In this paper, we introduce a quantity measure which is called (R, S)-norm entropy and discuss some of its major properties with Shannon’s and other entropies in the literature. Based on this (R, S)-norm entropy, we have proposed a new (R, S)-norm fuzzy information measure and discussed its validity and properties. Further, we have given its comparison with other fuzzy information measures to prove its effectiveness. Attribute weights play an important role in multiple-attribute decision-making problems. In the present communication, two methods of determining the attribute weights are introduced. First is the case when the information regarding attribute weights is incompletely known or completely unknown and second is when we have partial information about attribute weights. For the first case, the extension of ordinary entropy weight method is used to calculate attribute weights and minimum entropy principle method based on solving a linear programming model is used in the second case. Finally, two methods are explained through numerical examples.
R-norm entropy Shannon’s entropy Convex and concave function (R, S)-norm information measure (R, S)-norm fuzzy information measure MADM
Mathematics Subject Classification
94A15 94A24 26D15
This is a preview of subscription content, log in to check access.
The authors are thankful to anonymous referees for their valuable comments and suggestions to improve this manuscript.
Aczel J, Daroczy Z (1975) On measures of information and their characterization. Academic Press, New YorkMATHGoogle Scholar
Güneralpa B, Gertnera G, Mendozaa G, Anderson A (2007) Evaluating probabilistic data with a possibilistic criterian in land-restoration decision-making: effects on the precision of results. Fuzzy Sets Syst 158:1546–1560CrossRefGoogle Scholar
Havdra JH, Charvat F (1967) Quantification method classification process: concept of structral \(\alpha \)-entropy. Kybernetika 3:30–35MathSciNetGoogle Scholar
Joshi R, Kumar S (2016a) \((R, S)\)-norm information measure and a relation between coding and questionnaire theory. Open Syst Inf Dyn 23(3):1–12MathSciNetCrossRefMATHGoogle Scholar
Joshi R, Kumar S (2016b) A new approach in multiple attribute decision making using \(R\)-norm entropy and Hamming distance measure. Int J Inf Manag Sci 27(3):253–268Google Scholar
Joshi R, Kumar S (2017a) A new intuitionistic fuzzy entropy of order-\(\alpha \) with applications in multiple attribute decision making. Adv Intell Syst Comput 546:212–219Google Scholar
Joshi R, Kumar S (2017b) A new exponential fuzzy entropy of order \((\alpha, \beta )\) and its application in multiple attribute decision-making problems. Commun Math Stat 5:213–229MathSciNetCrossRefMATHGoogle Scholar
Joshi R, Kumar S (2017c) Parametric \((R, S)\)-norm entropy on intuitionistic fuzzy sets with a new approach in multiple attribute decision making. Fuzzy Inf Eng 9:181–203MathSciNetGoogle Scholar
Renyi A (1961) On measures of entropy and information. In: Proceedings of the 4th Barkley symposium on Mathemtaical statistics and probability, vol 1. University of California Press, p 547Google Scholar