on adjunctions between lim sl top and sl lim abstract consider l 1 be a commutative strictly two sided quantale with the underlying lattice l being meet continuous two adjunctions one is between limit spaces and stratified l limit spaces and the other is between stratified l limit spaces and stratified l topological spaces are established the first adjunction can be viewed as an extension of lowen s adjunction between the category of topological spaces and stratified 0 1 topological spaces the second is an extension of an adjunction between limit spaces and stratified l topological spaces established in u hohle and t kubiak hohle kubiak semigroup forum 2007

on stratified l convergence spaces in the classical theory of convergence spaces fischer s diagonal axiom ensures that a generalized convergence space is topological in this note we present a lattice valued fischer diagonal axiom and show that this axiom leads to the conclusion that a stratified l convergence space is l topological

pretopological and topological lattice valued convergence spaces we show that the classical axiom which characterizes pretopological convergence spaces splits into two axioms in the general heyting algebra valued case furthermore we present a generalization of kowalski s diagonal condition to the lattice valued case

lattice valued convergence spaces and regularity we define a regularity axiom for lattice valued convergence spaces where the lattice is a complete heyting algebra to this end we generalize the characterization of regularity by a dual form of a diagonal condition we show that our axiom ensures that a regular t1 space is separated and that regularity is preserved under initial constructions further we present an extension theorem for a continuous mapping from a subspace to a regular space a characterization in the restricted case that the lattice is a complete boolean algebra in terms of the closure of an l filter is given

modeling subjective evaluation for fuzzy group multicriteria decision making this paper presents a new fuzzy multicriteria decision making mcdm approach for evaluating decision alternatives involving subjective judgements made by a group of decision makers a pairwise comparison process is used to help individual decision makers make comparative judgements and a linguistic rating method is used for making absolute judgements a hierarchical weighting method is developed to assess the weights of a large number of evaluation criteria by pairwise comparisons to reflect the inherent imprecision of subjective judgements individual assessments are aggregated as a group assessment using triangular fuzzy numbers to obtain a cardinal preference value for each decision alternative a new fuzzy mcdm algorithm is developed by extending the concept of the degree of optimality to incorporate criteria weights in the distance measurement an empirical study of aircraft selection is presented to illustrate the effectiveness of the approach

the lower and upper p topological p regular modifications for lattice valued convergence spaces in this paper the notions of lower and upper topological regular modifications with respect to a stratified l generalized convergence structure and those with respect to a stratified l strong generalized convergence structure are defined and studied the basic properties and characterizations are presented in particular it is proved that the lower modifications behave reasonably well relative to final structures whereas the upper modifications exhibit comparable behavior relative to initial structures

diagonal conditions and continuous extension theorem abstract in this paper we obtain a generalization of kowalsky diagonal condition and that of fischer diagonal condition respectively namely kowalsky diagonal condition and fischer diagonal condition we show that our fischer diagonal condition assures a complete mv algebra valued convergence space proposed in this paper is strong l topological and kowalsky diagonal condition assures a principle or pretopological complete mv algebra valued convergence space is strong l topological also as applications we give a dual form of our fischer diagonal condition and obtain a concept of regular convergence space in addition we present an extension theorem for continuous maps from a dense subspace to a regular convergence space to show that our diagonal conditions works indeed

p topologicalness and p regularity for lattice valued convergence spaces in this paper p topologicalness and p regularity for jager s stratified l generalized convergence spaces and those for boustique et al s stratified l convergence spaces are studied through two different methods one method generalizes the well known fischer s dual diagonal condition the other method uses the neighborhood closure of stratified l filter in addition the p topologicalness and p regularity w r t initial constructions and final constructions are also discussed

preference programming through approximate ratio comparisons abstract in the context of hierarchical weighting this paper operationalizes interval judgments which allow the decision maker to enter ambiguous preference statements by indicating the relative importance of factors as intervals of values on a ratio scale through such judgments the decision maker can capture the subjective uncertainty in his preferences and thus avoid the often cumbersome elicitation of exact ratio estimates after each new statement the interval judgments are synthesized into dominance relations on the alternatives by solving a series of linear programming problems this leads to an interactive process of preference programming which provides more detailed results as the decision maker gradually enters a more specific preference description moreover the overall effort of preference elicitation is smaller than in the analytic hierarchy process because the most preferred alternative can usually be identified before all possible comparisons between pairs of factors have been completed

stratified lmn convergence tower groups and their stratified lmn uniform convergence tower structures abstract if l and m are frames and n is a quantale then using stratification mappings between frames we introduce a category of stratified lmn convergence tower groups a topological category we then prove that every stratified lmn limit tower group induces a stratified lmn uniform convergence tower space also we introduce a category of stratified lmn cauchy tower groups and show that the category of strongly normal stratified lmn limit tower groups is isomorphic to the category of stratified lmn cauchy tower groups we provide various examples in support of our theories so far developed herein the text

lattice valued convergence associated with cns spaces abstract in this paper in the context of meet continuous quantale we present a notion of conical topological lattice valued convergence space which provides the theory of lattice valued convergence associated with such conical neighborhood spaces

stratified lmn convergence tower spaces we develop a general theory of convergence for lattice valued spaces based on the concept of s stratified lm filters for different choices of the frames l and m different kinds of filters arise and suitable choices of the lattice n allow to view many existing fuzzy and probabilistic convergence spaces as special examples of our stratified lmn convergence tower spaces the stratification requires a certain relation between the frames l and m and we use a so called stratification mapping to this end the stratification condition is used to show that the resulting category is fiber small and hence cartesian closedness is equivalent to the existence of natural function spaces we give several examples for our spaces for different choices of the lattices l m and n with a special focus on enriched lm fuzzy topological spaces finally we study diagonal axioms and regularity

on many valued stratified l fuzzy convergence spaces based on complete residuated lattices the relations between stratified l fuzzy convergence spaces and enriched l fuzzy topological spaces are studied it is shown that as a reflective subcategory the category of enriched l fuzzy topological spaces can embedded in the category of stratified l fuzzy convergence spaces also the specialization l preorder of stratified l fuzzy convergence spaces is investigated

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

relationships between l ordered convergence structures and strong l topologies by making use of the intrinsic fuzzy inclusion orders on the fuzzy power set the relationships between l ordered convergence spaces and strong l topological spaces are researched where l is a commutative unital quantale it is shown that the category of strong l topological spaces can be embedded in the category of l ordered convergence spaces as a reflective subcategory as a result we observe that there is a galois correspondence between the category of l ordered convergence spaces and the category of strong l topological spaces further it is proved that the class of all strong l topological l ordered convergence spaces precisely is the class of all strong l topological spaces and the class of spaces with non idempotent l ordered interior operators is characterized as a subclass of the class of l ordered convergence spaces

lattice valued convergence spaces extending the lattice context we define a category of stratified l generalized convergence spaces for the case where the lattice is an enriched cl premonoid we then investigate some of its categorical properties and those of its subcategories in particular the stratified l principal convergence spaces and the stratified l topological convergence spaces for some results we need to introduce a new condition on the lattice which is always true in the case where the lattice is a frame but not always true in the more general case as examples where we may apply the more general lattice context we examine the stratified l topological spaces and probabilistic limit spaces we show that the category of stratified l topological spaces is a reflective subcategory of our category and that the category of probabilistic limit spaces under a t norm is both a reflective and a coreflective subcategory of our category if we choose the lattice context appropriately

stratified l ordered convergence structures in this paper a new kind of lattice valued convergence structures on a universal set called stratified l ordered convergence structures are presented by modifying the axiom for stratified l generalized convergence structures in the fuzzy setting so as to make use of the intrinsic fuzzy inclusion order on the fuzzy power set the category of stratified l ordered convergence spaces described here is shown to be a reflective full subcategory in the category of stratified l generalized convergence spaces and hence it is topological and cartesian closed as preparation a further investigation of stratified l filters is presented from the viewpoint that latticed valued filters should be compatible with the intrinsic fuzzy inclusion order on the fuzzy power set

on stratified l convergence spaces pretopological axioms and diagonal axioms this paper focuses on pretopological and diagonal axioms for stratified l convergence spaces recently defined by the authors in 2011 this notion is slightly stronger than jager s stratified l generalized convergence spaces in particular one pretopological axiom is stated without resorting to the notion of neighborhood l filters some generalizations of kowalsky s and fischer s diagonal conditions are presented the relationship between these axioms are investigated

menger curvature and rectifiability in metric spaces we show that for any metric space x the condition where c z1 z2 z3 is the menger curvature of the triple z1 z2 z3 and is the 1 dimensional hausdorff measure on x guarantees that x is rectifiable

gahler s neighborhood condition for lattice valued convergence spaces we generalize a neighborhood condition from the category of convergence spaces to the category of lattice valued convergence spaces for a space in the category of convergence spaces this condition is equivalent to being a topological space it turns out that there are two meaningful generalizations of this condition to the category of lattice valued convergence spaces the first one guarantees that a space in a certain subcategory is a lattice valued topological space the other one is a levelwise condition which is equivalent to a generalization of fischer s diagonal condition the latter generalization is preserved under the embedding of the categories of convergence approach spaces and of probabilistic limit spaces into the category of lattice valued convergence spaces

a method for dealing with inconsistencies in pairwise comparisons abstract the pairwise comparison method is a powerful inference tool for assessing the relative importance of a set of items formally its objective is to make compatible decision maker s assignments paired comparison with properties needed for obtaining an overall rank in this paper we propose a distance based framework for analysing this kind of compatibility in this context goal programming is proposed as an attractive and flexible tool

subcategories of lattice valued convergence spaces we study several subcategories of heyting algebra valued convergence spaces these categories generalize the well known categories of kent convergence spaces of limit spaces of pretopological spaces of pseudo topological spaces and of topological limit spaces to the many valued setting moreover a functorial mechanism is described for changing the basis lattice

monoidal closedness of the category of stratified l semiuniform convergence spaces abstract for an integral commutative unital quantale l we show that there exists a tensor product between stratified l semiuniform convergence spaces and with respect to this tensor product that the category of stratified l semiuniform convergence spaces and uniformly continuous maps is a symmetric monoidal category as a result we obtain the monoidal closedness of the category of stratified l semiuniform convergence spaces and uniformly continuous maps