Wojciech Sałabun

Decision Making with Uncertainty Using Hesitant Fuzzy Sets

Actual existing multi-criteria decision-making (MCDM) methods yield results that may be questionable and unreliable. These methods very often ignore the issue of uncertainty and rank reversal paradox, which are fundamental and important challenges of MCDM methods. In response to these challenges, the Characteristic Objects Method (COMET) was developed. Despite it being immune to the rank reversal paradox, classical COMET is not designed for uncertain, decisional problems. In this paper, we propose to extend COMET using hesitant fuzzy set (HFS) theory. Hesitant fuzzy set theory is a powerful tool to express the uncertainty that derives from an expert comparing characteristic objects and identifying membership functions for each criterion domain. We present the theoretical foundations and principles of COMET, and we provide an illustrative example to show how COMET handles uncertain decision problems both practically and effectively.

Group Decision-Making for Hesitant Fuzzy Sets Based on Characteristic Objects Method

There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision process. In such situations, we can observe an increasing importance of uncertainty. In this paper, the Multi-Criteria Decision-Making (MCDM) method called the Characteristic Objects Method (COMET) is extended to solve problems for Multi-Criteria Group Decision-Making (MCGDM) in a hesitant fuzzy environment. It is a completely new idea for solving problems of group decision-making under uncertainty. In this approach, we use L-R-type Generalized Fuzzy Numbers (GFNs) to get the degree of hesitancy for an alternative under a certain criterion. Therefore, the classical COMET method was adapted to work with GFNs in group decision-making problems. The proposed extension is presented in detail, along with the necessary background information. Finally, an illustrative numerical example is provided to elaborate the proposed method with respect to the support of a decision process. The presented extension of the COMET method, as opposed to others’ group decision-making methods, is completely free of the rank reversal phenomenon, which is identified as one of the most important MCDM challenges.

Comparative Analysis of MCDM Methods for Assessing the Severity of Chronic Liver Disease

The paper presents the Characteristic Objects method as a potential multi-criteria decision-making method for use in medical issues. The proposed approach is compared with TOPSIS and AHP. For this purpose, assessment of the severity of Chronic Liver Disease (CLD) is used. The simulation experiment is presented on the basis of the Model For End-Stage Liver Disease (MELD). The United Network for Organ Sharing (UNOS) and Eurotransplant use MELD for prioritizing allocation of liver transplants. MELD is calculated from creatinine, bilirubin and international normalized ratio of the prothrombin time (INR). The correctness of the selection is examined among randomly selected one million pairs of patients. The result is expressed as a percentage of agreement between the assessed method and MELD selection. The Characteristic Objects method is completely free of the rank reversal phenomenon, obtained by using the set of characteristic objects. In this approach, the assessment of each alternative is obtained on the basis of the distance from characteristic objects and their values. As a result, correctness of the selection obtained by using the Characteristic Objects method is higher than those obtained by TOPSIS or AHP techniques.

Identification of a multicriteria decision-making model using the characteristic objects method

This paper presents a new, nonlinear, multicriteria, decision-making method: the characteristic objects (COMET). This approach, which can be characterized as a fuzzy reference model, determines a measurement standard for decision-making problems.This model is distinguished by a constant set of specially chosen characteristic objects that are independent of the alternatives. After identifying a multicriteria model, this method can be used to compare any number of decisional objects (alternatives) and select the best one. In the COMET, in contrast to other methods, the rank-reversal phenomenon is not observed. Rank-reversal is a paradoxical feature in the decision-making methods, which is caused by determining the absolute evaluations of considered alternatives on the basis of the alternatives themselves. In the Analytic Hierarchy Process (AHP) method and similar methods, when a new alternative is added to the original alternative set, the evaluation base and the resulting evaluations of all objects change. A great advantage of the COMET is its ability to identify not only linear but also nonlinear multicriteria models of decision makers. This identification is based not on a ranking of component criteria of the multicriterion but on a ranking of a larger set of characteristic objects (characteristic alternatives) that are independent of the small set of alternatives analyzed in a given problem. As a result, the COMET is free of the faults of other methods.

Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome

Multi-criteria decision-making (MCDM) methods are commonly used in many fields of research, e.g., engineering and manufacturing systems, water resources studies , medicine, and etc. However, there is no effective approach of selecting a MCDM method to problem, which is solved. The formal requirements of each MCDM method are not sufficient because most methods would seem to be appropriate for most problems. Therefore, the main purpose of the paper is a comparison of accuracy selected MCDM methods. Proposed approach is presented on the example of mortality in patients with acute coronary syndrome. Additionally, the paper presents characteristic objects method (COMET) as a potential decision making method for use in medical problems, which accuracy is compared with TOPSIS and AHP. In the experimental study, the average and standard deviation of the root mean square error of evaluations are examined for groups of randomly selected patients, each described by age, blood pressure, and heart rate. Then, the correctness of choosing the patient in the best and worst condition is also examined among randomly selected pairs. As a result of the experimental study, rankings obtained by the COMET method are distinctly more accurate than those obtained by TOPSIS or AHP techniques. The COMET method, in the opposite of others method, is completely free of the rank reversal phenomenon, which is identified as a main source of problems with evaluations accuracy.

The Characteristic Objects Method: A New Intelligent Decision Support Tool for Sustainable Manufacturing

This paper presents a new multi-criteria decision-making method, which is called the Characteristic Objects method, in the field of sustainable manufacturing. This approach is an alternative for AHP, TOPSIS, ELECTRE or PROMETHEE methods. The paper presents the possibility of using the COMET method for sustainable manufacturing. For this purpose, a brief review of the literature is shown. Then the COMET method is presented in detail. At the end of the paper, a simple problem is solved by using the COMET method.

Green Supplier Selection Framework Based on Multi-Criteria Decision-Analysis Approach

The aim of this article is to present the framework for dynamic suppliers’ evaluation and selection. The proposed framework defines input information together with a methodological background required for decision support processes. Authors suggest using the multi-criteria decision-analysis (MCDA) methodology to propose a dynamic approach. Therefore, the fuzzy TOPSIS method has been selected as a method that provides the ability to aggregate numerical and linguistic data, which are obtained from various inputs. After discussions on a framework outline, an empirical study is given. The presented problem concerns the selection of a supplier for the company producing cable bundles. Finally, a ranking for 25 vendors (for 12 periods) is obtained as a result, which facilitates the diversification of supplies for the discussed company.

Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games

The classical matrix theory is deficient to express the vagueness of the real life. The fuzzy set theory has been successfully applied to bridge this gap. Much work has already been done on a two-person zero sum matrix game with fuzzy goals. In continuation, this paper is dedicated to define and study a multi-criteria two-person zero sum game with intuitionistic fuzzy goals. It is shown that solving such games is equivalent to solving two crisp multi object linear programming problems. Our work generalizes the previous study on a multi-criteria game with fuzzy goals by adopting the approach of linear programming with intuitionistic fuzzy sets. Finally, an illustrative numerical example is provided to elaborate the proposed approach.

Chaotic Dynamical State Variables Selection Procedure Based Image Encryption Scheme

Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led to rapid developments in cryptography, due to the imminent need for system security. Low-dimensional chaotic systems have low complexity and key space, yet they achieve high encryption speed. An image encryption scheme is proposed that, without compromising the security, uses reasonable resources. We introduced a chaotic dynamic state variables selection procedure (CDSVSP) to use all state variables of a hyper-chaotic four-dimensional dynamical system. As a result, less iterations of the dynamical system are required, and resources are saved, thus making the algorithm fast and suitable for practical use. The simulation results of security and other miscellaneous tests demonstrate that the suggested algorithm excels at robustness, security and high speed encryption.

Identification of a Multi-criteria Assessment Model of Relation Between Editorial and Commercial Content in Web Systems

Together with the increasing role of Internet in commercial activity growing intensity of marketing content is observed. Advertising clutter is interfering with web usability and is affecting processing of the editorial content by web users. Therefore, effective way to manage marketing content is needed. This problem can be solved by using a proper combination of multi-criteria decision-analysis methods. The presented research shows a unique approach to identify assessment model of tradeoffs between the editorial content and the intensity of marketing components. The fuzzy model is identified on the basis of the experiment with the use of eye tracker and a combination of PROMETHEE and COMET methods. As a result, we obtained the assessment model, which is a relation between a set of defined inputs and a set of permissible outputs with the property that each input is related to exactly one output (assessment). Therefore, this model can be used online to manage web systems with balance between editorial and commercial content.