The Analytic Hierarchy Process (AHP) which was developed by Saaty is a decision analysis tool. It has been applied to many different decision fields. Acquiring Pairwise Comparison Matrices (PCM) is the main step in AHP and also is frequently used in other multi-criteria decision-making methods. In a real problem when the number of alternatives/criteria to be compared is increased, the number of Pairwise Comparisons (PC) often becomes overwhelming. Since the Decision Maker’s (DM) performance in representing the relative preferences tends to deteriorate in such cases, it is preferred to gather fewer data from each individual DM in the form of pairwise comparisons. Missing values in Pairwise Comparison Matrices (PCM) in AHP is a spreading problem in areas dealing with great or dynamic data. The aim of this paper is to present an efficient mathematical programming model for estimating preference vector of pairwise comparison matrices with missing entries.

The Analytic Hierarchical Process (AHP) determines the relative importance of a set of alternatives in a multi-criteria decision problem. AHP has a hierarchial structure and based on pairwise comparisons of the project alternatives as well as pairwise comparisons of the multi criteria. Two separate algorithms have been presented for measuring the inconsistency ratioes of pairwise comparisons matrix and hierarchical structure. In this paper these algorithms and one of the approximation methods, have been extended for measuring the inconsistency ratioes and alternatives’ weights in fuzzy AHP. A numerical example is used to illustrate these methods.

The Analytic Hierarchy Process (AHP) is one of the most widely used techniques to determine the priority weights of alternatives from pairwise comparison matrices. Several fuzzy and intuitionistic fuzzy extensions of AHP have been proposed in the literature. However, these extensions are not appropriate to present some real-life situations. For this reason, several researchers extend the AHP to the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP). In the existing methods, an interval-valued Pythagorean fuzzy pairwise comparison matrix is transformed into a crisp matrix. Then crisp AHP is applied to obtain the normalized priority weights from the transformed crisp matrix. However, it is observed that the transformed crisp matrix, obtained on applying the step of existing methods, violates the reciprocal propriety of pairwise comparison matrices, and the obtained normalized priority weights are the weights of non-pairwise comparison matrices. Therefore, this paper discusses the shortcomings of the existing method, and a modified method is proposed to overcome these shortcomings. Finally, based on a real-life decision-making problem, the superiority of the proposed method over the existing method is shown.

Deriving weights from a pairwise comparison matrix (PCM) is a subject for which a wide range of methods have been presented. This paper proposes a common weight multi criteria decision analysis-data envelopment analysis (MCDA-DEA) approach with assurance region for weight derivation from a PCM. The proposed method has a more discrimination power over the conventional methods for weight derivation from a pairwise comparison matrix. Furthermore, the proposed model has several merits over the competing approaches and lacks the drawbacks of the well-known Data Envelopment Analysis HP and data envelopment analysis / assurance region methods (DEA/AR) methods. Some numerical examples and a case study are taken from the literature in order to confirm the merits of the proposed method and its applications in multi criteria decision making. Results disclose the advantages of the proposed approach.

The aim of this study is to propose a new method for portfolio optimization based on financial ratios. In this method, cross efficiency scores are produced from financial ratios, using Data Envelopment Analysis. Mathematical interpretation of these cross efficiency scores that allocates several score to each company is efficiency of company in probably future situations. Efficiency scores calculated based on proper financial ratios can be considered as financial strength. Thus cross efficiency scores produced from financial ratios, can be considered as potential financial strength. As future is not clear, potential financial strength can be presented in expectation and risk indices that are mean and variance of cross efficiencies. Fraction of expectation to risk for potential financial strengths can be used as a criterion for pairwise comparison of companies. Eigenvector associated with the biggest eigenvalue of pairwise comparison matrix reflects relative importance weights of companies. This paper proposes relative importance weights of companies as a basis for portfolio optimization. Based on sharp index Performance of proposed method is acceptable and better than marker portfolio and portfolio of one similar method.

As ranking is one of the most important issues in data envelopment analysis (DEA), many researchers have comprehensive studies on the subject and presented different approaches. In some papers, DEA and Analytic hierarchy process (AHP) are integrated to rank the alternatives. AHP utilizes pairwise comparisons between criteria and units, assessed subjectively by the decision maker, to rank the units. In this paper, a nonlinear programming (NLP) model is introduced to derive the true weights for pairwise comparison matrices in AHP. Genetic algorithm (GA) is used in order to solve this model. We use MATLAB software to solve proposed model for ranking the alternatives in AHP. A numerical example is applied to illustrate the proposed model.

This study aimed at designing a model of empowerment for knowledge based small and medium-sized enterprises. We conducted this study, considering the shortages of previous studies on comprehensive empowerment model of SMEs. We used a mixed method to collect data. The statistic population in both qualitative and quantitative parts of the study included academicians and the experts from SME enterprises.  In qualitative part of the study, we conducted a semi-structured interviews and in quantitative part, pairwise comparison questionnaire was used to be filled by experts.  Data were collected in qualitative part of the study by a semi-structured interviews and in quantitative part; pairwise comparison questionnaire was used for expert survey. We used theme analysis in the qualitative part of the study and the DEMATEL method for quantitative part of the study. The findings of theme analysis showed that the knowledge-based SME empowerment model is consisted of five dimensions; individual, financial, entrepreneurial, marketing and technology empowerment. The quantitative findings indicated that the factors affecting SME empowerment are individual and financial empowerment and impressible factors are entrepreneurial, marketing, and technology empowerment.

Dam break in recent decades has caused extensive damage to infrastructure and economic activities.Recently, the finite volume method based on shallow water equations with the ability to model shock waves has been welcomed by many researchers due to the high resolution of this method in the modeling of various supercritical, subcritical, steady, unsteady, continuous and discontinuous flows.. The five widely used methods are HLL, HLLC, Osher, FVS and REF (Roe with Entropy Fixed). Important features of mentioned numerical methods include five factors of accuracy, simulation time, ease of implementation, applicability for different issues and stability. The Analytical Hierarchy Process (AHP) and  Fuzzy Analytical Hierarchy Process (FAHP) provide convenient approaches for solving complex Multi-Criteria Decision-Making (MCDM) problems in engineering.Each methods are evaluated in terms of the decision criteria based on the weight of each criterion and pairwise comparisons are used to determine the relative importance of each method in terms of each criterion. Pairwise comparisons are quantified by using a scale.The results show that the Osher method appear to be superior to the other types of approximate Riemann solvers. Then the HLLC and the FVS methods, with slight difference in weight, are ranked next.

Today, despite many benefits of cloud computing technology, including cost savings, agility, increased flexibility and scalability the issue of information security is the main obstacle to the tendency of organizations towards cloud computing. In addition to infrastructure issues and political factors in Iran, there are many security risks in cloud computing technology. Therefore, the purpose of this study is to extract and rank these security risks. In this regard, by studying the theoretical foundations related to the research topic, these factors are extracted and categorized according to the opinion of experts, and then by designing questionnaires of different pairwise comparisons, collecting comments and combining different weighting methods based on pairwise comparisons by Copeland aggregation method, security risks were ranked. In this ranking, data privacy risk was the first priority of cloud computing security risks.

The aim of this study is designing the integrated framework of strategic planning and policy making in upstream oil and gas drilling sector. In this regard variety of‌‌‌‌‌‌‌‌‌ robust strategies were designed using SWOT matrix and in order to weighting and prioritizeing decision options, all effective factors and parameters were extracted and explained using Delphi technique and pairwise comparison questionnaires. PROMETHEE and ANP decision-making techniques have been used to prioritize strategies. In order to screen and perform pairwise comparisons of indicators, 51 questionnaires obtained by snowball sampling method were used and the validity and reliability of the questionnaires were assessed.The results show that the strategy of maximizing the efficiency of drilling operations and human resources in the North Drilling Company is the most important among other strategies.