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Complex Spherical Dombi Fuzzy Aggregation Operators for Decision-Making
Muhammad Akrama, Ayesha Khana and Faruk Karaaslan
A complex spherical fuzzy set (CSFS), an extension of spherical fuzzy set, is a worthwhile notion in which the range of degrees occur in the complex plane within unit disk. A CSFS possesses a broader and more flexible structure to effectively model the uncertainty for decision-making (DM) problems. By keeping the significance of Dombi t-norms and t-conorms, in this paper, we develop Dombi operations on CSFS. We present certain aggregation operators based on Dombi operators, including complex spherical Dombi fuzzy weighted arithmetic averaging (CSDFWAA) operator, complex spherical Dombi fuzzy weighted geometric averaging (CSDFWGA) operator, complex spherical Dombi fuzzy ordered weighted arithmetic averaging (CSDFOWAA) operator and complex spherical Dombi fuzzy ordered weighted geometric averaging (CSDFOWGA) operator. Furher, we investigate some crucial properties of these aggregation operators. These aggregation operators play a key role to provide an optimal solution in aggregation process. In addition, we state a multi-criteria decision-making (MCDM) approach and algorithm to handle the complex spherical fuzzy information. To exhibit the applicability of proposed approach, we provide a numerical example related to the selection of most suitable chemical industry to purchase chemicals for establishing a paint company. Besides this, we present a comparative analysis of proposed approach with existing operators to reveal the advantages and authenticity of our technique.
Keywords: Complex spherical fuzzy sets; Complex spherical Dombi fuzzy weighted; Ordered weighted aggre- gation operators; Decision matrix