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The inconsistency of judgments in the fuzzy Analytic Hierarchy Process (AHP) is a crucial issue. To make the appropriate decision, the inconsistency in decision maker's (DM) judgments needs to be eliminated or reduced. This paper proposes two mathematical models to deal with inconsistency in fuzzy AHP. In the first model, the DM's judgments are modified where the preference order of the DM's judgments remained unchanged. The second model allows reversing the preference orders of judgments. The proposed models aim to eliminate or reduce the inconsistency of fuzzy AHP by changing judgments. The models cause fewer changes for the high certain judgments. Two examples solved by the proposed models are included for purposes of illustration.

Purpose The purpose of this paper is to investigate a fuzzy hybrid approach for ranking the flare gas recovery methods and allocating to refineries. Design/methodology/approach The proposed approach is containing four stages: in the first stage, experts' assessment is applied to identify relevant criteria and sub-criteria in the evaluation of flare gas recovery methods. In the second stage, the corresponding weights of criteria and sub-criteria are determined via fuzzy decision-making trial and evaluation (DEMATEL)-analytical network process (ANP) (DANP) method. In the third stage, the flare gas recovery methods are ranked using fuzzy weighted aggregated sum product assessment method (WASPAS) multi-criteria decision-making (MADM) technique. In the fourth stage, an optimization model is developed to allocate gas recovery methods to refineries while maximizing the total utility of allocations based on model constraints. Findings According to the results of fuzzy DANP method, technical and operational criterion was the most important followed by economic, political, managerial and environmental criteria. With respect to sub-criteria, international sanctions and political stability were the most important. The results of fuzzy WASPAS method indicated that gas injection was the first ranked alternative. Finally, the mathematical modeling allocated the recovery methods to five refineries of South Pars gas field in Iran based on budget and time constraints. Originality/value The proposed approach provides a systematic tool in the selection of flare recovery methods and allocation to refineries. This approach uses a new combination of fuzzy DEMATEL-ANP (DANP) method, fuzzy WASPAS method and mathematical programming. The approach is effectively implemented in a case study for ranking the flare gas recovery methods and allocating to refineries of South Pars gas field in Iran.

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Mann-Whitney and Signed-Rank control charts are two well-known nonparametric charts used for controlling the center of the process when the distribution of the process parameter is unknown or nonnormal. Considering the effect of measurement error on the performance of control charts, the mentioned effect with additive model is investigated on Mann-Whitney and Signed-Rank charts. Furthermore, a comparison is made between the two charts and a Shewhart-typē X chart (as a parametric one) in the presence of the error. To do so, a simulation program is used and average run length (ARL) of the charts are calculated under three distributions. The results for all three distributions show that the existence of measurement error weakens the performances of both nonparametric charts and larger values of the variance of the error will increase the effect. A numerical example is also discussed to show the effect on the performance of the charts. Multiple measurements is used as a way to decrease the effect of measurement error. Knowing the fact that it requires extra time and money, it can be used in real cases depending on the financial limitations of the user.