Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-
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Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process Harish Garg1
· Dimple Rani1
© Springer Nature B.V. 2019
Abstract Complex intuitionistic fuzzy set (CIFS) is a distinctive intuitionistic fuzzy set (IFS) in which the membership degrees are determined on the unit disc of the complex plane and can more clearly express the imprecision and ambiguity in the data. The prevailing studies on IFS deal with the data over the subset of a real number and hence there is a sacrifice of some information during the method under certain conditions. As an alteration to these, CIFS characterized with supplementary terms in membership degrees called as phase terms and hence examine two-dimensional data concurrently in a single set. To get full utilization of these assets, in this paper, the aim of the practice is classified into two turns: (i) to define the possibility degree measure to order the numbers, and (ii) to define some novel operational laws and aggregation operators (AOs) to aggregate the various choices over CIFS environment. The beneficial features of the proposed weighted averaging and geometric AOs are addressed. Finally, a decision-making approach is extended for the multicriteria decision-making problem with complex intuitionistic fuzzy information, in which weights are managed objectively. A practical illustration is furnished to address the availability and advantages of the proposed method by comparison with some existing methods. Keywords Aggregation operators · MCDM · Uncertainty · Complex IFS · Possibility degree measures
1 Introduction Multiple criteria decision-making (MCDM) problems took great consideration to the effective problems where the goal is to select the excellent opportunity in distinction to the finite values under the various criteria. In our daily life, we constantly encounter different kinds of decision-making (DM) problems where our initial intention is to learn how to make a
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Harish Garg [email protected] http://sites.google.com/site/harishg58iitr/ School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab 147004, India
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H. Garg, D. Rani
decision. Traditionally, the DM process brings crisp data without examining the uncertainties in it. However, in sequence to treat the imprecision in the data, hypothesis such as fuzzy set (FS) (Zadeh 1965), intuitionistic FS (IFS) (Atanassov 1986), linguistic interval-valued IFS (Garg and Kumar 2019b), complex FS (Ramot et al. 2002), complex IFS (Alkouri and Salleh 2012), complex interval-valued IFS (Garg and Rani 2019e) are generally used. In these sets, each factor was drawn by an ordered pair including the degree of membership (MD) and nonmembership (NMD) with the intention that their sum is bounded to one (Klir and Yuan 2005; Kaur and Garg 2018; Xu and Yager 2006; Wang and Liu 2012; Kumar and Garg 2018a, b; Garg and Kumar 2018; Wang and Triantaphyllou 2008). From these studies, it is evident that the DM
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