Decision-making approaches based on color spectrum and D-TOPSIS method under rough environment
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Decision-making approaches based on color spectrum and D-TOPSIS method under rough environment Musavarah Sarwar1 Received: 11 March 2020 / Revised: 24 July 2020 / Accepted: 31 July 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract 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. Keywords Rough graph · Rough digraph · Spectrum · Color energy · Rough D-TOPSIS method · Agricultural farming investments · Illegal communication networks Mathematics Subject Classification 05C15 · 90B50 · 60L99 · 94D05
1 Introduction The mathematical models to evaluate and process multi-property (attribute) decision-making (MADM) problems have been introduced and applied to different domains of natural science and information technology including medical diagnosis, risk management and agricultural farming. The most implemented MADM approach is TOPSIS technique first studied by Hwang and Yoon (1981). This method evaluates the ranking of given alternatives through similarity using negative ideal and positive ideal solutions. The main idea behind this approach is that the targeted alternatives are not only farthest from negative ideal solution but also
Communicated by Marcos Eduardo Valle.
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Musavarah Sarwar [email protected] Department of Mathematics, Government College Women University, Sialkot, Pakistan 0123456789().: V,-vol
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nearest form positive ideal solution. The standard TOPSIS method plays an important role in various applications, but in some cases, more uncertainty appears due to the individual judgement of experts. To overcome the limitations of classical TOPSIS for dealing with uncertain behavior of given information, Chen (2000) extended the TOPSIS method to fuzzy TOPSIS method for solving group decision-making problems. Based on entropy weights and distance measures, Joshi and Kumar (2014) studied the TOPSIS method under intuitionistic fuzzy environment for multi-criteria decision-making. Akram et al. (2018) discussed TOPSIS and ELECTRE-I methods under bipo
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