Document Type : Article

**Authors**

School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala 147004, Punjab, India

**Abstract**

As a generalization of the intuitionistic fuzzy sets (IFSs), complex IFSs (CIFSs) is a powerful and worthy tool to realize the imprecise information by using complex-valued membership degrees with an extra term, named as phase term. Divergence measure is a valuable tool to determine the degree of discrimination between the two sets. Driven by these fundamental characteristics, it is fascinating to manifest some divergence measures to the CIFSs. In this paper, we explain a method to solve the multi-criteria decision-making (MCDM) problem under CIFS environment. For it, firstly, the divergence measures are introduced between two CIFSs and examined their several properties and relations. Secondly, a novel algorithm is given based on the proposed measures to solve the problems in which weights corresponding to criteria are resolved using maximizing deviation method. Thirdly, a reasonable example is provided to verify the developed approach and to exhibit its practicality and utility with a comparative analysis to show its more manageable and adaptable nature.

**Keywords**

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[44] Rani, D. and Garg, H. “Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision - making process”, International Journal for Uncertainty Quantification, 7 (5), pp. 423 – 439 (2017).

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[59] Garg, H. and Kumar, K. “Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis”, Expert Systems, 36 (4), pp. e12428 (2019), doi: 10.1111/exsy.12428

[52] Garg, H. and Rani, D. “Some results on information measures for complex intuitionistic fuzzy sets”, International Journal of Intelligent Systems, 34 (10), pp. 2319 – 2363 (2019).

[53] Yingming,W. “Using the method of maximizing deviations to make decision for multi-indices”, Journal of Systems Engineering and Electronics, 8 (3), pp. 21 – 26 (1997).

[54] Wang, J., H. Gao, and Wei, G. W. “The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making”, International Journal of Intelligent Systems, 34 (6), pp. 1158 – 1183 (2019).

[55] Tang, X. Y. and Wei, G. W. “Multiple attribute decision-making with Dual hesitant Pythagorean fuzzy information”, Cognitive Computation, 11 (2), pp. 193 – 211 (2019).

[56] Tang, M.,Wang, J., Lu, J. P.,Wei, G.W.,Wei, C. andWei, Y. “Dual hesitant Pythagorean fuzzy heronian mean operators in multiple attribute decision making”, Mathematics, 7 (4), pp. 344 (2019).

[57] Arora, R. and Garg, H. “Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties”, Computational and Applied Mathematics, 38 (2), pp. 1–36 (2019).

[58] Garg, H. and Nancy, “Linguistic single-valued neutrosophic power aggregation operators and their applications to group decision-making problems”, IEEE/CAA Journal of Automatic Sinica, pp. 1 – 13 (2019), doi: 10.1109/JAS.2019.1911522

[59] Garg, H. and Kumar, K. “Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis”, Expert Systems, 36 (4), pp. e12428 (2019), doi: 10.1111/exsy.12428

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[61] Peng, X. , Dai, J. and Garg, H. “Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function”, International Journal of Intelligent Systems, 33 (11), pp. 2255 – 2282 (2018).

[61] Peng, X. , Dai, J. and Garg, H. “Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function”, International Journal of Intelligent Systems, 33 (11), pp. 2255 – 2282 (2018).

[62] Peng, X. D. and Garg, H. “Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure”, Computers & Industrial Engineering, 119, pp. 439 – 452 (2018).

[63] Garai, T. and Garg, H. “Multi-objective linear fractional inventory model with possibility and necessity constraints under generalized intuitionistic fuzzy set environment”, CAAI Transactions on Intelligence Technology, 4 (3), pp. 175 – 181 (2019).

[63] Garai, T. and Garg, H. “Multi-objective linear fractional inventory model with possibility and necessity constraints under generalized intuitionistic fuzzy set environment”, CAAI Transactions on Intelligence Technology, 4 (3), pp. 175 – 181 (2019).

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July and August 2021Pages 2439-2456