Distance-Based Similarity Measure Between Interval Neutrosophic Sets and Multi Criteria Decision Making Method

Year 2019, Volume: 9 Issue: 2, 1057 - 1065, 01.06.2019

Gökçe Dilek Küçük

https://doi.org/10.21597/jist.457829

Abstract

In this paper, the weighted similarity measure based on Hamming and Euclidean distances is extended to interval neutrosophic sets. It has been previously used for single valued neutrosophic sets. Then a multicriteria decision-making (MCDM) method is established, in which the criterion weights are known. In the problem the values of each alternative corresponding to the criteria are given with interval neutrosophic numbers. Finally, alternatives are ranked by using the weighted similarity measure between the ideal alternative and each alternative, and the best one is determined.

Keywords

similarity measure, interval neutrosophic set, Hamming and Euclidean distances, multi criteria decision-making

Aralık Nötrosofik Kümeler Arasında Mesafe Tabanlı Benzerlik Ölçüsü ve Çok Kriterli Karar Verme Metodu

Abstract

Bu makalede, Hamming ve Öklid uzaklığa dayanan ağırlıklı benzerlik ölçüsü, aralık nötrosofik kümelere genişletilmiştir. Bu ölçü daha önce tek değerli nötrosofik kümeler için kullanılmıştır. Daha sonra kriter ağırlıkları bilinen çok kriterli bir karar verme metodu oluşturulmuştur. Problemde, her bir alternatifin kriterlere göre değerleri aralık nötrosofik sayılarla verilmiştir. Son olarak ideal alternatif ile her bir alternatif arasında ağırlıklı benzerlik ölçüsü kullanılarak alternatifler sıralanmış ve en iyi alternatif belirlenmiştir.

Keywords

Hamming ve Öklid uzaklık, benzerlik ölçüsü, aralık nötrosofik küme, çok kriterli karar verme

References

• Atanassov K, 1986. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96.
• Atanassov K, Gargov G, 1989. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst., 31(3): 343–349.
• Broumi S, Deli I, Smarandache F, 2014 a. Relations on Interval Valued Neutrosophic Soft Sets, Journal of New Results in Science 5: 01-20.
• Broumi S, Deli I, Smarandache F, 2014 b. Distance and Similarity Measures of Interval Neutrosophic Soft Sets. Critical Review, Center for Mathematics of Uncertainty, Creighton University, USA, 8: 14-31.
• Broumi S, Deli I, Smarandache F, 2014 c. Interval valued neutrosophic parameterized soft set theory and its decision making, Journal of New Results in Science 7: 58-71.
• Broumi S, Deli I, Smarandache F, 2015. N-valued Interval Neutrosophic Sets and Their Application in Medical Diagnosis. Critical Review, Center for Mathematics of Uncertainty, Creighton University, USA, 10: 46-69.
• Deli I, 2015. npn-Soft Sets Theory and Applications. Annals of Fuzzy Mathematics and Informatics, 10(6): 847-862.
• Deli I, Eraslan S, Çağman N, 2018. Ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure. Neural Computing and Applications, 29(1): 187–203. DOI 10.1007/s00521-016-2428-z.
• Chi P.P, Liu P.D, 2013. An extended TOPSIS method for the multiple attribute decision making Problems based on interval neutrosophic sets, Neutrosophic Sets and Systems 1(1) , 63–70.
• Peng JJ, Wang J, Wang J, Zhang HY, Chen XH, 2015. Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int. J. Systems Sci., 47(10): 2342–2358.
• Smarandache F, 1999. A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth.
• Şahin R, 2015. Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural computing and applications, 28(5): 1177-1187.
• Küçük GD, ŞAHİN R, 2018. A Novel Hybrid Approach for Simplified Neutrosophic Decision Making with Completely Unknown Weight Information, International Journal for Uncertainty Quantification, 8(2):161–173.
• Şahin R, Küçük GD, 2018. Group Decision Making with Simplified Neutrosophic Ordered Weighted Distance Operator. Mathematical Methods in The Applied Sciences, 41(12): 4795-4809.
• Wang H, Smarandache F, Zhang YQ, Sunderraman R, 2005. Interval neutrosophic sets and logic: Theory and applications in computing, Hexis, Phoenix, AZ:2005
• Wang H, Smarandache F, Zhang YQ, Sunderraman R, 2010. Single valued neutrosophic sets. Multispace and Multistructure, 4: 410–413.
• Ye J, 2013. Multiple attribute group decision-making method with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. International Journal Of General Systems, 42(5), 489-502.
• Ye J, 2014 a. Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making, Journal of Intelligent and Fuzzy Systems, 26(1), 165–172.
• Ye J, 2014 b. Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic enviroment. Journal of Intelligent and Fuzzy Systems, 27, 2927-2935.
• Xu Z.S, Yager R.R, 2009. Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimal and Decision Making 8, 123–139.
• Zadeh LA, 1965. Fuzzy sets. Inf Control;8, 338–353.
• Zhang HY, Wang JQ, Chen XH, 2014. Interval neutrosophic sets and their application in multicriteria decision making problems. The Scientific World Journal, 645953.