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October  2018, 14(4): 1501-1519. doi: 10.3934/jimo.2018018

## Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process

 Thapar Institute of Engineering & Technology (Deemed University), Patiala-147004, Punjab, India

Received  February 2017 Revised  July 2017 Published  January 2018

Fund Project: The author would like to thank the Editor-in-Chief and referees for providing very helpful comments and suggestions.

The objective of this work is to present novel correlation coefficients under the intuitionistic multiplicative preference relation (IMPR), for measuring the relationship between the two intuitionistic multiplicative sets, instead of intuitionistic fuzzy preference relation (IFPR). As IFPR deals under the conditions that the attribute values grades are symmetrical and uniformly distributed. But in our day-to-day life, these conditions do not fulfill the decision maker requirement and hence IFPR theory is not applicable in that domain. Thus, for handling this, an intuitionistic multiplicative set theory has been utilized where grades are distributed asymmetrical around 1. Further, under this environment, a decision making method based on the proposed novel correlation coefficients has been presented. Pairs of membership and non-membership degree are considered to be a vector representation during formulation. Three numerical examples have been taken to demonstrate the efficiency of the proposed approach.

Citation: Harish Garg. Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1501-1519. doi: 10.3934/jimo.2018018
##### References:

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##### References:
Comparison between the 0.1 - 0.9 scale and the 1 - 9 scale
 1 - 9 scale 0.1 - 0.9 scale Meaning 1/9 0.1 Extremely not preferred 1/7 0.2 Very strongly not preferred 1/5 0.3 Strongly not preferred 1/3 0.4 Moderately not preferred 1 0.5 Equally preferred 3 0.6 Moderately preferred 5 0.7 Strongly preferred 7 0.8 Very strongly preferred 9 0.9 Extremely preferred other values between 1/9 and 9 other values between 0 and 1 Intermediate value used to present compromise
 1 - 9 scale 0.1 - 0.9 scale Meaning 1/9 0.1 Extremely not preferred 1/7 0.2 Very strongly not preferred 1/5 0.3 Strongly not preferred 1/3 0.4 Moderately not preferred 1 0.5 Equally preferred 3 0.6 Moderately preferred 5 0.7 Strongly preferred 7 0.8 Very strongly preferred 9 0.9 Extremely preferred other values between 1/9 and 9 other values between 0 and 1 Intermediate value used to present compromise
Comparative analysis of Example 2
 Method Calculate value of Ranking $C_1$ $C_2$ $C_3$ Aggregation Operator[30] 0.6693 0.9110 0.3078 $C_2\succ C_1\succ C_3$ Hamming distance measure[25] 0.3509 0.0886 0.5367 $C_2\succ C_1\succ C_3$ Novel accuracy function[33] 0.3386 0.8220 0.1127 $C_2\succ C_1\succ C_3$ Correlation coefficient[34] 0.7465 0.9576 0.5612 $C_2\succ C_1\succ C_3$ Similarity measure ($S_C$)[4] 0.6401 0.9134 0.6262 $C_2\succ C_1\succ C_3$ Similarity measure ($S_H$)[18] 0.6401 0.9134 0.6093 $C_2\succ C_1\succ C_3$ Cosine Similarity measure[34] 0.5383 0.6913 0.4453 $C_2\succ C_1\succ C_3$ Improved score function [7] 0.6280 0.9466 0.5545 $C_2\succ C_1\succ C_3$
 Method Calculate value of Ranking $C_1$ $C_2$ $C_3$ Aggregation Operator[30] 0.6693 0.9110 0.3078 $C_2\succ C_1\succ C_3$ Hamming distance measure[25] 0.3509 0.0886 0.5367 $C_2\succ C_1\succ C_3$ Novel accuracy function[33] 0.3386 0.8220 0.1127 $C_2\succ C_1\succ C_3$ Correlation coefficient[34] 0.7465 0.9576 0.5612 $C_2\succ C_1\succ C_3$ Similarity measure ($S_C$)[4] 0.6401 0.9134 0.6262 $C_2\succ C_1\succ C_3$ Similarity measure ($S_H$)[18] 0.6401 0.9134 0.6093 $C_2\succ C_1\succ C_3$ Cosine Similarity measure[34] 0.5383 0.6913 0.4453 $C_2\succ C_1\succ C_3$ Improved score function [7] 0.6280 0.9466 0.5545 $C_2\succ C_1\succ C_3$
Comparative analysis of Example 3
 Method Calculate value of Ranking $Q_1$ $Q_2$ $Q_3$ $Q_4$ $Q_5$ Aggregation Operator[30] 0.6685 0.8705 0.5791 0.1606 0.4731 $Q_2\succ Q_1\succ Q_3 \succ Q_5 \succ Q_4$ Hamming distance measure[25] 0.4059 0.3806 0.3406 0.4686 0.4281 $Q_3\succ Q_2\succ Q_1 \succ Q_5 \succ Q_4$ Novel accuracy function[33] 0.3375 0.7410 0.1582 0.2066 0.5198 $Q_2\succ Q_5\succ Q_1 \succ Q_4 \succ Q_3$ Correlation coefficient [34] 0.7208 0.7047 0.7207 0.6103 0.6957 $Q_1\succ Q_3\succ Q_2 \succ Q_5 \succ Q_4$ Similarity measure ($S_C$)[4] 0.6856 0.6767 0.7249 0.5701 0.6490 $Q_3\succ Q_1\succ Q_2 \succ Q_5 \succ Q_4$ Similarity measure ($S_H$) [18] 0.6742 0.6713 0.7249 0.5701 0.6490 $Q_3\succ Q_1\succ Q_2 \succ Q_5 \succ Q_4$ Cosine Similarity measure [34] 0.4982 0.5091 0.5091 0.4328 0.5076 $Q_2 = Q_3\succ Q_5 \succ Q_1 \succ Q_4$ Improved score function [7] 0.6894 0.7343 0.5248 0.4676 0.5846 $Q_2\succ Q_1\succ Q_5 \succ Q_3 \succ Q_4$
 Method Calculate value of Ranking $Q_1$ $Q_2$ $Q_3$ $Q_4$ $Q_5$ Aggregation Operator[30] 0.6685 0.8705 0.5791 0.1606 0.4731 $Q_2\succ Q_1\succ Q_3 \succ Q_5 \succ Q_4$ Hamming distance measure[25] 0.4059 0.3806 0.3406 0.4686 0.4281 $Q_3\succ Q_2\succ Q_1 \succ Q_5 \succ Q_4$ Novel accuracy function[33] 0.3375 0.7410 0.1582 0.2066 0.5198 $Q_2\succ Q_5\succ Q_1 \succ Q_4 \succ Q_3$ Correlation coefficient [34] 0.7208 0.7047 0.7207 0.6103 0.6957 $Q_1\succ Q_3\succ Q_2 \succ Q_5 \succ Q_4$ Similarity measure ($S_C$)[4] 0.6856 0.6767 0.7249 0.5701 0.6490 $Q_3\succ Q_1\succ Q_2 \succ Q_5 \succ Q_4$ Similarity measure ($S_H$) [18] 0.6742 0.6713 0.7249 0.5701 0.6490 $Q_3\succ Q_1\succ Q_2 \succ Q_5 \succ Q_4$ Cosine Similarity measure [34] 0.4982 0.5091 0.5091 0.4328 0.5076 $Q_2 = Q_3\succ Q_5 \succ Q_1 \succ Q_4$ Improved score function [7] 0.6894 0.7343 0.5248 0.4676 0.5846 $Q_2\succ Q_1\succ Q_5 \succ Q_3 \succ Q_4$
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