a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

ranking of fuzzy intervals seen through the imprecise probabilistic lens within the fuzzy literature the issue of ranking fuzzy intervals has been addressed by many authors who proposed various solutions to the problem most of these solutions intend to find a total order on a given collection of fuzzy intervals however if one sees fuzzy intervals as descriptions of uncertain quantities an alternative to rank them is to use ranking rules issued from the imprecise probabilistic literature in this paper we investigate ranking rules based on different statistical features mean median and orderings and relate the obtained partial orders to some classical proposals in particular we propose a generic expression of stochastic orderings and then use it to systematically investigate extensions of the most usual stochastic orderings to fuzzy intervals we also show some relations between those extensions and explore their relation with existing fuzzy ranking proposals

interval random sets and entropy abstract the problem of proper choice from the class of interval random sets generated by some fuzzy set is considered this problem is determined for the maximum entropy criterion the class of interval random sets is studied

min and max operators for fuzzy intervals and their potential use in aggregation operators this paper aims at expressing min and max operations when triangular fuzzy intervals are taken as inputs that is when zadeh s extension principle is considered first presented approach consists in representing fuzzy intervals by means of their profiles in this context a computation algorithm can be easily derived for implementing the min and max operations another methodology based on interval relations is then proposed for determining a general analytical expression of the min and max operations the potential use of these expressions in the framework of uncertain aggregation operators is illustrated with the two additive choquet integral

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

the effects of temporal delays in a model for a food limited diffusing population we consider an adaptation of the well known logistic equation in mathematical ecology in which the population is assumed to diffuse and for which the average growth rate is a function of some specified delayed argument using a combination of analytical and numerical techniques we investigate the existence uniqueness and asymptotic stability of the nonnegative steady states of this equation

ranking fuzzy interval numbers in the setting of random sets abstract a new approach to the problem of extending interval order relations to the case of fuzzy interval numbers is presented in the approach the connectedness between fuzzy sets and random sets is used finally eight different fuzzy order relations are given some formal properties of these relations are investigated and the problem of computing the values of their membership functions discussed for trapezoidal fuzzy interval numbers the formulae depend on the parameters from which these numbers are derived

ranking fuzzy interval numbers in the setting of random sets further results abstract we present some new properties of several fuzzy order relations defined on the set of fuzzy numbers from among those introduced in s chanas m delgado j l verdegay m a vila information sciences 69 1993 201 217 the main result is proving that four from among the relations considered in s chanas m delgado j l verdegay m a vila information sciences 69 1993 201 217 are strongly transitive s transitive

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

single value simulation of fuzzy variable some further results abstract the problem of a proper choice from the class of random sets equivalent to a fuzzy set under one point coverages is considered the selected random variable is used for construction of a random variable probability distribution serving as a random generator of a value of the fuzzy variable with values restricted by the fuzzy set the problem is determined for two selection criteria i maximum probability possibility consistency and ii maximum entropy in the case of the entropy criterion the problem has been solved first by goodman and here only another proof of the result is presented

on diffusive population models with toxicants and time delays in this article we study the global stability in reaction diffusion models for single species population growth under environmental toxicants with or without time delays the existence and uniqueness of a positive steady state solution are established in those models it is shown that as long as the magnitude of the instantaneous self limitation and toxicant effects is larger than that of the time delay effects in the model with delays the solution of both reaction diffusion systems has the same asymptotic behavior extinction or converging to the positive steady state solution depending on the growth rate of the species numerical simulations for both cases with or without time delays are demonstrated for the purpose of comparison

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

atmospheric optical cdma communication systems via optical orthogonal codes we propose and consider using a class of multiple access sequences namely optical orthogonal codes oocs in atmospheric optical code division multiple access systems we obtain analytical solutions to the error probability for various channel models using positive intrinsic negative diode and avalanche photodiode photodetectors in our analysis the effects of atmospheric turbulence ambient light thermal noise and multiuser interference are considered in the context of a semiclassical photon counting approach the performance of the systems taking advantage of space diversity and error correcting codes are also evaluated two common and widely used optical modulations on off keying and pulse position modulation are considered receiver structures based on correlator and chip level are used for ooc detection unlike the traditional chip level receiver here a generalized form of chip level structure with two threshold levels is considered upper and lower bounds on the error probability for the above chip level receiver structure is obtained from our analytical results we can deduce that the chip level receiver outperforms a simple correlator in the absence or weak atmospheric fading however in a strong fading environment the simple correlator outperforms the chip level receiver

ocdma coded free space optical links for wireless optical mesh networks we propose a wireless optical mesh network based on optical code division multiple access ocdma coded free space optical links the performance of the proposed network under intermediate and strong turbulence channel conditions is investigated for synchronous and asynchronous ocdma we show that synchronous ocdma using complementary walsh hadamard codes operating at a raw bit rate of 622 mb s per user can achieve a bit error rate of 10 sup 9 this is achievable in channels with strong turbulence and high temporal correlation or in channels with intermediate turbulence conditions reasonable conditions based on channel characteristics inferred from the refractive index spectrum for asynchronous ocdma using optical orthogonal codes oocs using a lower bound we show that asynchronous ocdma using oocs cannot achieve acceptable performance for the same channel conditions due to interference limitations

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

a procedure for ranking fuzzy numbers using fuzzy relations abstract this paper presents a method to give fuzzy order relations between fuzzy numbers these are founded on the concept of comparison function defined in the paper and the use of fuzzy measures related with the same numbers the link of such relations with fuzzy operations is investigated too

selection of programme slots of television channels for giving advertisement a graph theoretic approach the present paper aims at developing a linear time algorithm to find a solution to the maximum weight 1 colouring problem for an interval graph with interval weight this algorithm has been applied to solve the problem that involves selecting different programme slots telecast on different television channels in a day so as to reach the maximum number of viewers it is shown that all programmes of all television channels can be modelled as a weighted interval graph with interval numbers as weights the programme slots are taken as the vertices of the graph and if the time durations of two programme slots have non empty intersection the corresponding vertices are considered to be connected by an edge the number of viewers of a programme is taken as the weight of the vertex in reality the number of viewers of a programme is not a fixed one generally it lies in an interval thus the weights of the vertices are taken as interval numbers we assume that a company sets the objective of selecting the popular programme in different channels so as to make its commercial advertisement reach the maximum number of viewers however the constraint imposed is that all selected programmes are mutually exclusive in respect of time scheduling the objective of the paper is therefore to helps the companies to select the programme slots which are mutually exclusive with respect to the time schedule of telecasting time in such a way that the total number of viewers of the selected programme slots rises to the optimum level it is shown that the solution of this problem is obtained by solving the maximum weight colouring problem on an interval graph an algorithm is designed to solve this optimization problem using o n time where n represents the total number of programmes of all channels

an approach to generalization of fuzzy topsis method the topsis method is a technique for establishing order preference by similarity to the ideal solution and was primarily developed for dealing with real valued data this technique is currently one of most popular methods for multiple criteria decision making mcdm in many cases it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are seen as fuzzy values a number of papers have been devoted to fuzzy extensions of the topsis method in the literature but these extensions are not complete since the ideal solutions are usually presented as real values not by fuzzy values or as fuzzy values which are not attainable in the decision matrix in most of these papers a defuzzification of elements of the fuzzy decision matrix is used which leads inevitably to a loss of important information and may even produce the wrong results in this paper we propose a new direct approach to the fuzzy extension of the topsis method which is free of the limitations of other known approaches we show that the distances of the alternatives from the ideal solutions may be treated in some sense as modified weighted sums of local criteria it is known that using weighted sums is not the best approach to the aggregation of local criteria in many real world situations therefore here we propose the use in addition to weighted sums some other types of local criteria aggregation in the topsis method and we develop a method for the generalization of different aggregation modes providing compromised final results

hard limiting performance analysis of 2 d optical codes under the chip asynchronous assumption the traditional chip synchronous assumption used in the analyses of optical codes in optical code division multiple access gives a pessimistic performance upper bound while a more realistic chip asynchronous assumption gives a more accurate performance it is also known that a hard limiter can be placed at the front end of an optical decoder to reduce the effects of multiple access interference and the near far problem in this paper the hard limiting performance of two dimensional 2 d optical codes is analyzed under the chip asynchronous assumption we apply a markov chain method for a more accurate analysis which can be generalized to 2 d optical codes with arbitrary maximum cross correlation values the performance of 2 d optical codes with the hard limiting and chip asynchronous assumptions is also compared with the soft limiting and chip synchronous assumptions