Intuitionistic Fuzzy PROMETHEE Technique for Multi-criteria Decision Making Problems Based on Entropy Measure
Entropy measures play an important role in the field of fuzzy set theory and generalized by various authors for different purposes. In the present communication, intuitionistic fuzzy entropy measure based on sine function is developed. Further, the modifi
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Abstract. Entropy measures play an important role in the field of fuzzy set theory and generalized by various authors for different purposes. In the present communication, intuitionistic fuzzy entropy measure based on sine function is developed. Further, the modified intuitionistic fuzzy PROMETHEE (IF-PROMETHEE) technique for multi-criteria decision making problems is discussed with the help of proposed entropy measure and the intuitionistic fuzzy preferences. Finally, the effectiveness of the technique is illustrated through a problem of selection of the antiretroviral drugs for HIV/AIDS to reduce the infection of HIV. Keywords: Fuzzy set Intuitionistic fuzzy set PROMETHEE Multi-criteria decision making
Entropy measure
1 Introduction To circumvent the scarcity of fuzzy systems, Atanassov [1] originated the idea of intuitionistic fuzzy sets (IFSs), which deal better results in the decision of inaccurate and hesitant information. IFSs are the generalized content of fuzzy sets which are characterized by the membership function, non-membership function and hesitancy function. Due to the complexity in real life situation, the use of IFSs has gained more concentration from researchers in the field of decision making, image processing, medical diagnosis, pattern recognition etc. [10, 16]. Entropy and similarity measures are fundamental concepts in the fuzzy set theory as well as intuitionistic fuzzy set theory [9]. The idea of entropy on interval-valued fuzzy sets and intuitionistic fuzzy sets has been discussed by Burillo and Bustince [8] to determine the degree of intuitionism. Szmidt and Kacprzyk [25] generalized the axiomatic definition of De Luca and Termini entropy on IFSs with a geometrical explanation of IFSs. Thereafter, numerous entropies on FSs, IVFSs and IFSs have been developed and applied in the various fields [14, 21–26, 28, 31, 33]. There are various techniques to solve the multi-criteria decision making (MCDM) problems which can be classified into utility theory based techniques such as Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) and outranking techniques such as Elimination Et Choice Translating Reality © Springer Nature Singapore Pte Ltd. 2017 M. Singh et al. (Eds.): ICACDS 2016, CCIS 721, pp. 290–301, 2017. DOI: 10.1007/978-981-10-5427-3_31
Intuitionistic Fuzzy PROMETHEE Technique for MCDM Problems
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(ELECTRE), Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) [19, 20]. In 1982, Brans [4] developed the concept of PROMETHEE to obtain the partial or complete ranking of the alternatives on the basis of positive outranking flow, negative outranking flow and net outranking flow. There are numerous types of PROMETHEE techniques that have been developed for different situations with crisp and fuzzy input data [2–7, 11, 12, 17, 18, 32]. These extensional forms of PROMETHEE technique can’t be applied to represent the support and opposition informatio
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