A heuristic approach for deriving the priority vector in AHP

This paper proposes an approach for deriving the priority vector from an inconsistent pair-wise comparison matrix through the nearest consistent matrix and experts judgments, which enables balancing the consistency and experts judgments. The developed algorithm for achieving a nearest consistent matrix is based on a logarithmic transformation of the pair-wise comparison matrix, and follows an iterative feedback process that identifies an acceptable level of consistency while complying with experts preferences. Three numerical examples are examined to illustrate applications and advantages of the developed approach.     

Preparation and characterization of alumina-zirconia composite material with different acid ratios by the sol-gel method

Alumina-zirconia composite materials were produced with different acid ratios by the sol-gel method using aluminum isopropoxide and zirconium chloride. The composites were produced by changing acid/alkoxside ratio in alumina. The composite materials were calcinated at 600°C, 900°C and 1300°C. The effects of acid concentration and calcination temperature on the surface area and pore radius were determined from the nitrogen adsorption isotherm at 77 K. The density of the composites was also measured. The minimum density of produced material was recorded as 1.35 g cm⁻³ at an acid/alkoxside ratio of 0.2. The highest specific surface area and pore diameter of the lightest material are 191.86 m² g⁻¹ and 18.4 Ǻ, respectively. Although pore diameter and specific surface area are not changed at any of the experimental temperatures which were tested by decreasing acid/alkoxside ratio, the density is slightly increased. However, it was observed that the calcination temperature significantly affects the surface area and density of the material.      

Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.     

Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction

Cardinal and ordinal inconsistencies are important and popular research topics in the study of decision making with pair-wise comparison matrices (PCMs). Few of the currently-employed tactics are capable of simultaneously dealing with both cardinal and ordinal inconsistency issues in one model, and most are heavily dependent on the method chosen for weight (priorities) derivation or the obtained closest matrix by optimization method that may change many of the original values. In this paper, we propose a Hadamard product induced bias matrix model, which only requires the use of the data in the original matrix to identify and adjust the cardinally inconsistent element(s) in a PCM. Through graph theory and numerical examples, we show that the adapted Hadamard model is effective in identifying and eliminating the ordinal inconsistencies. Also, for the most inconsistent element identified in the matrix, we develop innovative methods to improve the consistency of a PCM. The proposed model is only dependent on the original matrix, is independent of the methods chosen to derive the priority vectors, and preserves most of the original information in matrix A since only the most inconsistent element(s) need(s) to be modified. Our method is much easier to implement than any of the existing models, and the values it recommends for replacement outperform those derived from the literature. It significantly enhances matrix consistency and improves the reliability of PCM decision making.     

Effective and Functional Surface Design for Biosensing Applications Based on a Novel Conducting Polymer and PMMA/Clay Nanocomposite

Surface functionalization plays a crucial role in the design of biosensors. For this purpose, a novel functional monomer, 6‐(4,7‐bis(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)‐2H‐benzo[d][1,2,3]triazol‐2‐yl)hexan‐1‐amine (BEDOA‐6), was designed and synthesized. Poly(BEDOA‐6) was utilized as an immobilization matrix for glucose oxidase biosensor construction. Moreover, polymethylmethacrylate (PMMA) layered silicate nanocomposites were prepared by in situ suspension polymerization. Conducting polymer surface was modified with PMMA/clay nanocomposite material and a glucose biosensor was developed. In addition, XPS and SEM were utilized to characterize the surface properties. The biosensor shows a wide linear range between 2.8 µM and 1.2 mM to glucose with a low detection limit of 1.99 µM. Finally, the biosensor was tested on serum samples containing actual human blood. The results were in well‐agreement with a reference method.     

A statistical approach to measure the consistency level of the pairwise comparison matrix

The consistency of the pairwise comparison matrix (PCM) has been extensively studied in the Analytic Hierarchy Process. Most of the existing approaches for the consistency test of the PCM are based on the consistency ratio threshold (0.1) introduced by Saaty (1977). To accurately measure the consistency level of the PCM, a statistical approach based on the significance level is proposed in this paper by combining the hypothesis test and the random consistency index. The proposed statistical approach is applied to an education evaluation problem in order to demonstrate the rationality and reliability of it.     

Questionnaire design improvement and missing item scores estimation for rapid and efficient decision making

In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that we consider the reneging of customers at polling instants. In more detail, whenever the server starts or ends a visit to a queue, some of the customers waiting in each queue leave the system before having received service. The probability that a certain customer leaves the queue, depends on the queue in which the customer is waiting, and on the location of the server. We show that this system can be analysed by introducing customer subtypes, depending on their arrival periods, and keeping track of the moment when they abandon the system. In order to determine waiting time distributions, we regard the system as a polling model with varying arrival rates, and apply a generalised version of the distributional form of Little??s law. The marginal queue length distribution can be found by conditioning on the state of the system (position of the server, and whether it is serving or switching).     

An improved statistical approach for consistency test in AHP

The pair-wise comparison matrix (PCM) is widely used in multi-criteria decision making methods. If the PCM is inconsistent, the resulting priority vector is not reliable. Hence, it is necessary to measure the level of the inconsistency of the PCM. There are two approaches for testing the consistency of the PCM: deterministic approaches and statistical or stochastic approaches. In this paper, an improved statistical approach to test the consistency of the PCM is proposed, which combines hypothesis test and maximum likelihood estimation. The proposed statistical approach is flexible and reliable because it sets a suitable significance level according to different situations. Two numerical examples are introduced to illustrate the proposed statistical approach.     

A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP

Tests of consistency for the pair-wise comparison matrices have been studied extensively since AHP was introduced by Saaty in 1970s. However, existing methods are either too complicated to be applied in the revising process of the inconsistent comparison matrix or are difficult to preserve most of the original comparison information due to the use of a new pair-wise comparison matrix. Those methods might work for AHP but not for ANP as the comparison matrix of ANP needs to be strictly consistent. To improve the consistency ratio, this paper proposes a simple method, which combines the theorem of matrix multiplication, vectors dot product, and the definition of consistent pair-wise comparison matrix, to identify the inconsistent elements. The correctness of the proposed method is proved mathematically. The experimental studies have also shown that the proposed method is accurate and efficient in decision maker’s revising process to satisfy the consistency requirements of AHP/ANP.