optimal control of harvesting in a nonlinear elliptic system arising from population dynamics the aim of this article is to study an optimal control problem for a system of nonlinear elliptic equations with dirichlet boundary conditions u x a x x c x u x eu x u x x x 1 1 x b x u x d x x f x u x x x u x x 0 on 1 2 the authors were supported in part by cicyt ministry of education and culture spain under grant pb98 1343 by junta de andalucia fqm116 and by eec contract human capital and mobility program erbchrxct 940494 also they thank o arino for suggesting the study of this control problem

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

rough approximations on a complete completely distributive lattice with applications to generalized rough sets the generalizations of rough sets considered with respect to similarity relation covers and fuzzy relations are main research topics of rough set theory however these generalizations have shown less connection among each other and have not been brought into a unified framework which has limited the in depth research and application of rough set theory in this paper the complete completely distributive ccd lattice is selected as the mathematical foundation on which definitions of lower and upper approximations that form the basic concepts of rough set theory are proposed these definitions result from the concept of cover introduced on a ccd lattice and improve the approximations of the existing crisp generalizations of rough sets with respect to similarity relation and covers when t similarity relation is considered the existing fuzzy rough sets are the special cases of our proposed approximations on a ccd lattice thus these generalizations of rough sets are brought into a unified framework and a wider mathematical foundation for rough set theory is established

weak convergence of a relaxed and inertial hybrid projection proximal point algorithm for maximal monotone operators in hilbert space this paper introduces a general implicit iterative method for finding zeros of a maximal monotone operator in a hilbert space which unifies three previously studied strategies relaxation inertial type extrapolation and projection step the first two strategies are intended to speed up the convergence of the standard proximal point algorithm while the third permits one to perform inexact proximal iterations with fixed relative error tolerance the paper establishes the global convergence of the method for the weak topology under appropriate assumptions on the algorithm parameters

stability in semilinear problems abstract in the paper we derive results concerning a continuous dependence of solutions on the right hand side for a semilinear operator equation lu g u by assuming that l d l h h h a hilbert space is self adjont with a closed range and g h r is continuous convex on h and g teaux differentiable on d l using these results we obtain theorems on the continuous dependence of solutions on functional parameters for a semilinear problem of the second order u au d u f t u t 0 a e with the dirichlet boundary conditions u 0 u 0 where a 1 and is a functional parameter

on rough set and fuzzy sublattice let l be a lattice with the least element 0 and the greatest element 1 and let be a full congruence relation on l in this paper the notion of upper and lower approximations of a fuzzy subset of l is introduced and some important properties will be studied

bzmv dm algebras and stonian mv algebras applications to fuzzy sets and rough approximations the natural algebraic structure of fuzzy sets suggests the introduction of an abstract algebraic structure called de morgan bzmv algebra bzmv dm algebra we study this structure and sketch its main properties a bzmv dm algebra is a system endowed with a commutative and associative binary operator and two unusual orthocomplementations a kleene orthocomplementation and a brouwerian one as expected every bzmv dm algebra is both an mv algebra and a distributive de morgan bz lattice the set of all closed elements which coincides with the set of all idempotent elements turns out to be a boolean algebra the boolean algebra of sharp or crisp elements by means of and t wo modal like unary operators for necessity and for possibility can be introduced in such a way that a resp a can be regarded as the sharp approximation from the bottom resp top of a this gives rise to the rough approximation a a ofa finally we prove that bzmv dm algebras which are equationally characterized are the same as the stonian mv algebras and a rst representation theorem is proved c 1999 elsevier science b v all rights reserved

perturbed projections and subgradient projections for the multiple sets split feasibility problem we study the multiple sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space by casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case we further derive and analyze a perturbed projection method for the multiple sets split feasibility problem and additionally furnish alternative proofs to two known results

existence of optimal controls via continuous dependence on parameters abstract we consider a system of elliptic equations and derive sufficient conditions for solutions of the system to depend continuously on parameters these conditions are employed to obtain an existence result for an optimal control problem

convergence theorems for inertial km type algorithms this paper deals with the convergence analysis of a general fixed point method which unifies km type krasnoselskii mann iteration and inertial type extrapolation this strategy is intended to speed up the convergence of algorithms in signal processing and image reconstruction that can be formulated as km iterations the convergence theorems established in this new setting improve known ones and some applications are given regarding convex feasibility problems subgradient methods fixed point problems and monotone inclusions

convergence of new inertial proximal methods for dc programming we present iterative methods for finding the critical points and or the minima of extended real valued functions of the form phi psi g h where psi is a differentiable function and g and h are convex proper and lower semicontinuous the underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature and to obtain some convergence results the main theorems not only recover known convergence results in this field but also provide a theoretical basis for the development of new iterative methods

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

rough operations on boolean algebras in this paper we introduce two pairs of rough operations on boolean algebras first we define a pair of rough approximations based on a partition of the unity of a boolean algebra we then propose a pair of generalized rough approximations on boolean algebras after defining a basic assignment function between two different boolean algebras finally some discussions on the relationship between rough operations and some uncertainty measures are given to provide a better understanding of both rough operations and uncertainty measures on boolean algebras

optimal decay rates and the selfadjoint property in overdamped systems abstract we deal with abstract linear strongly damped wave equations in the so called overdamped regime we show the occurrence of two interesting phenomena the first is the existence of an explicit special inner product which makes the problem selfadjoint the second is an improvement of the decay rate for more regular solutions that will be of an exponential polynomial type furthermore we prove the optimality of this decay rate

rough matroids based on relations rough sets provide an efficient tool for attribute reduction and rule extraction however many important problems in rough set theory including attribute reduction are np hard and therefore the algorithms for solving them are usually greedy as a generalization of linear independence in vector spaces matroids have wide applications in diverse fields particularly in greedy algorithm design in this paper we propose an integration of rough sets and matroids to exploit the advantages of both theories specifically we present definitions of lower and upper rough matroids based on relations from the viewpoint of approximation operators it is interesting that lower rough matroids based on partial orders coincide with poset matroids which are a well known generalization of matroids a matroid is represented by the lower rough matroid based on both a partial order and an equivalence relation lower and upper rough matroids based on equivalence relations coincide with each other finally we present some special types of examples of rough matroids from the viewpoints of approximations and graphs these interesting results demonstrate the potential for the combination between rough sets and matroids

on equivalent forms of fuzzy logic systems nm and imtl the nilpotent minima are important t norms in fuzzy logic and fuzzy reasoning two interesting formal systems nilpotent minimum logic nm and l based on nilpotent minima have been proposed and have been intensively studied in this paper their equivalence is pointed out moreover coincidence of two related algebraic structures nm and r0 algebras is also proved in addition we give an equivalent form of involutive monoidal t norm based logic imtl

a triangular norm based propositional fuzzy logic in 1997 wang introduced the formal system l for a type of fuzzy propositional calculus given by a particular t norm different from the three famous ones lukasiewicz godel product recently pei proved the completeness theorem for l with respect to w semantic by developing a theory of algebraic systems in this paper we aim to prove it by essentially metamathematical method furthermore we discussed originally the completeness for the schematic extension l n of l with respect to w n semantic

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

fixed point iterations coupled with relaxation factors and inertial effects abstract this paper deals with a general fixed point method which unifies relaxation factors and a two step inertial type extrapolation these strategies are intended to improve the convergence of many existing algorithms a convergence theorem which improves the known ones is established in this new setting

three way decisions with probabilistic rough sets the rough set theory approximates a concept by three regions namely the positive boundary and negative regions rules constructed from the three regions are associated with different actions and decisions which immediately leads to the notion of three way decision rules a positive rule makes a decision of acceptance a negative rule makes a decision of rejection and a boundary rule makes a decision of abstaining this paper provides an analysis of three way decision rules in the classical rough set model and the decision theoretic rough set model the results enrich the rough set theory by ideas from bayesian decision theory and hypothesis testing in statistics the connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications

the superiority of three way decisions in probabilistic rough set models three way decisions provide a means for trading off different types of classification error in order to obtain a minimum cost ternary classifier this paper compares probabilistic three way decisions probabilistic two way decisions and qualitative three way decisions of the standard rough set model it is shown that under certain conditions when considering the costs of different types of miss classifications probabilistic three way decisions are superior to the other two

approximations and uncertainty measures in incomplete information systems there are mainly two methodologies dealing with uncertainty measurement issue in rough set theory pure rough set approach and information theory approach pure rough set approach is based on the concepts of accuracy roughness and approximation accuracy proposed by pawlak information theory approach is based on shannon s entropy or its variants several authors have extended the information theory approach into incomplete information systems however there are few studies on extending the pure rough set approach to incomplete information systems this paper focuses on constructing uncertainty measures in incomplete information systems by pure rough set approach three types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy roughness and approximation accuracy are investigated theoretical analysis indicates that two of the three types can be used to evaluate the uncertainty in incomplete information systems experiments on incomplete real life data sets have been conducted to test the two selected types the first type and the third type of uncertainty measures results show that the two types of uncertainty measures are effective

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

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

positive approximation an accelerator for attribute reduction in rough set theory feature selection is a challenging problem in areas such as pattern recognition machine learning and data mining considering a consistency measure introduced in rough set theory the problem of feature selection also called attribute reduction aims to retain the discriminatory power of original features many heuristic attribute reduction algorithms have been proposed however quite often these methods are computationally time consuming to overcome this shortcoming we introduce a theoretic framework based on rough set theory called positive approximation which can be used to accelerate a heuristic process of attribute reduction based on the proposed accelerator a general attribute reduction algorithm is designed through the use of the accelerator several representative heuristic attribute reduction algorithms in rough set theory have been enhanced note that each of the modified algorithms can choose the same attribute reduct as its original version and hence possesses the same classification accuracy experiments show that these modified algorithms outperform their original counterparts it is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets

a weak to strong convergence principle for feje monotone methods in hilbert spaces we consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly exploiting an idea originally proposed by haugazeau we present a simple modification of these methods that makes them strongly convergent without additional assumptions several applications are discussed