2-Öğeli Tam Dilsel Sezgisel Bulanık Küme Yaklaşımı: Karar Verme Üzerine Bir Uygulama

Year 2022, Volume: 10 Issue: 4, 826 - 840, 30.12.2022

Gürkan Işık

https://doi.org/10.29109/gujsc.1098529

Abstract

Dilsel bulanık modelleme (DBM), gerçek hayat problemlerine ilişkin belirsizliklerin kelimeler ve semboller yardımıyla ifade edilmesini sağlayan bir yaklaşımdır. DBM sayesinde belirsizlikler daha anlaşılır bir şekilde ifade edilebildiği için genellikle insanların dâhil olduğu süreçlerin modellemesi için kullanışlıdır. DBM ile ilgili önemli bir zayıflık, dilsel terimlere karşılık gelen bulanık kümelerin (BK) çekirdek ve destek noktalarının dilsel terimlerle (DT) olan doğrudan bağımlılığıdır. Bu bağımlılık, hassas modellemeyi kısıtladığı için bilgi kaybına neden olur. Bu sorunun üstesinden gelmek için literatürde, bir dilsel ifadeye bilgi farkı (BF) adlı sayısal bir değerin eşlik ettiği 2-öğeli DBM yaklaşımı önerilmiştir. 2-öğeli DBM tutarlılığı artırmada faydalı olsa da melez bir sayısal-dilsel yaklaşım olması nedeniyle “kelimelerle hesaplama” yaklaşımına zarar verir ve yorumlanabilirliği azaltır. Bu çalışmada, 2-öğeli DBM’nin daha kapsayıcı bir sürümü olan dilsel BF'ye sahip 2-Öğeli Tam DBM yaklaşımı önerilmiştir. Gerçek hayat problemlerinde daha kullanışlı bir modelleme yaklaşımı elde edebilmek amacıyla, önerilen yaklaşım sezgisel bulanık kümeler için genişletilmiş ve 2-öğeli tam dilsel sezgisel bulanık modelleme (DSBM) önerilmiştir. Önerilen yaklaşım, gerçek hayat davranışlarını modelleyebilme yeteneğini test etmek amacıyla enerji sektöründe bir karar verme problemi üzerinde uygulanmıştır. Görece küçük bir dilsel terim kümesi kullanılarak, duyarlılık analizi yapmaya elverişli, hassas ve literatür ile uyumlu sonuçlar elde edilmiştir.

Keywords

Bulanık küme, Karar verme, Sezgisel bulanık küme, 2-öğeli dilsel bulanık modelleme, 2-öğeli dilsel sezgisel bulanık modelleme

2-Tuple Full Linguistic Intuitionistic Fuzzy Set Approach: An Application on Decision Making

Abstract

Linguistic fuzzy modeling (LFM) is an approach that enables to express the uncertainties related to real life problems with the help of words and symbols. Since the uncertainties can be expressed more understandably with LFM, it is often useful for modeling processes involving humans. A significant issue about LFM is the dependency of the position of the kernel and support points of fuzzy sets (FS) to linguistic terms (LT). This dependency causes loss of information and reduces the accuracy of modeling. 2-tuple LFM approach has been proposed in the literature to deal with this issue, in which a linguistic expression consists of a linguistic term and a numerical value called difference of information (DOI). 2-tuple LFM is useful for increasing accuracy, but it partially damages the "computing with words" concept and reduces interpretability, because of being a hybrid numerical-linguistic approach. In this study, 2-tuple Full LFM (FLFM) approach having verbal BF, which is more inclusive version of ordinary 2-tuple LFM, has been proposed. To obtain a more useful modeling approach in real life problems, the proposed approach is extended for intuitionistic FSs (IFS) and 2-Tuple Full Linguistic Intuitionistic Fuzzy Modeling (FLIFM) has been proposed. The proposed approach has been applied to a decision-making problem in the energy sector to test its ability to model real-life behaviors. By using a relatively small set of linguistic terms, sensitive and literature-compliant results that are suitable for sensitivity analysis were obtained.

Keywords

Decision making, Fuzzy set, Intuitionistic fuzzy set, 2-tuple linguistic fuzzy modeling, 2-tuple linguistic intuitionistic fuzzy modeling

References

• L. A. Zadeh, «Fuzzy sets,» Information and Control, pp. 338-353, 1965.
• L. A. Zadeh, «The concept of a linguistic variable and its application to approximate reasoning—I,» Information sciences, pp. 199-249, 1975.
• J. Casillas, O. Cordon, F. Herrera ve L. Magdalena, «Accuracy improvements to find the balance interpretability-accuracy in linguistic fuzzy modeling: an overview,» in Accuracy improvements in linguistic fuzzy modeling, Springer, 2013, pp. 3-24.
• O. Cordón, F. Herrera ve I. Zwir, «Linguistic modeling by hierarchical systems of linguistic rules,» IEEE Transactions on fuzzy systems, cilt 10, no. 1, pp. 2-20, 2002.
• Z. Xu, «A method based on linguistic aggregation operators for group decision making under linguistic preference relations,» Information sciences, cilt 166, no. 1-4, pp. 19-30, 2004.
• F. Herrera, E. Herrera-Viedma ve L. Martínez, «A fuzzy linguistic methodology to deal with unbalanced linguistic term sets,» IEEE Transactions on fuzzy Systems, cilt 16, no. 2, pp. 354-370, 2008.
• M. Delgado, F. Herrera, E. Herrera-Viedma ve L. Martinez, «Combining numerical and linguistic information in group decision making,» Information Sciences, cilt 107, no. 1-4, pp. 177-194, 1998.
• F. Herrera ve L. Martínez, «A 2-tuple fuzzy linguistic representation model for computing with words,» IEEE Transactions on fuzzy systems, cilt 6, no. 8, pp. 746-752, 2000.
• F. Herrera ve L. Martinez, «The 2-tuple linguistic computational model: Advantages of its linguistic description, accuracy and consistency,» International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, cilt 9, no. 1, pp. 33-48, 2001.
• L. Martínez ve F. Herrera, «An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges,» Information Sciences, cilt 207, pp. 1-18, 2012.
• F. Herrera, E. Herrera-Viedma ve L. Martı́nez, «A fusion approach for managing multi-granularity linguistic terms sets in decision making,» Fuzzy sets and systems, cilt 114, no. 1, pp. 43-58, 2000.
• F. Herrera ve L. Martínez, «A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making,» IEEE Transactions on Systems, Man, and Cybernetics, cilt 31, no. 2, pp. 227-234, 2001.
• F. J. Estrella, M. Espinilla, F. Herrera ve L. Martínez, « FLINTSTONES: A fuzzy linguistic decision tools enhancement suite based on the 2-tuple linguistic model and extensions,» Information Sciences, cilt 280, pp. 152-170, 2014.
• Y. Xu ve H. Wang, «Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment,» Applied Soft Computing, cilt 11, no. 5, pp. 3988-3997, 2011.
• J. M. Merigó ve A. M. Gil-Lafuente, «Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making,» Information Sciences, cilt 236, pp. 1-16, 2013.
• J. H. Wang ve J. Hao, «A new version of 2-tuple fuzzy linguistic representation model for computing with words,» IEEE transactions on fuzzy systems, cilt 14, no. 3, pp. 435-445, 2006.
• Y. Dong, Y. Xu ve S. Yu, «Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model,» IEEE Transactions on Fuzzy Systems, cilt 17, no. 6, pp. 1366-1378, 2009.
• Y. Dong ve E. Herrera-Viedma, «Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relation,» IEEE transactions on cybernetics, cilt 45, no. 4, pp. 780-792, 2014.
• I. Beg ve T. Rashid, «An intuitionistic 2‐tuple linguistic information model and aggregation operators,» International Journal of Intelligent Systems, cilt 31, no. 6, pp. 569-592, 2016.
• G. Wei, M. Lu, F. E. Alsaadi, T. Hayat ve A. Alsaedi, «Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making,» Journal of Intelligent & Fuzzy Systems, cilt 33, no. 2, pp. 1129-1142, 2017.
• G. Wei, F. E. Alsaadi, T. Hayat ve A. Alsaedi, «Picture 2-tuple linguistic aggregation operators in multiple attribute decision making,» Soft Computing, cilt 22, no. 3, pp. 989-1002, 2018.
• M. Lu, G. Wei, F. E. Alsaadi, T. Hayat ve A. Alsaedi, «Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making,» Journal of Intelligent & Fuzzy Systems, cilt 33, no. 2, pp. 1197-1207, 2017.
• M. De Cock ve E. E. Kerre, «Fuzzy modifiers based on fuzzy relations,» Information Sciences, cilt 160, no. 1-4, pp. 173-199, 2004.
• I. Truck ve H. Akdag, «A tool for aggregation with words,» Information Sciences, cilt 179, no. 14, pp. 2317-2324, 2009.
• K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, pp. 87-96, 1986.
• Z. Xu, «Intuitionistic fuzzy aggregation operators,» IEEE Transactions on Fuzzy Systems, cilt 15, no. 6, pp. 1179-1187, 2007.
• A. T. Gümüş, A. Y. Yayla, E. Çelik and A. Yıldız, "A combined fuzzy-AHP and fuzzy-GRA methodology for hydrogen energy storage method selection in Turkey," Energies, vol. 6, no. 6, pp. 3017-3032, 2013.