fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation abstract the fundamental frequency coefficient for a rectangular plate with edges elastically restrained against both translation and rotation is calculated by using polynomial coordinate functions and the rayleigh ritz method the approach is simple and straightforward and allows the solution of a rather difficult elastodynamics problem complicating factors orthotropic properties in plane forces concentrated masses etc can also be taken into account without formal difficulties

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

a new approach to fuzzy topological spaces and various fuzzy topological notions defined by nets n fuzzy spaces introduced by the authors are further investigated various fuzzy topological motions such as fuzzy local compactness functions with closed fuzzy graph fuzzy subcontinuity inverse fuzzy subcontinuity etc are studied in the light of n i these notions are found to be more coherent in n i than in the chang s category

control limits for two state partially observable markov decision processes abstract a production process can be in either a good or a bad state the true state is unknown and can only be inferred from observations if the state is good during one period it may deteriorate and become bad during the next period two actions are available continue or replace for a fixed cost the objective is to maximize the expected discounted value of the total future profits we prove that dominance in expectation the expected profit is larger in the good state than in the bad state suffices for the optimal policy to be of a control limit clt type continue if and only if the good state probability exceeds the clt this condition is weaker than stochastic dominance which has been prevailing we also show that the expected profit function is convex strictly increasing

partially observable markov decision processes a geometric technique and analysis this paper presents a novel framework for studying partially observable markov decision processes pomdps with finite state action observation sets and discounted rewards the new framework is solely based on future reward vectors associated with future policies which is more parsimonious than the traditional framework based on belief vectors it reveals the connection between the pomdp problem and two computational geometry problems i e finding the vertices of a convex hull and finding the minkowski sum of convex polytopes which can help solve the pomdp problem more efficiently the new framework can clarify some existing algorithms over both finite and infinite horizons and shed new light on them it also facilitates the comparison of pomdps with respect to their degree of observability as a useful structural result

on the existence of stationary optimal policies for partially observed mdps under the long run average cost criterion abstract this paper studies the problem of the existence of stationary optimal policies for finite state controlled markov chains with compact action space and imperfect observations under the long run average cost criterion it presents sufficient conditions for existence of solutions to the associated dynamic programming equation that strengthen past results there is a detailed discussion comparing the different assumptions commonly found in the literature

fuzzy almost continuity and its pointwise characterization by dual points and fuzzy nets abstract we introduce the notions of fuzzy almost continuity and fuzzy weak continuity at a fuzzy point following the pointwise approach we investigate their fuzzy topological properties we also obtain a pointwise characterization of fuzzy almost continuous functions by dual points and fuzzy nets the main idea behind this work is to establish a local theory in the study of continuity and its weaker forms in general fuzzy topological spaces

analytical approximations for the modal acoustic impedances of simply supported rectangular plates coupling of the in vacuo modes of a fluid loaded vibrating structure by the resulting acoustic field while known to be negligible for sufficiently light fluids is still only partially understood a particularly useful structural geometry for the study of this problem is the simply supported rectangular flat plate since it exhibits all the relevant physical features while still admitting an analytical description of the modes here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number the modal acoustic impedances closed form solutions for these impedances do not exist and while their numerical evaluation is possible it greatly increases the computational cost of solving the coupled system of modal equations there is thus a need for accurate analytical approximations in this work such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions it is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations previous approximations davies j sound vib 15 1 107 126 1971 are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components but in general erroneous expressions for imaginary parts

analytical and experimental investigation on transmission loss of clamped double panels implication of boundary effects the air borne sound insulation performance of a rectangular double panel partition clamp mounted on an infinite acoustic rigid baffle is investigated both analytically and experimentally and compared with that of a simply supported one with the clamped or simply supported boundary accounted for by using the method of modal function a double series solution for the sound transmission loss stl of the structure is obtained by employing the weighted residual galerkin method experimental measurements with al double panel partitions having air cavity are subsequently carried out to validate the theoretical model for both types of the boundary condition and good overall agreement is achieved a consistency check of the two different models based separately on clamped modal function and simply supported modal function is performed by extending the panel dimensions to infinite where no boundaries exist the significant discrepancies between the two different boundary conditions are demonstrated in terms of the stl versus frequency plots as well as the panel deflection mode shapes

effects of panel boundedness on sound transmission problems a theory for sound transmission through a panel of finite width and infinite length mounted in a rigid baffle is formulated in order to discuss the effects of the panel boundedness on the sound transmission loss the results calculated from a rigorous solution are presented as the frequency characteristics curves however it seems to be difficult to evaluate the sound insulation efficiency of the panel using the rigorous results because of their violent peaks and dips owing to resonance a method for averaging the response over any frequency band is discussed the averaged response corresponds to the actual transmission measurement with a bandlimited excitation and allows one to evaluate the transmission characteristics from a viewpoint of practical noise control the effects of the panel boundedness including a comparison with an infinite panel are also discussed by means of this method

finite memory suboptimal design for partially observed markov decision processes we develop bounds on the value function and a suboptimal design for the partially observed markov decision process these bounds and suboptimal design are based on the m most recent observations and actions an a priori measure of the quality of these bounds is given we show that larger m implies tighter bounds an operations count analysis indicates that a z m 1 s multiplications and additions are required per successive approximations iteration of the suboptimal design algorithm where a z and s are the action observation and state spaces respectively suggesting the algorithm is of potential use for problems with large state spaces a preliminary numerical study indicates that the quality of the suboptimal design can be excellent

connectedness in fuzzy topological spaces abstract we introduce four notions of connectedness for an arbitrary fuzzy set and discuss all the implications that exist between them using these notions various equivalence relations are defined on the set of fuzzy points components and quasi components are formed as the union of certain equivalence classes a fuzzy space is shown to be a dispoint union of its components in all the four cases and non overlapping union of its quasi components

fuzzy subcontinuity inverse fuzzy subcontinuity and a new category of fuzzy topological spaces the notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting adopting fuzzy net theoretic approach various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied a category of fuzzy topological spaces is constructed canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity in the process n compactness is characterized and fuzzy unit interval is shown to be n compact also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous

some monotonicity results for partially observed markov decision processes this paper provides sufficient conditions for the optimal value in a discrete time finite partially observed markov decision process to be monotone on the space of state probability vectors ordered by likelihood ratios the paper also presents sufficient conditions for the optimal policy to be monotone in a simple machine replacement problem and in the general case for the optimal policy to be bounded from below by an easily calculated monotone function

various fuzzy topological notions and fuzzy almost continuity abstract we extend the notion of almost continuity in the sense of husain 1966 to the fuzzy setting we obtain a pointwise characterization of the notion by dual point and fuzzy net also we formulate conditions under which the two notions of fuzzy almost continuity the one defined in this paper and the one defined by ajmal and azad 1990 turn out to be equivalent the main idea behind this work is to show that using the localized approach developed in earlier papers the study of fuzzy almost continuity can be carried out as successfully as that of its counterpart in general topology in the process we exhibit the compatibility of various existing fuzzy topological notions such as fuzzy regularity c i connectedness i 3 4 c i local connectedness i 3 4 fuzzy t 1 axiom fuzzy t 2 axiom etc

the complexity of markov decision processes we investigate the complexity of the classical problem of optimal policy computation in markov decision processes all three variants of the problem finite horizon infinite horizon discounted and infinite horizon average cost were known to be solvable in polynomial time by dynamic programming finite horizon problems linear programming or successive approximation techniques infinite horizon we show that they are complete for p and therefore most likely cannot be solved by highly parallel algorithms we also show that in contrast the deterministic cases of all three problems can be solved very fast in parallel the version with partially observed states is shown to be pspace complete and thus even less likely to be solved in polynomial time than the np complete problems in fact we show that most likely it is not possible to have an efficient on line implementation involving polynomial time on line computations and memory of an optimal policy even if an arbitrary amount of precomputation is allowed finally the variant of the problem in which there are no observations is shown to be np complete

a new approach to fuzzy topological spaces and fuzzy perfect mappings abstract a net theoretic approach is provided for defining a fuzzy topological space fuzzy topological spaces so defined form a category the main features and advantages of this category which is denoted by n here are discussed the notion of a perfect mapping is introduced and studied in the fuzzy setting it is found that in n a fts is n compact iff any mapping x x where x is any singleton is fuzzy perfect a fuzzy continuous mapping x y from an n compact fts x to a hausdorff fts y is fuzzy perfect in n however these results do not hold in c the chang s category in general it is found that the divergences in the study of fuzzy perfect mappings disappear if the study is carried out in n instead of c

optimal infinite horizon undiscounted control of finite probabilistic systems a finite input finite state finite output stochastic control problem with imperfect state observation and classical information pattern is shown to be meaningful as the horizon increases without bound and the discount rate approaches unity the plant model a finite probabilistic system includes the markov decision and partially observed markov decision problems as special cases under conditions resembling controllability and observability in linear systems we show that an optimal strategy exists it may be realized by a stationary policy on the state estimate its performance does not depend on the initial state distribution and convergence rates for its finite horizon and discounted performances are readily established

category n and functions with closed fuzzy graph abstract a net theoretic approach for defining a fuzzy topological space is provided the fuzzy topological spaces so obtained form a category which we denote by n in this paper it is found that the limitations exhibited by the chang category particularly with respect to projections closure of a fuzzy set compactness etc no longer exist in n the notion of closed fuzzy graph is investigated the divergences shown by this notion are immediately put to rest if the study is carried out in n instead of c the chang category

connectedness and local connectedness in fuzzy topological spaces and heyting algebra valued sets abstract in this paper we introduce four notions of local connectedness in fuzzy topological spaces the question of these notions to be good extensions is discussed and their preservation under fuzzy quotients fuzzy sums and fuzzy products is investigated moreover we introduce the notion of quasi local connectedness which is a peculiarity of the fuzzy setting

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism

a categorical accommodation of various notions of fuzzy topology different definitions of fuzzy topology have been stated and developed in the literature but have not been satisfactorily related to each other and to ordinary topology to remedy this a new fuzzy topological category fuzz is defined it is a significant generalization of previous definitions it is the simplest setting yet constructed into which ordinary topology and these previous definitions may be placed by identifying each with a different subcategory of fuzz it therefore allows us to conveniently analyze the relative merits of previous definitions give coherence to known results and indicate appropriate directions for future development and it generates and may be viewed as both including and included in categories of fuzzy topological spaces which exhibit higher order fuzziness