The arithmetic of discrete Z-numbers

Best Worst Method (BWM) has recently been proposed as a method for Multi Criteria Decision Making (MCDM). Studies show that BWM compared with other methods such as Analytic Hierarchy Process (AHP), leads to lower inconsistency of the results while reducing the number of required pairwise comparisons. MCDM methods such as BWM require accurate information. However, it often happens in practice that a level of uncertainty accompanies the information. The main aim of this paper is to address this problem and provide an integration of BWM and Z-numbers, namely ZBWM. Providing BWM with Z-numbers enables the BWM method to handle the uncertainty of information of a multi-criteria decision. Additionally, the capabilities of the proposed method in the process of utilizing the linguistic information dealing with big data are highlighted. The proposed method is examined to address a supplier development problem. By experimental results, we show that ZBWM results lower inconsistency when compared with BWM. A Z-number contains subjectivity in its fuzzy part, which can be addressed in future applications of ZBWM.

https://openresearch-repository.anu.edu.au/bitstream/1885/212341/1/ZBWM_AAM.pdf

ZBWM: The Z-number extension of Best Worst Method and its application for supplier development

Forecasting natural gas consumption

Day-ahead natural gas demand forecasting based on the combination of wavelet transform and ANFIS/genetic algorithm/neural network model

Z-numbers are a new concept considering both the description of cognitive information and the reliability of information. Linguistic terms are useful tools to adequately and effectively model real-life cognitive information, as well as to characterize the randomness of events. However, a form of Z-numbers, in which their two components are in the form of linguistic terms, is rarely studied, although it is common in decision-making problems. In terms of Z-numbers and linguistic term sets, we provided the definition of linguistic Z-numbers as a form of Z-numbers or a subclass of Z-numbers. Then, we defined some operations of linguistic Z-numbers and proposed a comparison method based on the score and accuracy functions of linguistic Z-numbers. We also presented the distance measure of linguistic Z-numbers. Next, we developed an extended TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method based on the Choquet integral for multi-criteria decision-making (MCDM) problems with linguistic Z-numbers. Finally, we provided an example concerning the selection of medical inquiry applications to demonstrate the feasibility of our proposed approach. We then verified the applicability and superiority of our approach through comparative analyses with other existing methods. Illustrative and comparative analyses indicated that the proposed approach was valid and feasible for different decision-makers and cognitive environments. Furthermore, the final ranking results of the proposed approach were closer to real decision-making processes. Linguistic Z-numbers can flexibly characterize real cognitive information as well as describe the reliability of information. This method not only is a more comprehensive reflection of the decision-makers’ cognition but also is more in line with expression habits. The proposed method inherited the merits of the classical TODIM method and considers the interactivity of criteria; therefore, the proposed method was effective for dealing with real-life MCDM problems. Consideration about bounded rational and the interactivity of criteria made final outcomes convincing and consistent with real decision-making.

Multi-Criteria Decision-Making Method Based on Distance Measure and Choquet Integral for Linguistic Z-Numbers

Analytical Hierarchy Process (AHP) under uncertain environment is still an open issue. The objective of this study is to propose a new AHP method based on Z-number. First, Z-number are taken into consideration. Zadeh [1] proposed a notion, namely Z-number, which is an order pair of fuzzy numbers (A, B). The first component, A, plays the role of a fuzzy restriction and the second component B is a reliability of the first component. It is new concept which has more power to describe the knowledge of human being and will be widely used in the uncertain information process [2, 3]. Second, a new AHP method based on Z-number is proposed to deal with linguistic decision making problems. Finally, by Z-number analytical hierarchy process (Z-number-AHP) a model is developed to search the criteria's for the evaluation of best universities.

Z-AHP: A Z-number extension of fuzzy analytical hierarchy process

Resilience engineering (RE) is a new approach to measuring and maintaining safety in complex systems. The focus of RE is not on errors rather than on understanding and supporting normal work and what goes right. Using analytical hierarchy process (AHP), the present study aims to devise a validated method for improved assessment of RE in maintenance organizations. A standardized questionnaire containing RE and Performance Shaping Factors (PSFs) for generic maintenance operators is designed to collect data from employees in 11 regional maintenance departments of a large public gas company. Holding regular discussion sessions with experts in the field, the AHP is then built up based on the consensus emerged from the discussions. To form the middle-level criteria of the analytical hierarchy, RE items are clustered into 6 new categories using a verified k-means clustering. Given the large number of RE items in some categories, a complete sensitivity analysis is then performed by data envelopment analysis (DEA) to identify the most important items as the final level criteria. The designed AHP is used to assess RE in the 11 regional maintenance departments. For verification and validation of the proposed AHP, the linear relationship between AHP-based RE assessment and PSFs assessment is tested for its significance. The results confirm the close relationship between RE and PSFs.

A consensus-based AHP for improved assessment of resilience engineering in maintenance organizations

This paper presents an adaptive-network-based fuzzy inference system (ANFIS)-fuzzy data envelopment analysis (FDEA)) for long-term natural gas (NG) consumption forecasting and analysis. Six models are proposed to forecast annual NG demand. 104 ANFIS have been constructed and tested in order to find the best ANFIS for natural gas (NG) consumption. Two parameters have been considered in construction and examination of plausible ANFIS models. Six different membership functions and several linguistic variables are considered in building ANFIS. The proposed models consist of two input variables, namely, Gross Domestic Product (GDP) and Population. All trained ANFIS are then compared with respect to mean absolute percentage error (MAPE). To meet the best performance of the intelligent based approaches, data are pre-processed (scaled) and finally our outputs are post-processed (returned to its original scale). FDEA is used to examine the behavior of gas consumption. To show the applicability and superiority of the ANFIS-FDEA approach, actual gas consumption in six Southern America countries from 1980 to 2007 is considered. The gas consumption is then forecasted up to 2015. The ANFIS-FDEA approach is capable of dealing both complexity and uncertainty as well several other unique features discussed in this paper.

An adaptive network based fuzzy inference system-fuzzy data envelopment analysis for gas consumption forecasting and analysis: The case of South America

Fault detection and diagnosis has an effective role for the safe operation and long life of systems. Condition monitoring is an appropriate way of the maintenance techniques which is applicable in the fault diagnosis of rotating machinery faults. We considered the Support Vector Machine (SVM) method for classifying the condition of centrifugal pump into two types of faults through six features: flow, temperature, suction pressure, discharge pressure, velocity, and vibration. The SVM method is based on statistical learning theory (SLT) and powerful for the problem with small sampling, nonlinear and high dimension. (L.V. Ganyun et al 2005). The SVM classifying is implemented with 4 kernel functions and the results of them are compared. We use an Artificial Neural Network (ANN) as the second classifying method to have comparison among the performance of two methods. After applying the two methods to our data set we make the data set noisy and again we try our SVMs and ANN to compare their robustness in noisy conditions and the results obtained from two methods confirmed the superiority of SVM with some specific kernel functions.

Comparing performance and robustness of SVM and ANN for fault diagnosis in a centrifugal pump

A knowledge management (KM) system has a different schema that one of them has been studied in the present study. One of version of KM is based on artificial intelligence (AI) methods. KM based on AI has been investigated in the present work based on natural gas consumption estimation domain. Developing accurate and flexible model to natural gas consumption estimation is a strategic step in policy and decision-making process in energy sector. This paper provides a stage algorithm during that it gains optimal fuzzy regression model for studding natural gas consumption in sixteen countries according to data in years 1989 till 2007. Different countries have selected from Africa, America, Asia, Europe and Middle East based on high, middle and low GDP index and for every one of them nine fuzzy regression models have executed and the results and error of each model have calculated. Preprocess has been done on the initial data to gain better results which the min-max method has been used for this purpose. Two criterions have been used to determining suitable and appropriate fuzzy regression model in each country. Firstly, fuzzy regression models with MAPE value below 10 is deleted from the assessment and remained fuzzy regression models are compared with ANOVA. Upon logic that given algorithm sketches for some countries none of used models are proper while for other countries optimal model is gained in first or second filter of algorithm. To show the applicability and superiority of the proposed flexible Fuzzy regression model the data for oil consumption in Japan, Thailand, Bangladesh from Asia and Norway, Italy, Bulgaria from Europe and Qatar, Iran, Iraq from Middle East and The united state, Mexico, Bolivia from North America and Libya, Tunisia, Nigeria from Africa during 1989 to 2007 are used.

A knowledge management system based on artificial intelligence (AI) methods: A flexible fuzzy regression-analysis of variance algorithm for natural gas consumption estimation

A. Azadeh

Papers

Z-AHP: A Z-number extension of fuzzy analytical hierarchy process

A consensus-based AHP for improved assessment of resilience engineering in maintenance organizations

An adaptive network based fuzzy inference system-fuzzy data envelopment analysis for gas consumption forecasting and analysis: The case of South America

Comparing performance and robustness of SVM and ANN for fault diagnosis in a centrifugal pump

A knowledge management system based on artificial intelligence (AI) methods: A flexible fuzzy regression-analysis of variance algorithm for natural gas consumption estimation