An evaluation of household tissue softness

This study extends our 2019 paper, a study of the softness of household tissues using a tissue soft-ness analyzer (TSA) and hand-felt panels. It revisits the softness theory of Holger Hollmark by applying a reciprocal matrix approach to measure sheet bulk softness and surface softness, and then make comparisons with the results obtained using a TSA instrument. We ascertained that there was a high correlation of R=0.904 between panel-corrected hand-felt (CHF) softness and TSA softness (TSA-HF); and a low correlation of R=-0.678 between panel-corrected hand-felt surface softness (CHSS) and TSA smoothness (TS-750). Three hunches about TSA measurements were confirmed: 1) Hollmark’s theory was confirmed by a high correlation coefficient (R=0.895) between CHF and CHSS softness, indicating that the two parameters are mutually dependent; 2) TS-750 differs from CHSS and has partial influence on TSA-HF results with a correlation of R = -0.510; and 3) although TS-750 has only limited influences on TSA-HF, further opportunities for their application can be provided using pertinent regression equations.

A study of the softness of household tissues using a tissue softness analyzer and hand-felt panels

This study applied the reciprocal matrix approach to deduce the correlation between hand-felt (HF) and tissue softness analyzer (TSA) instrumental measurements of tissue softness. The research was conducted in three phases, which are discussed separately. In the phase one study, results indicated that systematic collection of samples and preparation of test specimens were the foundation of successful tests. TSA-HF and tensile strength exhibited a strong negative correlation. In the future, same-unit physical properties can provide a basis for discussing the commonality and complementary natures of hand-felt and TSA softness measurements. In phase two, through the reciprocal matrix approach, subjective softness assessments performed by humans were reliably quantified. The quantified values were further applied to a statistical analysis using the t-test to distinguish and train professional panelists. In phase three of HF panel test results, all independent panels were compared to one another under a uniform scale established by four standard samples. The calibrated HF panel values were incorporated with TSA-HF results to establish technical curves between the softness and tensile strength, which were helpful for onsite workers to carry out process controls.

Generating a Cancellable Fingerprint using Matrices Operations and Its Fingerprint Processing Requirements

Cancellable fingerprint uses transformed or intentionally distorted biometric data instead of the original biometric data for identifying person. When a set of biometric data is found to be compromised, they can be discarded, and a new set of biometric data can be regenerated. This initial principal is identical with a non-invertible concept in matrices operations. In matrix domain, a matrix cannot be transformed into its original form if it meets several requirements such as non-square form matrix, consist of one zero row/column, and no row as multiple of another row. These conditions can be acquired by implementing three matrix operations using Kronecker Product (KP) operation, Elementary Row Operation (ERO), and Inverse Matrix (INV) operation. KP is useful to produce a non-square form matrix, to enlarge the size of matrix, to distinguish and disguise the element of matrix by multiplying each of elements of the matrix with a particular matrix. ERO can be defined as multiplication and addition force to matrix rows. INV is utilized to transform one matrix to another one with a different element or form as a reciprocal matrix of the original. These three matrix operations should be implemented together in generating the cancellable feature to robust image. So, if once three conditions are met by imposter, it is impossible to find the original image of the fingerprint. The initial aim of these operations is to camouflage the original look of the fingerprint feature into an abstract-look to deceive an un-authorized personal using the fingerprint irresponsibly. In this research, several fingerprint processing steps such as fingerprint pre-processing, core-point identification, region of interest, minutiae extration, etc; are determined to improve the quality of the cancellable feature. Three different databases i.e. FVC2002, FVC2004, and BRC are utilized in this work.

Characterization of Consistent Completion of Reciprocal Comparison Matrices

Analytic hierarchy process (AHP) is a leading multi-attribute decision-aiding model that is designed to help make better choices when faced with complex decisions involving several dimensions. AHP, which enables qualitative analysis using a combination of subjective and objective information, is a multiple criteria decision analysis approach that uses hierarchical structured pairwise comparisons. One of the drawbacks of AHP is that a pairwise comparison cannot be completed by an actor or stakeholder not fully familiar with all the aspects of the problem. The authors have developed a completion based on a process of linearization that minimizes the matrix distance defined in terms of the Frobenius norm (a strictly convex minimization problem). In this paper, we characterize when an incomplete, positive, and reciprocal matrix can be completed to become a consistent matrix. We show that this characterization reduces the problem to the solution of a linear system of equations—a straightforward procedure. Various properties of such a completion are also developed using graph theory, including explicit calculation formulas. In real decision-making processes, facilitators conducting the study could use these characterizations to accept an incomplete comparison body given by an actor or to encourage the actor to further develop the comparison for the sake of consistency.

IMPROVED AHP-GROUP DECISION MAKING FOR INVESTMENT STRATEGY SELECTION

Investment strategy selection relies heavily on personal experience and behavior. This paper proposes an improved Analytical Hierarchy Process-group decision making (IAHP-GDM) model to reduce investment risk. This model applies the method of least squares to adjust group decision matrix in order to satisfy the property of positive reciprocal matrix in AHP. In addition, five experts from related fields are invited to evaluate investment risk that takes group wisdom to eliminate personal bias. An empirical study is conducted to compare the proposed model to AHP for group decision making model. The results show that the IAHP-GDM model is not only accurate and effective, but also consistent with realistic investment environment.

A reciprocal matrix approach to the analysis of hand-felt softness of facial tissues

Previous studies of household tissue softness based on the hand-felt approach used n2 or n-1 paired comparisons and ranking methods to distinguish the order of the samples. However, subjective perceptions and objective sample deviations could not easily be excluded. As an alternative, we used a reciprocal matrix analysis, a paired-comparison method to the n(n-1)/2 power, and found it capable of compensating for the biases of testers and samples and generating a more reasonable and robust ranking. We also were able to effectively quantify hand-felt softness of the samples by calculation of weighting eigenvectors. The proposed pretest training materials and method effectively enhanced the perceptive abilities of the examiners. The experience gained in the process can be used to strengthen standard test procedures and establish professional panels to evaluate hand-felt softness.

A MATRIX METHOD FOR THE FUZZY ANALYTIC HIERARCHY PROCESS

This paper proposes a new method for finding fuzzy weights in the fuzzy analytic hierarchy process (FAHP), which fuzzifies the derived formulation of an eigenvector directly. The presented formulation only needs information about the upper triangular matrix and the assumption of the reciprocal matrix in the original AHP is not necessary. This characteristic enables the FAHP to be used without concern for rationality of the reciprocal matrix. In addition, two applications are presented to demonstrate the applicability of the proposed method and to compare it with other FAHP models.