Gradation Of Openness Research Articles

THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES

Lim et al. [5] introduce the notion of ordinary smooth topologies by considering the gradation of openness[resp. closedness] of ordinary subsets of X. In this paper, we study a collection of all ordinary smooth topologies on X, say OST(X), in the sense of a lattice. And we prove that OST(X) is a complete lattice.

Implementation of Asphalt-Rubber Mixes into the Mechanistic Empirical Pavement Design Guide

ABSTRACT The Mechanistic-Empirical Pavement Design Guide (MEPDG) developed by the National Cooperative Highway Research Program (NCHRP) utilizes material properties to predict distresses in pavement structures. This new MEPDG is in the process of replacing the traditional pavement design based on the AASHTO 1993 Design Guide. The Arizona Department of Transportation (ADOT) uses Asphalt- Rubber (AR) mixes state-wide. These mixes include both gap and open gradation designs. However, the national calibration process that was undertaken for the MEPDG did not include asphalt-rubber mixes. Because of their unique characteristics, this paper addresses steps and efforts undertaken in a recent study to implement these AR mixes into the MEPDG. There were several issues and limitations identified pertaining to the implementation of AR mixes in the MEPDG. Short and long term recommendations were provided. An important outcome includes a modified Dynamic Modulus predictive equation for AR mixes that is expected to be used in a future implementation of AR mixes in MEPDG.

Laboratory Investigation of Open-Graded Friction-Course Mixtures Containing Polymers and Cellulose Fibers

Open-graded friction course (OGFC), which consists of an open gradation mostly of coarse size aggregate with little fines, is a special purpose mixture that is increasingly used in pavement surfacing around the world. The typical benefits of an OGFC mixture are increased surface permeability, noise reduction, and enhanced surface friction, especially in wet conditions. This paper presents results of a study focusing on the use and properties of OGFC mixtures containing reclaimed polyethylene modified binder (RPEB), crumb rubber modified binder (CRMB), and neat 60=70-grade binder with cellulose fibers. The relative performance of mixtures and an aspect relating to the design of such mixtures, based on the laboratory study, have been presented in detail. Several laboratory tests were carried out in this study to evaluate open-graded friction course mixture properties by adopting two different types of Marshall compaction. A draindown test, a Cantabro stone loss test, a permeability test, an indirect tensile strength test, a resilient modulus test, a rutting test, and a skid resistance test were used to evaluate the performance of OGFC mixtures. The addition of fiber stabilizers and polymerized asphalt significantly reduced the potential for draindown in OGFC mixtures. Mixtures compacted by 50 blows on one face by a Marshall hammer were found to give improved results with respect to abrasion and other related mixture properties of the OGFC mixtures. The test results indicated that polymer modi- fication of the binder enhances the relevant engineering properties of the OGFC mixtures. Tensile strength ratio (TSR) values were found to be less for mixtures with modified binders than the mixtures with unmodified binders and fibers. DOI: 10.1061/(ASCE)TE.1943-5436 .0000304. © 2012 American Society of Civil Engineers.

Implementation of Asphalt-Rubber Mixes into the Mechanistic Empirical Pavement Design Guide

ABSTRACT The Mechanistic-Empirical Pavement Design Guide (MEPDG) developed by the National Cooperative Highway Research Program (NCHRP) utilizes material properties to predict distresses in pavement structures. This new MEPDG is in the process of replacing the traditional pavement design based on the AASHTO 1993 Design Guide. The Arizona Department of Transportation (ADOT) uses Asphalt- Rubber (AR) mixes state-wide. These mixes include both gap and open gradation designs. However, the national calibration process that was undertaken for the MEPDG did not include asphalt-rubber mixes. Because of their unique characteristics, this paper addresses steps and efforts undertaken in a recent study to implement these AR mixes into the MEPDG. There were several issues and limitations identified pertaining to the implementation of AR mixes in the MEPDG. Short and long term recommendations were provided. An important outcome includes a modified Dynamic Modulus predictive equation for AR mixes that is expected to be used in a future implementation of AR mixes in MEPDG.

INTERVAL-VALUED SMOOTH TOPOLOGICAL SPACES

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.

Characterization of OGFC Mixtures Containing Reclaimed Polyethylene Fibers

Open-graded friction course (OGFC) mixture is a special purpose mixture that is being increasingly used in pavement surfacing around the world. OGFC mixtures consist of an open gradation, mostly of coarse size aggregate with little fines. Asphalt contents for OGFC mixtures are generally slightly higher than for dense-graded mixtures. This paper deals with the viability of using reclaimed polyethylene (PE) fibers derived from low-density polyethylene (LDPE) tote bags collected from domestic waste as an additive in OGFC mixtures. Draindown test results indicated that OGFC mixtures with PE fibers can be effectively used to retard draindown of the binder and mineral filler. Mixture designs were performed for a range of 4.5–6.0% asphalt content. Laboratory tests were carried out on OGFC mixtures to determine the resistance to fatigue damage, unaged and aged abrasion, tensile strength, moisture-induced damage, and plastic deformation. The test results indicated that OGFC mixtures with reclaimed PE fibers showed improvement in tensile strength and improved resistance to permanent deformation, fatigue-induced damage, and moisture susceptibility when compared with mixtures without fibers.

SOME RESULTS ON INTUITIONISTIC FUZZY TOPOLOGICAL SPACES DEFINED BY INTUITIONISTIC GRADATION OF OPENNESS

In this paper, we introduce the concepts of closure and interior deflned by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and sev- eral types of compactness, and obtain some characterizations.

Evaluation of Open-Graded Friction Course Mixtures Containing Cellulose Fibers and Styrene Butadiene Rubber Polymer

Open-graded friction course (OGFC) or porous mixtures consist of an open gradation, mostly of coarse size aggregate with little fines. The benefits of an OGFC mixture are typically increased surface permeability, noise reduction, and enhanced surface friction, especially in wet weather. This paper presents the results of a study investigating four different OGFC mixes containing no additives, cellulose fibers, styrene butadiene rubber (SBR) polymer, and a combination of both fibers and SBR polymer. Mix designs were performed according to the design procedure proposed by the National Center of Asphalt Technology for a range of 4.5–6.5% asphalt content. The mixture containing fibers and SBR polymer was selected as an acceptable mix design with an optimum asphalt content of 6.5%. The moisture susceptibility of the selected mix at optimum asphalt content was evaluated. Results were compared with that for a dense mix.

α‐fuzzy compactness in I‐topological spaces

Using a gradation of openness in a (Chang fuzzy) I‐topological space, we introduce degrees of compactness that we call α‐fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α‐locally compact spaces and construct a one‐point α‐fuzzy compactification of an I‐topological space.

On intuitionistic gradation of openness

In this paper, we introduce a concept of intuitionistic gradation of openness on fuzzy subsets of a nonempty set X and define an intuitionistic fuzzy topological space. We prove that the category of intuitionistic fuzzy topological spaces and gradation preserving mappings is a topological category. We study compactness of intuitionistic fuzzy topological spaces and prove an analogue of Tychonoff's theorem.

The complete lattice [formula omitted] of smooth fuzzy topologies

Smooth fuzzy topologies are an extension of both crisp topologies and fuzzy topologies, in the sense that not only the objects are fuzzified, but also the axiomatics. In this article, we will complete the proof of the result given in (Chattopadhyay et al., Fuzzy Sets and Systems 49 (1992) 237), stating that the collection of smooth fuzzy topologies, equipped with the pointwise order, is a complete lattice. To this end, we will establish a subbase and base lemma for these by proving that any valuation function can be modified to construct a gradation of openness.

Gradations of openness and Chang’s fuzzy topologies

We study some properties of gradations of openness defined on a set X and prove that each gradation of openness δ is the supremum (infimum) of a strictly increasing (decreasing) sequence of gradations of openness which are equivalent to δ. Also, we characterize those fuzzy topological spaces (X, T) with the property that there exists a gradation of openness σ from I X onto I such that G∈ T iff σ(G)>0.

On S-quasi-fuzzy proximity spaces

In 1992, a new definition for a fuzzy topological space was given by introducing the concept of a gradation of openness (Chattopadhyay et al., 1992). In 1996, we gave a new definition for a fuzzy proximity space by introducing the concept of a gradation of proximity (Ghanim et al., 1996). In this paper we introduce the concept of a gradation of S-quasi-proximity. We show that each gradation of S-quasi-proximity induces two gradations of openness. Some relations between a gradation of S-quasi-proximity and its induced gradations of openness are also investigated.

Gradation of supra-openness

In 1992 a new definition of a fuzzy topological space was given by Chattopadhyay et al. (1992) by introducing the concept of a gradation of openness. In this paper a new definition of a fuzzy supra-topological (resp. supra-proximity, supra uniform) space is given by introducing the concept of a gradation of supra-openness (resp. supra-proximity, supra-uniformity) on a non-empty set X. How to construct a gradation of supra-openness induced by a gradation of supra-proximity (resp. supra-uniformity) is explained. The connection between gradations of supra-proximity and gradations of supra-uniformity are investigated. Throughout this paper, the class of all fuzzy subsets on a non-empty set X will be denoted by I X and fuzzy subsets will be denoted by small Greek letters. Also, we identify each subset with its characteristic function.

Gradations of uniformity and gradations of proximity

In 1992, a new definition of a fuzzy topological space was given by introducing the concept of a gradation of openness. In this paper, a new definition of a fuzzy uniform (resp. proximity) space is given by introducing the concept of a gradation of uniformity (resp. proximity) on a non empty set X. How to construct a gradation of openness induced by a gradation of uniformity (resp. proximity) is explained. The connexions between gradations of proximity and gradations of uniformity are investigated.

Gradation of openness: fuzzy topology

In an earlier paper, we have given a new definition of fuzzy topology by introducing a concept of gradation of openness of fuzzy subsets. In order to make the concept more appropriate, in this paper we modify the definition of gradation function and then study subspace of fuzzy topological spaces, gradation preserving maps and category of fuzzy topological spaces and gradation preserving maps.

Fuzzy topology redefined

In this paper we give a new definition of fuzzy topology by introducing a concept of gradation of openness of fuzzy subsets, and then study fuzzy continuity.