetic tabu genetic simulated annealing and finally genetic glit all outperform both pure genetic and pure local search algorithms

observations on the monoidal t norm logic the paper is a contribution to the theory of the monoidal t norm based logic mtl and stronger logics analogous to the well known extensions of the basic fuzzy logic lukasiewicz godel and product logic main attention is payed to the logic iimtl mtl plus the characteristic axioms ii1 ii2 of product logic

the logic of tied implications part 2 syntax an implication operator a is said to be tied if there is a binary operation t that ties a that is the identity a a a b z a t a b z holds for all a b z we aim at the construction of a complete predicate logic for prelinear tied adjointness algebras we realize this in three steps in the first step we establish a propositional calculus adjtpc complete for the class of all tied adjointness algebras on partially ordered sets without prelinearity and ignoring the lattice operations for that we supply a hilbert system based on seven axioms and one deduction rule modus ponens in the second and third steps we extend adjtpc to propositional and predicate calculi complete for prelinear tied adjointness algebras we apply a duality principle due to morsi in all three calculi through which we manage to cut down the number of proofs

on two types of stable subconstructs of fts abstract in the topological construct fts of fuzzy topological spaces and continuous functions the subconstructs t fls of fuzzy t locality spaces and t fns of fuzzy t neighbourhood spaces are simultaneously bireflective and bicoreflective in fts for certain infinite sets of triangular norms t we identify their stabilizing total fuzzy topologies t fls and t fns on 0 1 in the sense of lowen and wuyts 1993 the special case of t min has already been dealt with by lowen and wuyts we also establish a symmetrically defined order reversing bijection between t fns and a basis for t fls

a small set of axioms for residuated logic we show that a set of three axioms together with modus ponens suffices to build up a formal system for the class r of all quadruples l t j in which l is a partially ordered set with a top element and t is a triangular norm on l that has a residuated implication j we show that this r is not a variety

1d lda vs 2d lda when is vector based linear discriminant analysis better than matrix based recent advances have shown that algorithms with 2d matrix based representation perform better than the traditional 1d vector based ones in particular 2d lda has been widely reported to outperform 1d lda however would the matrix based linear discriminant analysis be always superior and when would 1d lda be better in this paper we investigate into these questions and have a comprehensive comparison between 1d lda and 2d lda in theory and in experiments we analyze the heteroscedastic problem in 2d lda and formulate mathematical equalities to explore the relationship between 1d lda and 2d lda then we point out potential problems in 2d lda it is shown that 2d lda has eliminated the information contained in the covariance information between different local geometric structures such as the rows or the columns which is useful for discriminant feature extraction whereas 1d lda could preserve such information interestingly this new finding indicates that 1d lda is able to gain higher fisher score than 2d lda in some extreme case furthermore sufficient conditions on which 2d lda would be bayes optimal for two class classification problem are derived and comparison with 1d lda in this aspect is also analyzed this could help understand how 2d lda is expected to achieve at its best further discover its relationship with 1d lda and well support other findings after the theoretical analysis comprehensive experimental results are reported by fairly and extensively comparing 1d lda with 2d lda in contrast to the existing view that some 2d lda based algorithms would perform better than 1d lda when the number of training samples for each class is small or when the number of discriminant features used is small we show that it is not always true and show that some standard 1d lda based algorithms could perform better in those cases on some challenging data sets

a branch and cut algorithm for the hierarchical network design problem the hierarchical network design problem consists of locating a minimum cost bi level network on a graph the higher level sub network is a path visiting two or more nodes the lower level sub network is a forest connecting the remaining nodes to the path we optimally solve the problem using an ad hoc branch and cut procedure relaxed versions of a base model are solved using an optimization package and if binary variables have fractional values or if some of the relaxed constraints are violated in the solution cutting planes are added once no more cuts can be added branch and bound is used the method for finding valid cutting planes is presented finally we use different available test instances to compare the procedure with the best known published optimal procedure with good results in none of the instances we needed to apply branch and bound but only the cutting planes

multiple rank multi linear svm for matrix data classification matrices or more generally multi way arrays tensors are common forms of data that are encountered in a wide range of real applications how to classify this kind of data is an important research topic for both pattern recognition and machine learning in this paper by analyzing the relationship between two famous traditional classification approaches i e svm and stm a novel tensor based method i e multiple rank multi linear svm mrmlsvm is proposed different from traditional vector based and tensor based methods multiple rank left and right projecting vectors are employed to construct decision boundary and establish margin function we reveal that the rank of transformation can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence we also proposed an effective approach to solve the proposed non convex optimization problem the convergence behavior initialization computational complexity and parameter determination problems are analyzed compared with vector based classification methods mrmlsvm achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrmlsvm performs better for matrix data classification promising experimental results on various kinds of data sets are provided to show the effectiveness of our method highlightswe have proposed a novel method i e mrmlsvm for matrix data classification we have revealed the essence of mrmlsvm from the view of learning theory we have provided an effective way to solve the proposed non convex problem our proposed approach is a common model and mrmlsvm is just an instance

interval valued fuzzy backward reasoning the importance and efficiency of backward reasoning in nonfuzzy reasoning has been stressed for a long time especially in the case of expert systems and decision support systems the extension of this reasoning method to fuzzy theory however has never been considered in this paper the authors propose a definition of fuzzy backward reasoning based on the generalized modus ponens and show the necessity of considering interval valued fuzzy backward reasoning then the authors propose solving methods for fuzzy backward reasoning in the case of a rule with one or several conditions as well as in the case of several rules

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

modeling and heuristic worst case performance analysis of the two level network design problem this paper studies a multi facility network synthesis problem called the two level network design tlnd problem that arises in the topological design of hierarchical communication transportation and electric power distribution networks we are given an undirected network containing two types of nodes primary and secondary and fixed costs for installing either a primary or a secondary facility on each edge primary nodes require higher grade interconnections than secondary nodes using the more expensive primary facilities the tlnd problem seeks a minimum cost connected design that spans all the nodes and connects primary nodes via edges containing primary facilities the design can use either primary or secondary edges to connect the secondary nodes the tlnd problem generalizes the well known steiner network problem and the hierarchical network design problem in this paper we study the relationship between alternative model formulations for this problem e g directed and undirected models an

addition min fuzzy relation inequalities with application in bittorrent like peer to peer file sharing system abstract the data transmission mechanism in bittorrent like peer to peer p2p file sharing systems may be reduced to some addition min fuzzy relation inequalities the solution set of addition min fuzzy relation inequalities plays an important role in the corresponding optimization problem in this paper we study some properties of the solutions to such system convexity of the solution set and number of minimal solutions are discussed with comparison to those of the classical max t fuzzy relation equations or inequalities besides vertex solution and variable ordering minimal solution are also investigated with application in bittorrent like p2p file sharing system two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable ordering solution

implicative fuzzy associative memories associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern in this paper we introduce implicative fuzzy associative memories ifams a class of associative neural memories based on fuzzy set theory an ifam consists of a network of completely interconnected pedrycz logic neurons with threshold whose connection weights are determined by the minimum of implications of presynaptic and postsynaptic activations we present a series of results for autoassociative models including one pass convergence unlimited storage capacity and tolerance with respect to eroded patterns finally we present some results on fixed points and discuss the relationship between implicative fuzzy associative memories and morphological associative memories

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

the hierarchical network design problem abstract in this paper the authors introduce the hierarchical network design problem hndp the object of the hndp is to identify the least cost two level hierarchical network the network must include a primary path from a predetermined starting node to a predetermined terminus node in addition each node not on the primary path must be connected to some node on that path by means of a secondary path the problem is initially formulated as an integer linear program an heuristic is then presented which employs a k shortest path algorithm and a minimum spanning tree algorithm heuristic results of two sample problems are presented and compared to the results obtained by solving the integer lp formulation potential applications of the formulation are also discussed

novel neural algorithms based on fuzzy d rules for solving fuzzy relation equations part iii abstract in this paper we first design a fuzzy neuron which possesses some generality this fuzzy neuron is founded by replacing the operators of the traditional neuron with a pair of abstract fuzzy operators as which we call fuzzy neuron operators for example it may be or etc it is an extended fuzzy neuron and a network composed o such neurons is an extended fuzzy neural network then we discuss the relationship between the fuzzy neuron operators and t norm and t conorm and point out fuzzy neuron operators are based on t norm but much wider than t norm in this paper we will emphatically discuss a two layered network and its training algorithm which will have to satisfy a set of various operators this work is very related to solving fuzzy relation equations so it can be used to resolve fuzzy relation equations furthermore the new fuzzy neural algorithm is found to be stronger than other existing methods to some degree some simulation results will be reported in detail

algebraic structures in fuzzy logic abstract common features in various fuzzy logical systems are investigated it turns out that adjoint couples and residuated lattices are very often present though not always explicitly expressed some minor new results are also proved

fuzzy t neighbourhood spaces part 2 t neighbourhood systems we explore a notion of fuzzy t neighbourhood spaces for any continuous triangular norm t and we present on this notion a unified treatment our theory on one hand generalizes the theory of lowen fuzzy sets and systems 7 1982 65 from t min to arbitrary t which has been the progenitor of this work and on the other hand it is strongly related to the theory of l neighbourhoods of hohle mathematics of fuzzy sets logic topology and measure theory kluwer academic publishers dordrecht 1999 when l is restricted to the lattice 0 1 we study the t neighbourhood bases and systems of our spaces their level topologies as well as their relationship to the lowen hohle fuzzy t uniformities j math anal appl 82 1981 370 manuscripta math 38 1982 289 and to our fuzzy t proximities introduced in part 1 we show that the nearness concept underlying a fuzzy t neighbourhood space is a fuzzy relation of closeness between its ordinary subsets and ordinary points in particular our spaces are in canonical one to one correspondence with the t probabilistic topological spaces of frank j math anal appl 34 1971 67 we demonstrate that each full subcategory t fns of fts of fuzzy t neighbourhood spaces is a topological category to do that we characterize t fns within fts and we characterize continuity of functions within t fns in terms of t neighbourhood bases

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

solvability of fuzzy relational equations and manipulation of fuzzy data abstract the problem of characterization of fuzzy relational equations with respect to their solvability property is studied some aspects of manipulation of fuzzy data with the aid of fuzzy relational equations are considered two stages of manipulation process are indicated combining pieces of evidence and inferring their mutual correspondence both of them are formulated and solved by the use of fuzzy relational equations the role of a solvability index is extensively studied numerical considerations give an illustration of the approach we propose and deal with some real data used for fuzzy controllers

lda qr an efficient and effective dimension reduction algorithm and its theoretical foundation lda qr a linear discriminant analysis lda based dimension reduction algorithm is presented it achieves the efficiency by introducing a qr decomposition on a small size matrix while keeping competitive classification accuracy its theoretical foundation is also presented

optimizing splitter and fiber location in a multilevel optical ftth network due to the emergence of bandwidth requiring services telecommunication operators are being compelled to renew their fix access network most of them favoring the fiber to the home ftth technology this paper focuses on the optimization of ftth deployment which is of prime importance due to the economic stakes the key design issue here is locating splitters and routing fi bers in an existing network infrastructure to which is associated a graph with given capacities on the edges no assumption is made on the structure of the graph first we propose a mixed integer formulation for this decision problem then valid inequalities and problem size reduction schemes are presented finally efficiency of solving approaches is assessed through extensive numerical tests performed on orange real life data

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

fuzzy relation equations and inequalities abstract this paper generalizes a method of solution of fuzzy relation equations introduced by sanchez 1976 and developed by pedrycz 1982 we find the greatest or the least solution of a composite l fuzzy relation equation with arbitrary monotone composition

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

tableau method for residuated logic abstract residuated logic is a generalization of intuitionistic logic which does not assume the idempotence of the conjunction operator such generalized conjunction operators have proved important in expert systems in the area of approximate reasoning and in some areas of theoretical computer science here we generalize the intuitionistic tableau procedure and prove that this generalized tableau method is sound for the semantics the class of residuated algebras of residuated propositional calculus rpc since the axioms of rpc are complete for the semantics we may conclude that whenever a formula 0 is tableau provable it is deducible in rpc we present two different approaches for constructing residuated algebras which give us countermodels for some formulas which are not tableau provable the first uses the fact that the theory of residuated algebras is equational to construct quotients of free algebras the second uses finite algebras we end by discussing a number of open questions

propositional calculus under adjointness we develop a formal system for the class of all implications a and conjunctions k on partially ordered sets l with top elements 1 such that a and k are related by adjointness and they satisfy the neutrality principle that is 1 is their left identity element we call the resulting logic propositional calculus under adjointness abbreviated adjpc most algebraic theorems on those l a and k are inequalities in the posets l of truth values in consequence we have to find means for abstracting inequalities within syntax which must be free from partial truth values this is achieved by employing a further implication like adjoint h of a and k whereby the partial order of l coincides with the binary relation h 1 accordingly the semantical domain for adjpc should become the class of all such quintuples l a k h which we call adjointness algebras our axiom scheme for adjpc features seven axioms however it may be the case that no finite set of axioms can complete adjpc if inference is carried out by means of modus ponens mp alone this is because adjpc is too general it lacks some basic theorems of the more restricted logics such as residuated logic and intuitionistic logic as a result we have to adopt four inference rules for adjpc namely mp and three bits of the substitution theorem we deduce enough theorems and inferences in adjpc to delineate its basic structure this enables us to establish the completeness of adjpc for the semantical domain of adjointness algebras by means of a quotient algebra structure a lindenbaum type of algebra we also show how certain models can help disprove some incorrect inferences in adjpc we end by developing complete syntax with fewer axioms and inference rules for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

efficient image classification via multiple rank regression the problem of image classification has aroused considerable research interest in the field of image processing traditional methods often convert an image to a vector and then use a vector based classifier in this paper a novel multiple rank regression model mrr for matrix data classification is proposed unlike traditional vector based methods we employ multiple rank left projecting vectors and right projecting vectors to regress each matrix data set to its label for each category the convergence behavior initialization computational complexity and parameter determination are also analyzed compared with vector based regression methods mrr achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrr performs better for matrix data classification promising experimental results on face object and hand written digit image classification tasks are provided to show the effectiveness of our method

on the convex combination of td and continuous triangular norms the problem of when t l 1 l t d lt l 0 1 is a triangular norm where t d is the drastic product and t is a continuous triangular norm is studied it is shown that t l cannot be a triangular norm when t is nilpotent it is also shown that t l is a triangular norm if t is strict and its additive generator f satisfies f lx f x f l for all x 0 1 the cases that t t m and t is the ordinal sum of continuous archimedean summands are also discussed some left continuous t norms which can be combined with each other are given

infinitely distributive t norms on complete lattices and pseudo complements in this paper we have introduced the concepts of t prime element t prime radical element and t semi prime element and have studied their properties we have investigated the construction methods of new infinitely distributive t norms from given infinitely distributive t norms by means of t prime elements and pseudo complements if every element of l is t prime radical element then we show that l is a complete brouwerian lattice and email protected if l is an algebraic lattice t is a t norm on l and every compact element of l is idempotent then we obtain that email protected we show that l r is a complete lattice and that the restriction of t to l r is an infinitely distributive t norm on l r when t is an infinitely distributive t norm on l and 0 is a t prime we present infinitely distributive t norms on a complete sublattice l and study their properties

a dual ascent approach for steiner tree problems on a directed graph the steiner tree problem on a directed graph stdg is to find a directed subtree that connects a root node to every node in a designated node setv we give a dual ascent procedure for obtaining lower bounds to the optimal solution value the ascent information is also used in a heuristic procedure for obtaining feasible solutions to the stdg computational results indicate that the two procedures are very effective in solving a class of stdg s containing up to 60 nodes and 240 directed 120 undirected arcs