A novel dissimilarity measure on picture fuzzy sets and its application in multi-criteria decision making
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A novel dissimilarity measure on picture fuzzy sets and its application in multi-criteria decision making Truong Thi Thuy Duong1 • Nguyen Xuan Thao2,3
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract With the increase in complexity of real problems, more and more, the decision makers are involved remarkably in the decision-making processes. It is required more efficient technique or tool to give reliable outcomes. This paper proposes a new dissimilarity measure on picture fuzzy sets. A multi-criteria decision-making problem is utilized to apply this new measure to select the optimal alternative. Finally, an example uses the proposed measure to evaluate and select the optimal market segment. Keywords Picture fuzzy sets Dissimilarity measures MCDM Market segment
1 Introduction Multi-criteria decision making has been successfully applied in many social economic fields (a large number of papers have been listed, see, for example, Ananda and Herath 2009; Aruldosset al. 2013; Kahraman et al. 2015). The complexity of studied problems leads to the results less reliable when all aspect of problems are considered by the experts. Their opinions depend significantly on the transparency information, experience, knowledge. In some specific circumstances, the information is not really clear, the experts have a difficulty to give evaluation of objects or attributes by the real numbers, in these cases, they have to use the linguistic variables. In such situations, their judgments will fall into four components expressing positive, negative, neutral or refusal degree. For example, in marketing strategy, supposing the top managers took Communicated by A. Di Nola. & Truong Thi Thuy Duong [email protected] Nguyen Xuan Thao [email protected] 1
Banking Academy, Ha Noi, Vietnam
2
Institute of Research and Development, Duy Tan University, Danang 550000, Vietnam
3
The Faculty of Information Technology, Duy Tan University, Danang 550000, Vietnam
responsibility considering to expand a market segment. After considering the relevance of market segments under criteria, the firm resources and their potentiality, three managers agreed to perform it, two managers did not support this, while the other two ones gave abstained vote and the other two gave a refusal vote. The set is expressed by these aspects including agreement, disagreement and neutral to be called the picture fuzzy set (PFS), which was proposed by Cuong (2014). Though intuitionistic fuzzy set (Atanassov 1986) extended the fuzzy set (Zadel1965) when adding the non-membership function to remedy the limitation of fuzzy set (Ejegwaet al. 2014; Hatzimichailidis et al. 2012; Lindblad and Sladoje 2014; Maheshwari and Srivastava 2016; Montes et al. 2015; Muthukumar and Krishnan 2016); however, it can’t express the neutral degree which appears in many real life such as decision making, personnel selection (true positive, true negative, false positive, false negative), vote (yes, n
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