Critical Analysis on the Using of the Entropy in Multicriteria Decision Making Problems Under Interval-Valued Intuitionistic Fuzzy Environment

Yıl 2022, Cilt: 25 Sayı: 2, 799 - 811, 01.06.2022

Melda Kokoç , Süleyman Ersöz

https://doi.org/10.2339/politeknik.764082

Öz

Entropy, developed to measure information uncertainty, is taken place in the literature as an important concept after adapting to the fuzzy set theory. Fuzzy entropy gives a measure of the uncertainty of the situation, which is considered the average amount of information lost when passing from a classical pattern to the fuzzy pattern. One of the areas where entropy is used is multi-criteria decision making (MCDM) problems. In some of the studies on MCDM problems, entropy is used to calculate weights of criteria or experts, or to rank alternatives. In this study, the compatibility of entropy measures developed for the interval-valued intuitionistic fuzzy (IVIF) environment with MCDM problems is investigated. As a result of the exemplary calculations and discussions, it is seen that that the entropy functions developed for ADSB clusters does not work effectively in MCDM problems due to its theoretical properties.

Anahtar Kelimeler

interval -valued intuitionistic fuzzy sets, entropy, multi-criteria decision making

Aralık-Değerli Sezgisel Bulanık Ortamda Entropinin Çok Kriterli Karar Verme Problemlerinde Kullanılmasına İlişkin Eleştirel Analiz

Öz

Bilgi belirsizliğini ölçmek için geliştirilen entropi, bulanık küme teorisine uyarlandıktan sonra önemli bir kavram olarak literatürde yer edinmiştir. Bulanık entropi, klasik bir kalıptan bulanık paterne geçerken kaybolan ortalama bilgi miktarı olarak kabul edilen durumun belirsizliğinin bir ölçüsünü sunmaktadır. Entropinin kullanıldığı alanlardan biri de çok kriterli karar verme (ÇKKV) problemleridir. ÇKKV problemleri ile ilgili çalışmaların bazılarında, kriter veya uzman ağırlıklarını hesaplamak ya da alternatifleri sıralamak için entropiden yararlanılmaktadır. Bu çalışmada, aralık-değerli sezgisel bulanık (ADSB) ortam için geliştirilen entropi fonksiyonlarının, ÇKKV problemleri ile uyumu araştırılmıştır. Gerçekleştirilen örnek hesaplamalar ve tartışmalar sonucunda, ADSB kümeler için geliştirilen entropi fonksiyonlarının, sahip olduğu teorik özelliklerden dolayı ÇKKV problemlerinde etkili çalışmadığı görülmüştür.

Anahtar Kelimeler

Aralık-değerli sezgisel bulanık küme, entropi, çok kriterli karar verme

Kaynakça

• [1] Hajiagha S. H. R., Hashemi S. S., Mohammadi Y., Zavadskas E. K., "Fuzzy belief structure based VIKOR method: an application for ranking delay causes of Tehran metro system by FMEA criteria", Transport, 31:108-18, (2016).
• [2] Dubois D., Prade H., "A Class of Fuzzy Measures Based on Triangular Norms - a General Framework for the Combination of Uncertain-Information", International Journal of General Systems, 8:43-61, (1982).
• [3] Klir G. J., "Where do we stand on measures of uncertainty,ambiguity, fuzziness, and the like?", Fuzzy Sets and Systems, 24:141-60, (1987).
• [4] Inuiguchi M., Ramik J., "Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem", Fuzzy Sets and Systems, 111:3-28, (2000).
• [5] Zadeh L., "Fuzzy logic and approximate reasoning", Synthese, 30:407-28, (1975).
• [6] Atanassov K. T., "Intuitionistic Fuzzy-Sets", Fuzzy Sets and Systems, 20:87-96, (1986).
• [7] Pedrycz W., "Granular computing: analysis and design of intelligent systems", CRC press, (2018).
• [8] Atanassov K., Gargov G., "Interval Valued Intuitionistic Fuzzy-Sets", Fuzzy Sets and Systems, 31:343-9, (1989).
• [9] Wan S. P., Dong J. Y., "Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees", Information Fusion, 26:49-65, (2015).
• [10] Wan S., Xu G., Wang F., Dong J., "A new method for Atanassov’s interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information", Information sciences, 316:329-47, (2015).
• [11] Park J. H., Cho H. J., Kwun Y. C., "Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information", Fuzzy Optimization Decision Making, 10:233-53, (2011).
• [12] Park J. H., Park I. Y., Kwun Y. C., Tan X. G., "Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment", Applied Mathematical Modelling, 35:2544-56, (2011).
• [13] Razavi Hajiagha S. H., Hashemi S. S., Zavadskas E. K., "A complex proportional assessment method for group decision making in an interval-valued intuitionistic fuzzy environment", Technological Economic Development of Economy, 19:22-37, (2013).
• [14] Wu J., Huang H. B., Cao Q. W., "Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems", Applied Mathematical Modelling, 37:9898-906, (2013).
• [15] Long S. P., Geng S., "Decision framework of photovoltaic module selection under interval-valued intuitionistic fuzzy environment", Energy Conversion and Management, 106:1242-50, (2015).
• [16] Chen T., "An IVIF-ELECTRE outranking method for multiple criteria decision-making with interval-valued intuitionistic fuzzy sets", Technological Economic Development of Economy, 22:416-52, (2016).
• [17] Wang Y., Shi Y., "Measuring the Service Quality of Urban Rail Transit Based on Interval-Valued Intuitionistic Fuzzy Model", KSCE Journal of Civil Engineering, 24:647-56, (2020).
• [18] Kong D. P., Chang T. Q., Wang Q. D., Sun H. Z., Dai W. J., "A threat assessment method of group targets based on interval-valued intuitionistic fuzzy multi-attribute group decision-making", Applied Soft Computing, 67:350-69, (2018).
• [19] Ye J., "Multiple Attribute Group Decision-Making Methods with Completely Unknown Weights in Intuitionistic Fuzzy Setting and Interval-Valued Intuitionistic Fuzzy Setting", Group Decision and Negotiation, 22:173-88, (2013).
• [20] Wei C. P., Zhang Y. Z., "Entropy Measures for Interval-Valued Intuitionistic Fuzzy Sets and Their Application in Group Decision-Making", Mathematical problems in engineering, 2015 (2015).
• [21] Guo K. H., Song Q., "On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge", Applied Soft Computing, 24:328-40, (2014).
• [22] Wei C.P., Wang P., Zhang Y.Z., "Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications", Information sciences, 181:4273-86, (2011).
• [23] Qi X., Liang C., Zhang E., Ding Y., "Approach to interval-valued intuitionistic fuzzy multiple attributes group decision making based on maximum entropy", Systems Engineering-Theory & Practice, 10 (2011).
• [24] Ye J., "Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets", Applied Mathematical Modelling, 34:3864-70, (2010).
• [25] Abdullah L., Zulkifli N., Liao H. C., Herrera-Viedma E., Al-Barakati A., "An interval-valued intuitionistic fuzzy DEMATEL method combined with Choquet integral for sustainable solid waste management", Engineering Applications of Artificial Intelligence, 82:207-15, (2019).
• [26] Rani P., Jain D., Hooda D. S., "Shapley Function Based Interval-Valued Intuitionistic Fuzzy Vikor Technique for Correlative Multi-Criteria Decision Making Problems", Iranian Journal of Fuzzy Systems, 15:25-54, (2018).
• [27] Wang L., Liu H., Quan M., "Evaluating the risk of failure modes with a hybrid MCDM model under interval-valued intuitionistic fuzzy environments", Computers & Industrial Engineering, 102:175-85, (2016).
• [28] Xu J., Shen F., "A new outranking choice method for group decision making under Atanassov’s interval-valued intuitionistic fuzzy environment", Knowledge-Based Systems, 70:177-88, (2014).
• [29] Zhang Y., Ma P., Su X., Zhang C. Entropy on interval-valued intuitionistic fuzzy sets and its application in multi-attribute decision making. 14th International Conference on Information Fusion: IEEE; 2011. p. 1-7.
• [30] Chen X. H., Yang L., Wang P., Yue W., "A Fuzzy Multicriteria Group Decision-Making Method with New Entropy of Interval-Valued Intuitionistic Fuzzy Sets", Journal of Applied Mathematics, 2013 (2013).
• [31] Liu P. D., Qin X. Y., "An Extended VIKOR Method for Decision Making Problem with Interval-Valued Linguistic Intuitionistic Fuzzy Numbers Based on Entropy", Informatica, 28:665-85, (2017).
• [32] Xian S., Dong Y., Liu Y., Jing N., "A novel approach for linguistic group decision making based on generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid operator and TOPSIS", International Journal of Intelligent Systems, 33:288-314, (2018).
• [33] Mishra A. R., Rani P., Mardani A., Pardasani K. R., Govindan K., Alrasheedi M., "Healthcare evaluation in hazardous waste recycling using novel interval-valued intuitionistic fuzzy information based on complex proportional assessment method", Computers Industrial Engineering, 139:106140, (2020).
• [34] Abdullah L., Najib L., "A new preference scale mcdm method based on interval-valued intuitionistic fuzzy sets and the analytic hierarchy process", Soft Computing, 20:511-23, (2016).
• [35] Shannon C. E., "A mathematical theory of communication", The Bell system technical journal, 27:379-423, (1948).
• [36] Zadeh L., "Probability measures of fuzzy events", Journal of mathematical analysis applications, 23:421-7, (1968).
• [37] Burillo P., Bustince H., "Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets", Fuzzy Sets and Systems, 78:305-16, (1996).
• [38] Liu X., Zheng S., Xiong F. Entropy and subsethood for general interval-valued intuitionistic fuzzy sets. International Conference on Fuzzy Systems and Knowledge Discovery: Springer; 2005. p. 42-52.
• [39] Atanassov K. T., "Operators over Interval Valued Intuitionistic Fuzzy-Sets", Fuzzy Sets and Systems, 64:159-74, (1994).
• [40] Chen X. H., Yang L., Wang P., Yue W., "An Effective Interval-Valued Intuitionistic Fuzzy Entropy to Evaluate Entrepreneurship Orientation of Online P2P Lending Platforms", Advances in Mathematical Physics,(2013).
• [41] Mishra A. R., Rani P., Pardasani K. R., Mardani A., Stevic Z., Pamucar D., "A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method", Soft Computing:1-21, (2020).
• [42] Zhang Q. S., Xing H. Y., Liu F. C., Ye J., Tang P., "Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures", Information sciences, 283:55-69, (2014).
• [43] Zhao N., Xu Z. S., "Entropy Measures for Interval-Valued Intuitionistic Fuzzy Information from a Comparative Perspective and Their Application to Decision Making", Informatica, 27:203-29, (2016).
• [44] Rashid T., Faizi S., Zafar S., "Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making", Advances in Fuzzy Systems, (2018).
• [45] Zhang Q. S., Jiang S. Y., Jia B. G., Luo S. H., "Some information measures for interval-valued intuitionistic fuzzy sets", Information sciences, 180:5130-45, (2010).
• [46] Büyüközkan G., Göçer F., "An extension of ARAS methodology under interval valued intuitionistic fuzzy environment for digital supply chain", Applied Soft Computing, 69:634-54, (2018).
• [47] İntepe G., Bozdag E., Koc T., "The selection of technology forecasting method using a multi-criteria interval-valued intuitionistic fuzzy group decision making approach", Computers & Industrial Engineering, 65:277-85, (2013).
• [48] Nur F., Alrahahleh A., Burch R., Babski-Reeves K., Marufuzzaman M., "Last mile delivery drone selection and evaluation using the interval-valued inferential fuzzy TOPSIS", Journal of Computational Design and Engineering, 7:1-15, (2020).
• [49] Oztaysi B., Onar S. C., Kahraman C., Yavuz M., "Multi-criteria alternative-fuel technology selection using interval-valued intuitionistic fuzzy sets", Transportation Research Part D: Transport Environment, 53:128-48, (2017).
• [50] Onar S. C., Oztaysi B., Otay İ., Kahraman C., "Multi-expert wind energy technology selection using interval-valued intuitionistic fuzzy sets", Energy, 90:274-85, (2015).
• [51] Kahraman C., Öztayşi B., Onar S. Ç., "An integrated intuitionistic fuzzy AHP and TOPSIS approach to evaluation of outsource manufacturers", Journal of Intelligent Systems, 29:283-97, (2018).