New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis.

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.

Generalised framework for multi-criteria method selection: Rule set database and exemplary decision support system implementation blueprints.

This data article describes the analysis of 56 MCDA (Multi-Criteria Decision Analysis) methods in regards to 9 decision-making problem characteristics structured into 3 levels. The impact of uncertainty in decision-making problem description on MCDA method selection is studied. 450,000 possible descriptions of a decision problem were studied, resulting in sets of rules which can serve as input to uncertainty-aware MCDA method selection decision support systems. Comprehensive analyses of the obtained rule sets are provided. An exemplary decision support system based on the presented data was created and is available at http://www.mcda.it. Moreover the technical documentation needed to create and expand such system is provided in this data article. The data and system can be easily extended and the authors invite all researchers to contribute.

Multi-criteria decision support for planning and evaluation of performance of viral marketing campaigns in social networks.

The current marketing landscape, apart from conventional approaches, consists of campaigns designed especially for launching information diffusion processes within online networks. Associated research is focused on information propagation models, campaign initialization strategies and factors affecting campaign dynamics. In terms of algorithms and performance evaluation, the final coverage represented by the fraction of activated nodes within a target network is usually used. It is not necessarily consistent with the real marketing campaigns using various characteristics and parameters related to coverage, costs, behavioral patterns and time factors for overall evaluation. This paper presents assumptions for a decision support system for multi-criteria campaign planning and evaluation with inputs from agent-based simulations. The results, which are delivered from a simulation model based on synthetic networks in a form of decision scenarios, are verified within a real network. Last, but not least, the study proposes a multi-objective campaign evaluation framework with several campaign evaluation metrics integrated. The results showed that the recommendations generated with the use of synthetic networks applied to real networks delivered results according to the decision makers' expectation in terms of the used evaluation criteria. Apart from practical applications, the proposed multi-objective approach creates new evaluation possibilities for theoretical studies focused on information spreading processes within complex networks.