Crisp Point Research Articles

A novel class of bipolar soft separation axioms concerning crisp points

Abstract The main objective of this study is to define a new class of bipolar soft (BS) separation axioms known as BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space ( i = 0 , 1 , 2 , 3 , 4 ) \left(i=0,1,2,3,4) . This type is defined in terms of ordinary points. We prove that BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space implies BS T ˜ ˜ i − 1 {\widetilde{\widetilde{T}}}_{i-1} -space for i = 1 , 2 i=1,2 ; however, the opposite is incorrect, as demonstrated by an example. For i = 0 , 1 , 2 , 3 , 4 i=0,1,2,3,4 , we investigate that every BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space is soft T ˜ i {\widetilde{T}}_{i} -space; and we set up a condition in which the reverse is true. Moreover, we point out that a BS subspace of a BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space is a BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space for i = 0 , 1 , 2 , 3 i=0,1,2,3 .

Inspection of the Production Lot Using Two Successive Occasions Sampling Under Neutrosophy

The efficiency of the measuring tools and operators is a significant part of lot sentencing decisions. These tools have to pass some pre-specified quality levels to avoid problems during the quality assessment scenarios. These measurements have a serious risk to be encountered with any extent of ambiguity, doubt, or indeterminacy due to any of the factors like variation among the operating regimes, warming effects in the hot climatic conditions, the operators’ casual attitude, and so on. These factors as the most significant sources of extraneous variations can deeply affect the efficacy of lot sentencing decisions. Hence, the decision when based on the measurement through the operating tools and these tools have to pass which have fulfilled some adequate standards only then lot sentencing may avoid or save from the rejection of a good lot. The authors have put their focus on dealing with the factors that arise by measuring variability among the measured or determined values despite having the normal population distribution. In this study, the auxiliary information is used to estimate the variable of interest over the two successive occasions under the neutrosophic interval numbers and proved helpful to overcome this issue. The presented approach has discussed that in blurred, doubted, uncertain and undetermined datasets partially or completely, the efficacy of the decision for the whole lot cannot be decided on the single point crisped value. But the range of values around such a single crisp point in the form of neutrosophic theory is proved far better. In this context, the neutrosophic interval number successive sampling-based sampling plan is proposed which is the major contribution to the existing literature. It is explained in terms of operating characteristic function and the plan parameters are determined through the neutrosophic non-linear optimization approach. The comparative analysis is presented with the existing sampling plans and found efficient. Moreover, a real-life industrial dataset is used as an application of the concept.

On Binary Neutrosophic Crisp Points And Binary Neutrosophic Neighborhoods

As a generalization of crisp topology, neutrosophic crisp topology was introduced. As a progression, binary neutrosophic crisp sets were introduced in this article and their properties were also studied. With the idea that neutrosophic crisp points forms the basis for the neutrosophic neighborhood structures, new points namely binary neutrosophic crisp points were introduced in this article. Owing to the new points, binary neutrosophic neighborhood structure in the new space named as binary neutrosophic crisp topological space is framed. Eventually properties of binary neutrosophic crisp neighborhoods were discussed.

Fractal transforms for fuzzy valued images

The aim of this paper is to construct a complete metric space of fuzzy valued image functions and to define a fractal transform operator T. Contraction of T is guarantees the existence of its fixed point. A fuzzy point is considered for this purpose as a crisp point and approached through classical method on proving the completeness of the space.

Separation Axioms in Nnc Topological Spaces via Nnc e-open Sets

The main idea of this research is to define a new neutrosophic crisp points in neutrosophic crisp topological space namely (NncPN ), the concept of Nnc limit point was defined using (NncPN ), with some of its properties, the separation axioms (Nnceτi -space (i = 0,1, 2) were constructed in neutrosophic crisp topological space using (NncPN ) and examine the relationship between them in details.

Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is ( space if each coordinate space is soft space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

Automatic skull-face overlay and mandible articulation in data science by AIRS-Genetic algorithm

Craniofacial superimposition (CFS) is an innovative method of identifying the missing skull of a human and has received serious attention in forensic research. Optimal overlaying of skull face is one of the fundamental issues found on forensic technology. CFS methodology generally initiates with the marking the accurate landmarking of skull and face extracted from the scanning device which is termed as ground truth data. These extracted features of skull and face will be in crisp image as 3D and 2D. Consequent of this advanced technology, CFS has upgraded to automatic level to investigate different cases. Regardless, the forensic expert invests more for investigation and it consumes large time for completing it. Most of the review study proofs that the computer-aided methods can improve the efficiency of the CFS technique can improve much better than other techniques. The introduction of computerized 3D-2D CFS in forensic research proves to be a novel one and define as most advance CFS technique in research today. This methodology can automate the operation of CFS by reducing the error on over-layered model. Due to the involvement of machine learning process in forensic field, executing the CFS problem is much easier. Coevolutionary algorithms (CEAs) are nature-inspired and very optimistic in solving complex problems by measuring the fitness of the problem. In this research work, automatic CFS is proposed for skull-face overlay and mandible articulation. Conventionally, a fuzzy set is proposed for extracting the features of skull especially the landmarking. In this work the Artificial Immune Recognition System (AIRS) model is implemented for distance calculated for crisp point of the extracted image. Due to the increase of computation time for crisp landmarks, an efficient algorithm is needed. With the point of decreasing the time of computation not by losing the accuracy the cooperative coevolutionary algorithm is proposed. Similar to the AIRS function, the Euclidean distance metrics are calculated between the AIRS set and crisp points. Hence the fitness is calculated form the algorithm for better layout of landmarking for better skull face overlying. Ultimately, the outcome of the progression is compared with the existing methodologies for measuring the level of effectiveness respectively.

Neutrosophic Crisp Semi Separation Axioms In Neutrosophic Crisp Topological Spaces

The main goal of this paper is to propose a new type of separation axioms via neutrosophic crisp semi open sets and neutrosophic crisp points in neutrosophic crisp topological spaces, namely neutrosophic crisp semi separation axioms. Finally, we examine the relationship between them in details. And also includes the study of the connections between these neutrosophic crisp semi separation axioms and the existing neutrosophic crisp separation axioms. Moreover, many examples are presented, to illustrate the concepts introduced in this paper. and investigate their fundamental properties, relationships and characterizations.

Pre Separation Axioms In Neutrosophic Crisp Topological Spaces

In this paper, A new type of separation axioms in the neutrosophic crisp Topological space named neutrosophic crisp pre separation axioms is going to be defined , in which neutrosophic crisp pre open set and neutrosophic crisp point are to be depended on. Also, relations among them and the other type are going to be found.

Collaborative filtering recommendation algorithm based on user fuzzy similarity

In order to reflect the actual case of users' decisions and rating patterns, and solve the sparsity problem of traditional collaborative filtering recommendation algorithms, a trapezoid fuzzy rating model is proposed, which fuzzifies crisp point into trapezoid fuzzy number based on the rating stat istical information of users. The trapezoid fuzzy number contains personalized information of users and can reasonably represent user's preference degree and rating pattern. Based on this model, the user fuzzy similarity-based collaborative filtering recommendation algorithm is designed. We prove that this algorithm is a fuzzy extension of Cosine similarity, and analyze the application scopes of this method. The experimental results show that our method can obtain better performance than other traditional methods, especially when implemented in a sparse dataset with high ratio between users and items.

Rough Possibilistic Type-2 Fuzzy C-Means clustering for MR brain image segmentation

Pixel clustering in spectral domain is an important approach for the soft-tissue categorization of magnetic resonance (MR) brain images. In this regard, clustering algorithms based on type-1 fuzzy set theory are suitable for the overlapping partitions while the rough set based clustering algorithms deal with uncertainty and vagueness. However, additional degree of fuzziness makes the clustering more challenging for various subtle uncertainties and noisy data in the overlapping areas. Hence, this fact motivates us to propose a hybrid technique, called Rough Possibilistic Type-2 Fuzzy C-Means clustering with the integration of Random Forest. In the proposed method, possibilistic approach handles the noisy data better, whereas the other various uncertainties and inherent vagueness are taken care by type-2 fuzzy set and rough set theories. After clustering, it produces rough and crisp points. Thereafter, such crisp points are used to train the Random Forest classifier in order to classify the rough points for yielding better clustering solution. The performance of the proposed method has been demonstrated in comparison with several other recently proposed methods for MR brain image segmentation. Finally, superiority of the results produced by the proposed hybrid method has also been validated through statistical significance test.

Local iterative DLT soft-computing vs. interval-valued stereo calibration and triangulation with uncertainty bounding in 3D reconstruction

The use of stereo vision for 3D data gathering is affected by constraints in the position of the cameras, the quality of the optical elements and the numerical algorithms for calibration and matching. Also, there is not a wide agreement on the best procedure for bounding the 3D errors within an uncertainty volume. In this work, this problem is solved by implementing the whole set of computations, including calibration and triangulation, with interval data. This is in contrast with previous works that rely on Direct Linear Transform (DLT) as a camera model. To keep better with real lens aberrations, a local iterative modification is proposed that provides an on-demand set of calibration parameters for each 3D point, comprising those nearest in 3D space. In this way, the estimated camera parameters are closely related with camera aberrations at the lens area through which that 3D point is imaged. To further reduce the triangulation uncertainty volume, a Soft Computing approach is proposed that represents each 3D point uncertainty as a cloud of crisp points compatible with interval-valued calibration data.Real data from previous works in related research areas is used to judge whether the new approach improves the precision and accuracy of other crisp and interval-valued estimations without degrading precision, and it is concluded that the new technique is able to significantly improve the uncertainty volumes.

An analytical solution to fuzzy TOPSIS and its application in personnel selection for knowledge-intensive enterprise

Personnel selection is a critical enterprise strategic problem in knowledge-intensive enterprise. Fuzzy number which can be described as triangular (trapezoid) fuzzy number is an adequate way to assess the evaluation and weights for the alternatives. In that case, fuzzy TOPSIS, as a classic fuzzy multiple criteria decision making (MCDM) methods, has been applied in personnel selection problems. Currently, all the researches on this topic either apply crisp relative closeness but causing information loss, or employ fuzzy relative closeness estimate but with complicated computation to rank the alternatives. In this paper, based on Karnik–Mendel (KM) algorithm, we propose an analytical solution to fuzzy TOPSIS method. Some properties are discussed, and the computation procedure for the proposed analytical solution is given as well. Compared with the existing TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative closeness instead of the crisp point or approximate fuzzy relative closeness estimate. It can both avoid information loss and keep computational efficiency in some extent. Moreover, the global picture of fuzzy relative closeness provides a way to further discuss the inner properties of fuzzy TOPSIS method. Detailed comparisons with approximate fuzzy relative closeness method are provided in personnel selection application.

New Neutrosophic Crisp Topological Concepts

In this paper, we introduce the concept of crisp neighborhoods system for the neutrosophic crisp point . Added to, we introduce and study the concept of neutrosophic crisp local function, and construct a new type of neutrosophic crisp topological space via neutrosophic crisp ideals. Possible application to GIS topology rules are touched upon.

English

In this paper, I have studied some properties of fuzzy soft topological space. We define fuzzy soft intuitionistic separation axioms and basic definition of intuitionistic fuzzy soft normal spaces and theorems. Lastly, introduced intuitionistic fuzzy soft completely normal spaces. There are many problems encountered in real life. Various mathematical set theories such as soft set initiated by Molodtsov(2) in 1999 for modeling uncertainty present in real life. Xio(13) and Pie and Mio (3) discussed the relationship between soft sets is a parameterized classification of the objects of the universe. Atanassov (7) introduced the fundamental concept of intuitionistic fuzzy topological spaces, fuzzy continuity , fuzzy compactness and some other related concepts. Mahanta and Das(6) established the neighbourhood structures in fuzzifying topological spaces. Some others (1),(4),(8),(10).studied some separation axioms and their separation axioms are discussed on crisp points not on fuzzy points. My main aim in this paper is to develop the basic properties of intuitionistic fuzzy soft separation axioms and established several equivalent forms of fuzzy soft spaces.

Neutrosophic Crisp Points & Neutrosophic Crisp Ideals

The purpose of this paper is to define the so called neutrosophic crisp points and neutrosophic crisp ideals, and obtain their fundamental properties. Possible application to GIS topology rules are touched upon.

N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS

Abstract. CharacterizationsofN-subalgebraoftype(∈,∈∨q)arepro-vided. ThenotionofN-subalgebrasoftype(∈,∈∨q)isintroduced,andits characterizations are discussed. Conditions for an N-subalgebra oftype(∈,∈∨q)(resp. (∈,∈∨q))tobeanN-subalgebraoftype(∈,∈)areconsidered. 1. IntroductionA (crisp) set A in a universe X can be defined in the form of its character-istic function µ A : X → {0,1} yielding the value 1 for elements belonging tothe set A and the value 0 for elements excluded from the set A. So far mostof the generalization of the crisp set have been conducted on the unit inter-val [0,1] and they are consistent with the asymmetry observation. In otherwords, the generalization of the crisp set to fuzzy sets relied on spreading pos-itive information that fit the crisp point {1} into the interval [0,1]. Because nonegative meaning of information is suggested, we now feel a need to deal withnegative information. To do so, we also feel a need to supply mathematicaltool. To attain such object, Jun et al. [5] introduced a new function whichis called negative-valued function, and constructed N-structures. They ap-plied N-structures to BCK/BCI-algebras, and discussed N-subalgebras andN-ideals in BCK/BCI-algebras. Jun et al. [6] considered closed ideals inBCH-algebras based on N-structures. Also, using N-structures, Jun and Leeintroduced the notion of an N-essence in a subtraction algebra, and inves-tigated related properties. They discussed relations among an N-ideal, anN-subalgebra and an N-essence (see [4]). To obtain more general form of anN-subalgebra in BCK/BCI-algebras, Jun et al. defined the notions of N-subalgebras of types (∈,∈), (∈, q), (∈,∈ ∨q), (q,∈), (q, q) and (q,∈ ∨q),and investigated related properties. They provided a characterization of an N-subalgebra of type (∈,∈∨q). They also gave conditions for an N-structure to

Experimental Study on the Formula of Recycled Rubber Power Modified Asphalt

Recycled rubber powder modified asphalt is the trend of road asphalt, and rubber power is low cost, high performance modifier. In this experiment, by analyzing the equivalent softening point and equivalent crisp point, uses orthogonal experiment to obtain the formula that made the pavement property of recycled tire rubber powder modified asphalt for optimal.

Self-calibration for a 3D laser

In this paper we describe a method for the automatic self-calibration of a 3D laser sensor. We wish to acquire crisp point clouds and so we adopt a measure of crispness to capture point cloud quality. We then pose the calibration problem as the task of maximizing point cloud quality. Concretely, we use Rényi Quadratic Entropy to measure the degree of organization of a point cloud. By expressing this quantity as a function of key unknown system parameters, we are able to deduce a full calibration of the sensor via an online optimization. Beyond details on the sensor design itself, we fully describe the end-to-end intrinsic parameter calibration process and the estimation of the clock skews between the constituent microprocessors. We analyse performance using real and simulated data and demonstrate robust performance over 30 test sites.

Analysis of the Low Temperature Performance of Warm Mix Asphalt

This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text. The warm mix asphalt (WMA) refers to technologies that allow a significant reduction of mixing and compaction temperatures of asphalt mixes through lowering the viscosity of asphalt binders. In this paper, Shell90 # and SK70 # are two matrix asphalt with Sasobit® modifier to prepare for WMA's penetration and ductility, and calculate the equivalent crisp points, evaluate the low temperature performance at 5°C and 15°C, respectively. The results indicate that compared with the Shell90# without and with 5% Sasobit®, its penetration and ductility were reduced by 24.5%, 65.5% at 15°C. For SK70#, its penetration and ductility were reduced by 25.0%, 67.1%. WMA equivalent crisp points test with Shell90 # and SK70 #, compared with the matrix asphalt reduced by 10.03°C and 4.02°C, the addition of 3% Sasobit® to two matrix asphalt binders may also reduce ductility by 22.5% and 26.2%, respectively at 5°C.