honey pot constrained searching with local sensory information in this paper we investigate the problem of searching for a hidden target in a bounded region of the plane using an autonomous robot which is only able to use local sensory information the problem is naturally formulated in the continuous domain but the solution proposed is based on an aggregation refinement approach in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem a solution to the original problem is obtained through a refinement procedure that lifts the discrete path into a continuous one we show that the discrete optimization is computationally difficult np hard but there are computationally efficient approximation algorithms for solving it the resulting solution to the continuous problem is in general not optimal but one can construct bounds to gauge the cost penalty incurred due to i the discretization of the problem and ii the attempt to approximately solve the np hard problem in polynomial time numerical simulations show that the algorithms proposed behave significantly better than naive approaches such as a random walk or a greedy algorithm c 2006 elsevier ltd all rights reserved

application of fuzzy soft set in decision making problems based on grey theory there are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets however the basis of evaluation of the decision method is single and simple the same decision problem can obtain different results from using a different evaluation basis in this paper in order to obtain the right result we discuss fuzzy soft set decision problems a new algorithm based on grey relational analysis is presented the evaluation bases of the new algorithm are multiple there is more information in a decision result based on multiple evaluation bases which is more easily accepted and logical to one s thinking for the two cases examined the results show that the new algorithm is efficient for solving decision problems

applications of soft sets in ideal theory of bck bci algebras the notion of soft ideals and idealistic soft bck bci algebras is introduced and several examples are given relations between soft bck bci algebras and idealistic soft bck bci algebras are provided the intersection union and operation and or operation of soft ideals and idealistic soft bck bci algebras are established

soft sets and soft groups molodtsov introduced the concept of soft set theory which can be used as a generic mathematical tool for dealing with uncertainty in this paper we introduce the basic properties of soft sets and compare soft sets to the related concepts of fuzzy sets and rough sets we then give a definition of soft groups and derive their basic properties using molodtsov s definition of the soft sets

fuzzy filters of mtl algebras characterizations of fuzzy filters in mtl algebras are given the fuzzy filter generated by a fuzzy set is considered the notion of boolean fuzzy filters and mv fuzzy filters are introduced and related properties are investigated a condition for a fuzzy filter to be boolean is provided a characterization of a boolean fuzzy filter is given a congruence relation on a mtl algebra induced by a fuzzy filter is established and we show that the set of all congruence relations induced by a fuzzy filter is a completely distributive lattice

the transfer matrices of the self similar fractal potentials on the cantor set on the basis of an exact formalism a system of functional equations for the tunnelling parameters of self similar fractal potentials ssfps is obtained three different families of solutions are found for these equations two of them having one parameter and one being free of parameters both one parameter solutions are shown to be described in the long wave limit by a fractal dimension at the same time the third solution yields transfer matrices which are analytical in this region similar to the case of structures with the euclidean geometry we have revealed some manifestations of scale invariance in the physical properties of ssfps nevertheless in the common case these potentials do not possess strictly speaking this symmetry the point is that ssfps in the common case are specified in contrast to the cantor set by two length scales but not one a particular case when ssfps are exactly scale invariant to an electron with well defined energy is found

evaluation of the coulomb force via the fredholm integral equation the electrostatic force between two conducting spheres is solved exactly from coulomb s law the force is evaluated in two steps i the charge distribution on each of the spheres is calculated as a function of separation distance by way of a solution to the fredholm integral equation ii the effect of the known charge distribution is integrated to obtain the electrostatic force evaluation of the electrostatic force is fast because the series expression for the charge distribution is super converging a characteristic trait for some fredholm type equations

the complexity of the optimal searcher path problem in this note we show that the problem of finding an optimal searcher path that maximizes the probability of detecting a stationary target by the end of a fixed time is np complete we also demonstrate that the problem of finding a path that minimizes mean time to detection is np hard

fuzzy subinclines ideals of incline algebras the fuzzification of subinclines ideals in inclines are considered and some related properties are investigated we also state the product of fuzzy subinclines ideals and the projections of fuzzy subinclines ideals we discuss fuzzy relations fuzzy characteristic subinclines ideals

involutory and invertible fuzzy bck algebras the concept of a fuzzy annihilator in a commutative bck algebra will be introduced and then we investigate some basic properties using this notion we define an involutory resp invertible fuzzy ideal we prove that i every bounded implicative bck algebra is an involutory fuzzy bck algebra and ii every categorical commutative bck algebra is an invertible fuzzy bck algebra let x be an involutory and invertible fuzzy bck algebra and let fi x denote the set of all fuzzy ideals of x we show that iii fi x is a distributive lattice and iv fi x is a quasi boolean algebra

lever aggregation operators we make use of the physical concept of lever to generalize well known operators based on weights all these operators can be understood as levers in equilibrium with weights masses located at the points in 0 1 that opinions represent

generalised fuzzy soft sets in this paper we define generalised fuzzy soft sets and study some of their properties application of generalised fuzzy soft sets in decision making problem and medical diagnosis problem has been shown

an optimal branch and bound procedure for the constrained path moving target search problem a searcher and target move among a finite set of cells c 1 2 n in discrete time at the beginning of each time period one cell is searched if the target is in the selected cell j it is detected with probability qj if the target is not in the cell searched it cannot be detected during the current time period after each search a target in cell j moves to cell k with probability pjk the target transition matrix p pjk is known to the searcher the searcher s path is constrained in that if the searcher is currently in cell j the next search cell must be selected from a set of neighboring cells cj the object of the search is to minimize the probability of not detecting the target in t searches

the normal parameter reduction of soft sets and its algorithm this paper is concerned with the reduction of soft sets and fuzzy soft sets firstly the problems of suboptimal choice and added parameter set of soft sets are analyzed then we introduce the definition of normal parameter reduction in soft sets to overcome these problems in addition a heuristic algorithm of normal parameter reduction is presented two new definitions parameter important degree and decision partition are proposed for analyzing the algorithm of normal parameter reduction furthermore the normal parameter reduction is also investigated in fuzzy soft sets

solving constrained matrix games with payoffs of triangular fuzzy numbers constrained matrix games with payoffs of triangular fuzzy numbers tfns are a type of matrix games with payoffs expressed by tfns and sets of players strategies which are constrained so far as we know no study have yet been attempted for constrained matrix games with payoffs of tfns since there is no effective way to simultaneously incorporate the payoffs fuzziness and strategies constraints into classical and or fuzzy matrix game methods the aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of tfns in this methodology we introduce the concepts of alpha constrained matrix games for constrained matrix games with payoffs of tfns and the values by the duality theorem of linear programming it is proven that players gain floor and loss ceiling always have a common interval type value and hereby any alpha constrained matrix game has an interval type value moreover using the representation theorem for the fuzzy set it is proven that any constrained matrix game with payoffs of tfns always has a tfn type fuzzy value the auxiliary linear programming models are derived to compute the lower and upper bounds of the interval type value and optimal strategies of players for any alpha constrained matrix game in particular the mean and the lower and upper limits of the tfn type fuzzy value of any constrained matrix game with payoffs of tfns can be directly obtained through solving the derived three linear programming models with data taken from only 1 cut and 0 cut of payoffs hereby the tfn type fuzzy value of any constrained matrix game with payoffs of tfns are easily computed the proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example

on fuzzy h ideals in hemirings the fuzzy setting of a left h ideal in a hemiring is constructed and basic properties are investigated using a collection of left h ideals of a hemiring s fuzzy left h ideals of s are established the notion of a finite valued fuzzy left h ideal is introduced and its characterization is given fuzzy relations on a hemiring s are discussed

fuzzy strong implicative hyper bck ideals of hyper bck algebras the fuzzy setting of strong implicative hyper bck ideals in hyper bck algebras is considered some of their properties are investigated relations among fuzzy strong hyper bck ideals fuzzy implicative hyper bck ideals and fuzzy strong implicative hyper bck ideals are given a characterization of a fuzzy strong implicative hyper bck ideal is provided the hyper homomorphic preimage of a fuzzy strong implicative hyper bck ideal is discussed

detection of an anomalous cluster in a network we consider the problem of detecting whether or not in a given sensor network there is a cluster of sensors which exhibit an unusual behavior formally suppose we are given a set of nodes and attach a random variable to each node we observe a realization of this process and want to decide between the following two hypotheses under the null the variables are i i d standard normal under the alternative there is a cluster of variables that are i i d normal with positive mean and unit variance while the rest are i i d standard normal we also address surveillance settings where each sensor in the network collects information over time the resulting model is similar now with a time series attached to each node we again observe the process over time and want to decide between the null where all the variables are i i d standard normal and the alternative where there is an emerging cluster of i i d normal variables with positive mean and unit variance the growth models used to represent the emerging cluster are quite general and in particular include cellular automata used in modelling epidemics in both settings we consider classes of clusters that are quite general for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic by far the most popular method in practice achieves that same rate within a logarithmic factor our results are not limited to the normal location model but generalize to any one parameter exponential family when the anoma lous clusters are large enough

an optimal algorithm for euclidean shortest paths in the plane we propose an optimal time algorithm for a classical problem in plane computational geometry computing a shortest path between two points in the presence of polygonal obstacles our algorithm runs in worst case time o n log n and requires o n log n space where n is the total number of vertices in the obstacle polygons the algorithm is based on an efficient implementation of wavefront propagation among polygonal obstacles and it actually computes a planar map encoding shortest paths from a fixed source point to all other points of the plane the map can be used to answer single source shortest path queries in o log n time the time complexity of our algorithm is a significant improvement over all previously published results on the shortest path problem finally we also discuss extensions to more general shortest path problems involving nonpoint and multiple sources

soft bck bci algebras molodtsov d molodtsov soft set theory first results comput math appl 37 1999 19 31 introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches in this paper we apply the notion of soft sets by molodtsov to the theory of bck bci algebras the notion of soft bck bci algebras and soft subalgebras are introduced and their basic properties are derived

the optimal search for a moving target when the search path is constrained a search is conducted for a target moving in discrete time among a finite number of cells according to a known markov process the searcher must choose one cell in which to search in each time period the set of cells available for search depends upon the cell chosen in the last time period the problem is to find a searcher path i e a sequence of search cells that maximizes the probability of detecting the target in a fixed number of time periods we formulate the problem as a partially observable markov decision process and present a finite time horizon pomdp solution technique which is simpler than the standard linear programming methods

a new type of solution of the schrodinger equation on a self similar fractal potential scattering of a quantum particle by a self similar fractal potential on a cantor set is investigated we present a new type of solution of the functional equation for the transfer matrix of this potential which was derived earlier from the schrodinger equation

soft semirings molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we initiate the study of soft semirings by using the soft set theory the notions of soft semirings soft subsemirings soft ideals idealistic soft semirings and soft semiring homomorphisms are introduced and several related properties are investigated

hamilton paths in grid graphs a grid graph is a node induced finite subgraph of the infinite grid it is rectangular if its set of nodes is the product of two intervals given a rectangular grid graph and two of its nodes we give necessary and sufficient conditions for the graph to have a hamilton path between these two nodes in contrast the hamilton path and circuit problem for general grid graphs is shown to be np complete this provides a new relatively simple proof of the result that the euclidean traveling salesman problem is np complete

combination of interval valued fuzzy set and soft set the soft set theory proposed by molodtsov can be used as a general mathematical tool for dealing with uncertainty by combining the interval valued fuzzy set and soft set models the purpose of this paper is to introduce the concept of the interval valued fuzzy soft set the complement and and or operations are defined on the interval valued fuzzy soft sets the demorgan s associative and distribution laws of the interval valued fuzzy soft sets are then proved finally a decision problem is analyzed by the interval valued fuzzy soft set some numerical examples are employed to substantiate the conceptual arguments

fuzzy prime ideals and invertible fuzzy ideals in bck algebras we state the relation between fuzzy prime ideals and invertible fuzzy ideals in commutative bck algebras

soft bl algebras based on fuzzy sets by means of soft sets and q soft sets some characterizations of implicative positive implicative and fantastic filteristic soft bl algebras are investigated finally we prove that a soft set is an implicative filteristic soft bl algebra if and only if it is both a positive implicative filteristic soft bl algebra and a fantastic filteristic soft bl algebra

discrete sequential search with positive switch cost suppose one object is hidden in one of n boxes according to a known probability distribution p1 pn the boxes are to be searched sequentially the probability of overlooking the object if we search box k and if the object is in box k is denoted by qk the cost of a search of box k amounts to ck if we decide to search box k directly after box k we have to pay some extra cost called switch cost tk k the problem is under some reasonable assumptions to construct a strategy with minimal expected cost if t 0 the problem has a well known solution unfortunately there are many reasons which establish the conjecture that there does not exist an easy construction rule for optimal strategies in the general case we give necessary and sufficient conditions for the existence of optimal strategies which are ultimately periodic u p since we state bounds on the length not only of the transient phase but also of the period of optimal u p strategies we may construct these optimal strategies by comparing finitely many strategies if optimal u p strategies exist we prove some other results to reduce the number of strategies which we have to compare at last we present a numerical example

application of level soft sets in decision making based on interval valued fuzzy soft sets molodtsov s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty research on fuzzy soft set based decision making has received much attention in recent years this paper aims to give deeper insights into decision making involving interval valued fuzzy soft sets a hybrid model combining soft sets with interval valued fuzzy sets the concept called reduct fuzzy soft sets of interval valued fuzzy soft sets is introduced using reduct fuzzy soft sets and level soft sets flexible schemes for decision making based on weighted interval valued fuzzy soft sets are proposed and some illustrative examples are employed to show that the proposals presented here are not only more reasonable but more efficient in practical applications

soft subsets and soft product operations molodtsov s soft set theory provides a general mathematical framework for dealing with uncertainty it is known that soft subsets and soft equal relations are of vital importance in soft set theory this paper aims to give a systematic study on several types of soft subsets and various soft equal relations induced by them we give some equivalent characterizations of different soft subsets and endeavor to ascertain the interrelations among these notions illustrated by a number of concrete examples we also consider ontology based soft sets and show that soft l subsets generalize both soft m subsets and ontology based soft subsets moreover by means of soft l subsets and some related notions we give a theoretical study concerning soft product operations such as products and products we consummate some incomplete results concerning soft product operations existing in the literature and investigate the algebraic properties of soft product operations in detail finally we consider free soft algebras associated with soft product operations it is shown that soft l equal relations are congruence relations over free soft algebras and the corresponding quotient structures form commutative semigroups

fuzzy positive implicative and fuzzy associative filters of lattice implication algebras we fuzzify the concept of positive implicative filters and associative filters in lattice implication algebras we prove that i every fuzzy positive implicative filter is a fuzzy implicative filter and ii every fuzzy associative filter is a fuzzy filter we provide equivalent conditions for both fuzzy positive implicative filter and fuzzy associative filter

discounted mean bound for the optimal searcher path problem with non uniform travel times we consider an extension of the optimal searcher path problem osp where a searcher moving through a discretised environment may now need to spend a non uniform amount of time travelling from one region to another before being able to search it for the presence of a moving target in constraining not only where but when the search of each cell can take place the problem more appropriately models the search of environments which cannot be easily partitioned into equally sized cells an existing osp bounding method in literature the mean bound is generalised to provide bounds for solving the new problem in a branch and bound framework the main contribution of this paper is an enhancement discounted mean dmean which greatly tightens the bound for the new and existing problems alike with almost no additional computation we test the new algorithm against existing osp bounding methods and show it leads to faster solution times for moving target search problems

fuzzy soft set theory applied to bck bci algebras abstract in the paper p k maji r biswas a r roy fuzzy soft sets j fuzzy math 9 3 2001 589 602 maji et al introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem the aim of this manuscript is to apply fuzzy soft set for dealing with several kinds of theories in bck bci algebras the notions of fuzzy soft bck bci algebras closed fuzzy soft ideals and fuzzy soft p ideals are introduced and related properties are investigated

on operations of soft sets soft set theory proposed by molodtsov has been regarded as an effective mathematical tool to deal with uncertainties in this paper first we prove that certain de morgan s law hold in soft set theory with respect to different operations on soft sets then we discuss the basic properties of operations on soft sets such as intersection extended intersection restricted union and restricted difference moreover we illustrate their interconnections between each other also we define the notion of restricted symmetric difference of soft sets and investigate its properties the main purpose of this paper is to extend the theoretical aspect of operations on soft sets

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

quotient structures of some implicative algebras via fuzzy implicative filters in this paper we discuss quotient implicative algebras induced by fuzzy implicative filters and establish the fuzzy fundamental homomorphism theorem for some implicative algebras

pruning method for optimal solutions of intm intn decision making scheme abstract this paper aims to find a faster method for optimal solutions of feng et al s int m int n decision making scheme we first give theoretical characterizations of optimal decision sets then we develop a pruning method which filters out those objects that cannot be elements of any optimal decision sets in the beginning experimental results have shown that our method has higher efficiency in computing the optimal solutions of this scheme particularly when we are processing soft sets with a great quantity of data

letter to the editor comment on a fuzzy soft set theoretic approach to decision making problems the algorithm for identification of an object in a previous paper of a r roy et al a r roy p k maji a fuzzy soft set theoretic approach to decision making problems j comput appl math 203 2007 412 418 is incorrect using the algorithm the right choice cannot be obtained in general the problem is illustrated by a counter example

on fuzzy ideals in bcc algebras the purpose of this paper is description of properties of fuzzy bcc ideals in bcc algebras and its images we describe also an extension of a fuzzy bcc ideal of a given bcc subalgebra s of x to a fuzzy bcc ideal of x such that and have the same image