×

Decision-making approaches based on color spectrum and D-TOPSIS method under rough environment. (English) Zbl 1476.05061

Summary: A rough set, an extension of a crisp set, is a mathematical tool to understand and model uncertainty without much prior information, additional adjustments or pre-defined membership functions. To manipulate the subjectivity and vagueness of decision-making problems, rough models provide more objective description of given information using upper and lower approximations. In this research paper, we study the absurdity and falsity of existing definition of rough graph. Based on rough relations, we introduce the concepts of rough graphs and rough digraphs and establish certain formulae, lower and upper bounds of color energy of rough graphs. Using \(D\) numbers, rough weights and rough entropy weights, we develop rough \(D\)-TOPSIS method which incorporates the capability to analyze uncertain and vague information without additional assumptions. We study the importance of rough information for the evaluation of water requirement in agricultural farming, investment analysis in organic and inorganic farming systems and illegal communication networks.

MSC:

05C15 Coloring of graphs and hypergraphs
05C72 Fractional graph theory, fuzzy graph theory
91B06 Decision theory

Software:

Mathematica
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adiga, C.; Sampathkumar, E.; Sriraj, MA, Color energy of a graph, Proc Jangjeon Math Soc, 16, 3, 335-351 (2013) · Zbl 1306.05140
[2] Akram, M.; Luqman, A., Granulation of ecological networks under fuzzy soft environment, Soft Comput, 24, 11867-11892 (2020) · Zbl 1491.05177
[3] Akram, M.; Zafar, F., Hybrid soft computing models applied to graph theory. Studies in fuzziness and soft computing (2020), Berlin: Springer, Berlin · Zbl 1415.90001
[4] Akram, M.; Shumaiza; Smarandache, F., Decision-making with bipolar neutrosophic TOPSIS and bipolar neutrosophic ELECTRE-I, Axioms, 7, 2, 33 (2018)
[5] Akram, M.; Habib, A.; Alcantud, JCR, An optimization study based on Dijkstra algorithm for a network with trapezoidal picture fuzzy numbers, Neural Comput Appl (2020)
[6] Alghamdi, MA; Alshehri, NO; Akram, M., Multi-criteria decision-making methods in bipolar fuzzy environment, Int J Fuzzy Syst, 20, 6, 2057-2064 (2018)
[7] Anjali, N.; Mathew, S., Energy of a fuzzy graph, Ann Fuzzy Maths Inform, 6, 455-65 (2013) · Zbl 1302.05152
[8] Chang, TW; Lo, HW; Chen, KY; Liou, JJ, A novel FMEA model based on rough BWM and rough TOPSIS-AL for risk assessment, Mathematics, 7, 10, 874 (2019)
[9] Chen, CT, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets Syst, 114, 1, 1-9 (2000) · Zbl 0963.91030
[10] Deng, Y., \(D\) numbers: theory and applications, J Inf Comput Sci, 9, 9, 2421-2428 (2012)
[11] Fei, L.; Hu, Y.; Xiao, F.; Chen, L.; Deng, Y., A modified topsis method based on \(D\) numbers and its applications in human resources selection, Math Probl Eng, 2016, 14 (2016) · Zbl 1400.90190
[12] Feng, F., Soft rough sets applied to multicriteria group decision making, Ann Fuzzy Math Inform, 2, 1, 69-80 (2011) · Zbl 1301.91010
[13] Feng, F.; Liu, X.; Leoreanu-Fotea, V.; Jun, YB, Soft sets and soft rough sets, Inf Sci, 181, 6, 1125-1137 (2011) · Zbl 1211.68436
[14] Gutman, I., The energy of a graph, Ber Math Stat Sekt Forschungsz Graz, 103, 1-22 (1978) · Zbl 0402.05040
[15] Gutman, I., The energy of a graph: old and new results, Algebraic combinatorics and applications, 196-211 (2001), Berlin: Springer, Berlin · Zbl 0974.05054
[16] He, T.; Shi, K., Rough graph and its structure, J Shandong Univ, 41, 6, 46-50 (2006)
[17] Hwang, CL; Yoon, K., Methods for multiple attribute decision making, Multiple attribute decision making, 58-191 (1981), Berlin: Springer, Berlin
[18] Jiang, H.; Zhan, J.; Sun, B.; Alcantud, JCR, An MADM approach to covering-based variable precision fuzzy rough sets: an application to medical diagnosis, Int J Mach Learn Cybern, 11, 2181-2207 (2020)
[19] Joshi, D.; Kumar, S., Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making, Egypt Inform J, 15, 2, 97-104 (2014)
[20] Leoreanu-Fotea, V., The lower and upper approximations in a hypergroup, Inf Sci, 178, 18, 3605-3615 (2008) · Zbl 1156.68585
[21] Li, D-F; Nan, J-X, Extension of the TOPSIS for multi-attribute group decision making under Atanassov IFS environments, Int J Fuzzy Syst Appl (IJFSA), 1, 4, 47-61 (2011)
[22] Li, J.; Fang, H.; Song, W., Sustainable supplier selection based on SSCM practices: a rough cloud TOPSIS approach, J Clean Prod, 222, 606-621 (2019)
[23] Ma, X.; Akram, M.; Zahid, K.; Alcantud, JCR, Group decision-making framework using complex Pythagorean fuzzy information, Neural Comput Appl (2020)
[24] Ma, X.; Zhan, J.; Sun, B.; Alcantud, JCR, Novel classes of coverings based multigranulation fuzzy rough sets and corresponding applications to multiple attribute group decision-making, Artif Intell Rev (2020)
[25] Mahapatra, T.; Ghorai, G.; Pal, M., Fuzzy fractional coloring of fuzzy graph with its application, J Ambient Intell Humaniz Comput (2020)
[26] Nagarani, A.; Vimala, S., Energy of fuzzy regular and graceful graphs, Asian Res J Math, 4, 2, 1-8 (2017)
[27] Nicoletti, MC; Uchôa, JQ; Baptistini, MT, Rough relation properties, Int J Appl Math Comput Sci, 11, 3, 621-635 (2001) · Zbl 0986.03041
[28] Poulik, S.; Ghorai, G., Detour g-interior nodes and detour g-boundary nodes in bipolar fuzzy graph with applications, Hacettepe J Math Stat, 49, 1, 106-119 (2020) · Zbl 1488.05422
[29] Poulik, S.; Ghorai, G., Certain indices of graphs under bipolar fuzzy environment with applications, Soft Comput, 24, 5119-5131 (2020) · Zbl 1490.05231
[30] Pawlak, Z., Rough sets, Int J Comput Inf Sci, 11, 5, 341-356 (1982) · Zbl 0501.68053
[31] Pawlak, Z., Rough sets, rough relations and rough functions, Fundam Inform, 27, 2-3, 103-108 (1996) · Zbl 0854.04008
[32] Sarwar, M.; Akram, M.; Zafar, F., Decision making approach based on competition graphs and extended TOPSIS method under bipolar fuzzy environment, Math Comput Appl, 23, 68 (2018)
[33] Sarwar, M.; Akram, M.; Alshehri, NO, A new method to decision-making with fuzzy competition hypergraphs, Symmetry, 10, 404 (2018) · Zbl 1423.05115
[34] Sarwar, M.; Akram, M.; Ali, U., Double dominating energy of \(m\)-polar fuzzy graphs, J Intell Fuzzy Syst, 38, 2, 1997-2008 (2020)
[35] Sharbaf, SR; Fayazi, F., Laplacian energy of a fuzzy graph, Iran J Math Chem, 5, 1, 1-10 (2014) · Zbl 1367.05172
[36] Skiena, S., Implementing discrete mathematics: combinatorics and graph theory with mathematica (1990), Reading: Addison-Wesley, Reading · Zbl 0786.05004
[37] Song, W.; Ming, X.; Wu, Z.; Zhu, B., A rough TOPSIS approach for failure mode and effects analysis in uncertain environments, Qual Reliab Eng Int, 30, 4, 473-486 (2014)
[38] Suder, A.; Kahraman, C., Multiattribute evaluation of organic and inorganic agricultural food investments using fuzzy TOPSIS, Technol Econ Dev Econ, 24, 3, 844-858 (2018)
[39] Sudha, AS; Anitha, S., Applying Topsis method for evaluating the water requirement of agricultural crops, Int J Future Revolut Comput Sci Commun Eng, 3, 8, 197-202 (2017)
[40] Wan, N.; Li, L.; Ye, C.; Wang, B., Risk assessment in intelligent manufacturing process: a case study of an optical cable automatic arranging robot, IEEE Access, 7, 105892-901 (2019)
[41] Zafar, F.; Akram, M., A novel decision-making method based on rough fuzzy information, Int J Fuzzy Syst, 20, 3, 1000-1014 (2018)
[42] Zhan, J.; Jiang, H.; Yao, Y., Three-way multi-attribute decision-making based on outranking relations, IEEE Trans Fuzzy Syst (2020)
[43] Zhan, J.; Sun, B.; Zhang, X., PF-TOPSIS method based on CPFRS models: an application to unconventional emergency events, Comput Ind Eng, 139, 106192 (2020)
[44] Zhang, K.; Zhan, J.; Wu, WZ, On multi-criteria decision-making method based on a fuzzy rough set model with fuzzy \(\alpha -\) neighborhoods, IEEE Trans Fuzzy Syst (2020)
[45] Zhang, K.; Zhan, J.; Wu, WZ, Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making, Fuzzy Sets Syst, 383, 92-126 (2020) · Zbl 1465.03093
[46] Zhang, L.; Zhan, J.; Yao, Y., Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems, Inf Sci, 517, 315-339 (2020)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.