Multi-criteria decision making problem for evaluating ERP system using entropy weighting approach and q-rung orthopair f
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ORIGINAL PAPER
Multi-criteria decision making problem for evaluating ERP system using entropy weighting approach and q-rung orthopair fuzzy TODIM Vikas Arya1 • Satish Kumar1 Received: 2 July 2020 / Accepted: 4 October 2020 Springer Nature Switzerland AG 2020
Abstract The q-rung orthopair fuzzy set theory is a flexible tool for dealing with the ambiguity of human judgements information as compared to the fuzzy, Atanassov intuitionistic fuzzy and Pythagorean fuzzy models. However, there is very few investigation for the entropy measure of q-rung orthopair fuzzy sets. Therefore, this paper firstly proposed a new entropy measure for q-rung orthopair fuzzy set along with their elegant properties. By changing the parameter q, q 1, q-rung orthopair fuzzy set can adjust the range of indication of decision information. Based on the proposed entropy measure, we proposed a new method to deal with MCDM problems under the q-rung orthopair fuzzy environment where the information about criteria weights is are partially known. We extend the TODIM (an Acronym in Portuguese of interactive and multicriteria decision making) approach for solving the multi-criteria decision-making problems (MCDM) where the behaviour of specialists are taken into account and elements of a set are interdependent. In addition, a numerical example is provided in solving real-life problems to illustrate the highlight of this study. The experimental and comparative results show the effectiveness and flexibility of the developed approach in solving real-life problems. Keywords q-Rung orthopair fuzzy set Entropy MCDM TODIM
1 Introduction In real life, there exist some situation that cannot be represented adequately by mathematical forms, for instance, the words ‘‘big’’, ‘‘fast’’, ‘‘rich’’, ‘‘beautiful’’ and so on. It encourages people to obtain a more effective way to study and handle such type of uncertain problems. In 1965, Zadeh (1965) proposed the concept of fuzzy set (FS), which contains only the membership degree/grade. After that, the theory of Zadeh’s fuzzy set has been developed to describe the uncertainty and applied them in decisionmaking problems from various angles (Chen et al. 2012; Chen and Wang 2010; Chen and Chen 2014; Arya and Kumar 2020a, b). Intuitionistic fuzzy set (IFS) proposed by & Vikas Arya [email protected] Satish Kumar [email protected] 1
Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana-Ambala, Ambala 133207, India
Atanassov (1986), which takes account of the membership grade, the negative/ non-membership grade and the hesitance grade. IFS theory includes more detail to discriminate various objects as compared to fuzzy set and it opens the door of intuitionistic fuzzy research. Due to their applicability and flexibility, many researchers have been started research work on Atanassov intuitionistic fuzzy theory. More and more interesting applications have been developed in many fields including risk analysis, medical diagnos
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