probabilistic metrization of fuzzy uniformities abstract modifying the structure of fuzzy uniform spaces introduced by lowen 5 we propose a further concept of fuzzy uniformities so called fuzzy t

a note on fixed point theorems of hadzci c abstract in this paper we give a fixed point theorem for multi valued probabilistic contraction mappings on a menger space as a special case a fixed point theorem for multi valued contraction mappings on a fuzzy metric space is obtained the results presented improve and generalize in a sense some recent fixed point theorems proved by had ic

torsion units in integral group rings of some metabelian groups let g be an extension of an elementary abelian p group a by an abelian group x with faithful and irreducible action then any torsion unit of the integral group ring zg is rationally conjugate to a trivial unit this confirms a conjecture of zassenhaus for these groups g

fuzzy metric neighbourhood spaces abstract hohle founded the first coherent topological study of menger s probabilistic metric spaces by endowing them with fuzzy t uniformities we continue hohle s work in the special case when the triangular norm t used is min that is when the resulting probabilistic metric uniformities are lowen fuzzy uniformities in this case we call the induced fuzzy topological spaces fuzzy pseudo metric neighbourhood spaces we introduce axioms of n regularity and n normality which are satisfied in fuzzy pseudo metric neighbourhood spaces we introduced a lowen fuzzy uniform topology on the fuzzy real line ri called the n euclidean topology by means of a fuzzy probabilistic metric on r i called the axiom of n complete regularity which characterizes the lowen fuzzy uniform topologies

a multicriteria pareto optimal path algorithm abstract in this paper we present an algorithm for finding in a multicriteria network pareto optimal paths one each for each efficient objective vector validation of the algorithm and two illustrative examples are included computational experience is also reported this algorithm is a generalization of an earlier one for the bicriterion case

enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an earth observing satellite we consider a satellite following orbits around the earth in order to take shots corresponding to images requested by various customers the daily operations of such a satellite consist of defining a feasible and satisfactory shot sequence this problem involves both combinatorial and multiple criteria difficulties indeed the number of feasible shot sequences grows significantly with the number of images asked for and the evaluation of a shot sequence is based on several conflicting criteria we propose to formulate this problem as the selection of a multiple criteria path in a graph without circuit our approach for solving this problem involves two stages generation of efficient paths and selection of a satisfactory path using a multiple criteria interactive procedure

on a conjecture of zassenhaus on torsion units in integral group rings ii suppose that a group g has a normal subgroup c where c and g c are cyclic of relatively prime orders then any torsion unit in zg is rationally conjugate to a trivial unit

a counterexample to the first zassenhaus conjecture abstract hans j zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group g there exists a unit a in the rational group algebra of g such that a 1 u a g for some g g we disprove this conjecture by first proving general results that help identify counterexamples and then providing an infinite number of examples where these results apply our smallest example is a metabelian group of order 2 7 3 2 5 7 2 19 2 whose integral group ring contains a unit of order 7 19 which in the rational group algebra is not conjugate to any element of the form g

fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces abstract this paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces by virtue of this concept some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained these new results are a unified approach to generalize several fixed point theorems for fuzzy mappings

units of integral group rings of metabelian groups abstract let u1 z g denote the units of augmentation one of the integral group ring z g of the finite group g we prove that g has a normal torsion free complement in u1 z g if g has an abelian normal subgroup a and g a is abelian of odd order or of exponent dividing 4 or 6

a note on compactness in a fuzzy metric space we study the compactness in a fuzzy metric space we also give a generalization of niemytzki tychonoff theorem for a fuzzy metric space

fixed point theorems for multivalued mappings in some classes of fuzzy metic spaces abstract using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved as an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

multiobjective shortest path problems with lexicographic goal based preferences abstract multiobjective shortest path problems are computationally harder than single objective ones in particular execution time is an important limiting factor in exact multiobjective search algorithms this paper explores the possibility of improving search performance in those cases where the interesting portion of the pareto front can be initially bounded we introduce a new exact label setting algorithm that returns the subset of pareto optimal paths that satisfy a set of lexicographic goals or the subset that minimizes deviation from goals if these cannot be fully satisfied formal proofs on the correctness of the algorithm are provided we also show that the algorithm always explores a subset of the labels explored by a full pareto search the algorithm is evaluated over a set of problems with three objectives showing a performance improvement of up to several orders of magnitude as goals become more restrictive

generalized hicks contractions an extension of a result of žikic abstract in a recent paper of this journal ikic dosenovic has established a coincidence point theorem for three mappings in menger spaces we relax some conditions of ikic s theorem in order to connect it to some known results in fixed point theory in probabilistic metric spaces among consequences an improvement of a theorem from the book o had ic e pap fixed point theory in probabilistic metric spaces kluwer academic publishers dordrecht 2001 concerning generalized hicks c contractions is obtained

continuity of fuzzy multiplication in the n euclidean space abstract the n euclidean space m i is a fuzzy normed vector space whose underlying set is the smallest real vector space including all nonnegative fuzzy real numbers the fuzzy multiplication on the fuzzy real line easily extends to a multiplication on m i we show that under that multiplication m i is a fuzzy normed algebra in consequence fuzzy multiplication is shown to be continuous in the n euclidean topology on m i

on a multicriteria shortest path problem abstract multicriteria shortest path problems have not been treated intensively in the specialized literature despite their potential applications in fact a single objective function may not be sufficient to characterize a practical problem completely for instance in a road network several parameters as time cost distance etc can be assigned to each arc clearly the shortest path may be too expensive to be used nevertheless the decision maker must be able to choose some solution possibly not the best for all the criteria in this paper we present two algorithms for this problem one of them is an immediate generalization of the multiple labelling scheme algorithm of hansen for the bicriteria case based on this algorithm it is proved that any pair of nondominated paths can be connected by nondominated paths this result is the support of an algorithm that can be viewed as a variant of the simplex method used in continuous linear multiobjective programming a small example is presented for both algorithms

compact probabilistic metrics on bounded closed intervals of distribution functions a menger space a special type of probabilistic metric spaces is said to be compact if its strong uniformity is compact we construct in a natural way menger t metrics on the set of distribution functions one for each copula t a special type of continuous t norms we show that on each bounded closed interval of distribution functions the strong uniformities of all our spaces are induced by the modified levy metric hence they are compact we establish an alternative description and a number of good properties of our menger spaces which may render them well behaved examples for workers in the field

completeness of the standard fuzzy real line for fns abstract we consider a special class of fuzzy metric neighbourhood spaces where the fuzzy distance is induced by a fuzzy pseudo norm this class is contained in lowen s well known category fns of fuzzy neighbourhood spaces we define the fuzzy limit of a sequence a fuzzy cauchy sequence and fuzzy convergence in fuzzy metric neighbourhood spaces we prove that the set of all nonnegative fuzzy real numbers r i under the n euclidean metric the standard fuzzy real line for fns is complete but that the smallest fuzzy neighbourhood real algebra m i including r i is not complete we also characterize the fuzzy cauchy sequences in m i in terms of their corresponding real sequences of cuts

fuzzy inner product spaces abstract the n euclidean space m i is a fuzzy pseudo normed algebra whose underlying set is the smallest real vector space including all nonnegative fuzzy real numbers we introduce axioms for a fuzzy inner product on a unitary m i module with values in m i we establish the fuzzy schwarz inequality for fuzzy inner products we introduce the cartesian product of fuzzy inner product spaces and investigate the relations between their underlying topologies we conclude the research by supplying two interesting examples of fuzzy inner product spaces

multivalued generalizations of probabilistic contractions we generalize some well known fixed point theorems for probabilistic contractions to multivalued contractions the contraction maps are considered in generalized menger spaces

a fixed point theorem in probabilistic metric spaces and an application abstract the notion of a c contraction type multivalued mapping is introduced this notion is a generalization of the notion of c contraction introduced by t l hicks univ u novom sadu zb rad prirod mat fak ser mat 13 1983 63 72 a fixed point theorem for c contraction is proved an application on the existence of a random fixed point for random operator f m m where m d is a separable metric space and a m a measure space with a decomposable measure of nsa type is given

fuzzy contractive mappings and fixed points in fuzzy metric spaces in the paper we introduce a new concept of fuzzy contraction which is a generalization of a fuzzy contractive mapping initiated in the article v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 252 for this type of contraction the conditions guaranteeing the existence of fixed point in fuzzy m complete metric spaces in the sense of george and veeramani are established the result is supported by examples

coincidence theorems for set valued mappings and ekeland s variational principle in fuzzy metric spaces abstract in this paper we establish a coincidence theorem for set valued mappings in fuzzy metric spaces with a view to generalizing downing kirk s fixed point theorem in metric spaces as consequences we obtain caristi s coincidence theorem for set valued mappings and a more general type of ekeland s variational principle in fuzzy metric spaces further we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces some applications of these results to probabilistic metric spaces are presented

separation axioms and the fuzzy real lines we show that for each lattice l which is completely distributive and equipped with an order reversing involution the canonical topology of the fuzzy real line l is uniformizable in the sense of hutton furthermore this uniformity induces a pseudometric which induces the canonical topology consequently l satisfies the higher order separation axioms of hutton and sarkar more generally we answer most of the open questions concerning l and its subspaces with respect to each of the separation axiom schemes of hutton and sarkar answer some of these same questions for the stratified fuzzy real line c l and its subspaces and analyze c l and its subspaces with respect to the separation axioms of rodabaugh

multiobjective a search with consistent heuristics the article describes and analyzes namoa an algorithm for multiobjective heuristic graph search problems the algorithm is presented as an extension of a an admissible scalar shortest path algorithm under consistent heuristics a is known to improve its efficiency with more informed heuristics and to be optimal over the class of admissible algorithms in terms of the set of expanded nodes and the number of node expansions equivalent beneficial properties are shown to prevail in the new algorithm

a comparison of heuristic best first algorithms for bicriterion shortest path problems abstract a variety of algorithms have been proposed to solve the bicriterion shortest path problem this article analyzes and compares the performance of three best first label setting algorithms that accept heuristic information to improve efficiency these are namoa moa and tung chew s algorithm tc a set of experiments explores the impact of heuristic information in search efficiency and the relative performance of the algorithms the analysis reveals that namoa is the best option for difficult problems its time performance can benefit considerably from heuristic information though not in all cases the performance of tc is similar but somewhat worse however the time performance of moa is found to degrade considerably with the use of heuristic information in most cases explanations are provided for these phenomena

coincidence point theorems and minimization theorems in fuzzy metric spaces abstract in this paper some new versions of coincidence point theorems and minimization theorems for single valued and multi valued mappings in generating spaces of the quasi metric family are obtained as applications we utilize our main theorems to prove coincidence point theorems fixed point theorems and minimization theorems for single valued and multi valued mappings in fuzzy metric spaces and probabilistic metric spaces

the urysohn lemma for fuzzy neighbourhood spaces abstract the framework fns of lowen s fuzzy neighbourhood spaces is a special environment for the study of fuzzy topology it encompasses its own metrics uniformities and proximities among other interesting constructions this is a fresh and fast growing field of research it promises to develop quickly to a calculus which combines depth with applicability within this framework we establish the urysohn lemma for the mashhour morsi axiom of n normality the formulation employs the mashhour morsi n euclidean space as the suitable fuzzy analogue of the real line the proof makes use of the artico moresco fuzzy proximities the lowen fuzzy uniformities and the mashhour morsi axiom of n complete regularity

fuzzy t neighbourhood spaces part 3 t separation axioms we address the problem of identifying a useful set of mutually compatible separation axioms for each category t fns of t neighbourhood spaces it should contain one of t complete regularity that characterizes t uniformizability as indeed we achieve here this seems to necessitate the parameterization of most separation axioms by the triangular norm t with the exception of the two axioms t0 and r0 which have categorical definitions valid in any topological category we introduce t separation axioms in terms of t and fuzzy closure operators only making them meaningful for the whole of fts we then characterize them within t fns in terms of t fuzzy closures of crisp fuzzy subsets and t neighbourhoods we study our t axioms and establish some entailments between them our t complete regularity commits us to investigate a t real line which is a t neighbourhood space induced by a certain probabilistic t metric due to hohle fuzzy sets and systems 1 1978 311

a fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces in this paper we shall generalize a fixed point theorem for multivalued mappings in probabilistic metric spaces proved in j math anal appl 202 1996 433 449 as a corollary a fixed point result in menger spaces s f t where t is a strict t norm is obtained some special cases where t is a member of dombi schweizer sklar and aczel alsina families of t norms are investigated an application in fuzzy metric spaces is presented

multi objective vehicle routing problems routing problems such as the traveling salesman problem and the vehicle routing problem are widely studied both because of their classic academic appeal and their numerous real life applications similarly the field of multi objective optimization is attracting more and more attention notably because it offers new opportunities for defining problems this article surveys the existing research related to multi objective optimization in routing problems it examines routing problems in terms of their definitions their objectives and the multi objective algorithms proposed for solving them

on fixed point theorems in fuzzy metric spaces abstract the purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces the results presented improve and generalize some recent results