Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor
Abstract
:1. Introduction
2. Preliminaries
3. Linguistic Neutrosophic Cubic Numbers and Operators
- 1.
- If , then
- 2.
- If and , then
- 3.
- If and , then
- 4.
- If and , then
- If we can obtain
- if , then:
- When the LNCHM operator in (16) will be reduced to the LNCHA (linguistic neutrosophic cubic Hamy averaging) operator:
- When the LNCHM operator in (16) will reduce to the LNCHA (linguistic neutrosophic cubic Hamy averaging) operator:
4. Entropy of LNCSs
- if and only if
- if and only if
- if and only if H is less fuzzy than , i.e., if or if
- if and only if (H non-fuzzy)
- if and only if
- if and only if H is less than , i.e., if and for or if and for
- 1.
- îf H is a crisp set;
- 2.
- if and only if and if and only if ;
- 3.
- if and only if H is less indeterminable than , i.e., if and
- 4.
5. The Method for MAGDM Based on the WLNCHM Operator
6. Numerical Applications
6.1. Procedure
6.2. Comparison Analysis
7. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
- Zadeh, L.A. Fuzzy sets. Inform. Control 1965, 8, 338–353. [Google Scholar] [CrossRef] [Green Version]
- Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20, 87–96. [Google Scholar] [CrossRef]
- Jun, Y.B.; Kim, C.S.; Yang, K.O. Cubic sets. Ann. Fuzzy Math. Inform. 2012, 4, 83–98. [Google Scholar]
- Akram, M.; Yaqoob, N.; Gulistan, M. Cubic KU-subalgebras. Int. J. Pure Appl. Math. 2013, 89, 659–665. [Google Scholar] [CrossRef]
- Yaqoob, N.; Mostafa, S.M.; Ansari, M.A. On cubic KU-ideals of KU-algebras. ISRN Algebra 2013. [Google Scholar] [CrossRef]
- Rashid, S.; Yaqoob, N.; Akram, M.; Gulistan, M. Cubic graphs with application. Int. J. Anal. Appl. 2018, 16, 733–750. [Google Scholar]
- Aslam, M.; Aroob, T.; Yaqoob, N. On cubic Γ-hyperideals in left almost Γ-semihypergroups. Ann. Fuzzy Math. Inform. 2013, 5, 169–182. [Google Scholar]
- Gulistan, M.; Yaqoob, N.; Vougiouklis, T.; Wahab, H.A. Extensions of cubic ideals in weak left almost semihypergroups. J. Intell. Fuzzy Syst. 2018, 34, 4161–4172. [Google Scholar] [CrossRef]
- Gulistan, M.; Khan, M.; Yaqoob, N.; Shahzad, M. Structural properties of cubic sets in regular LA-semihypergroups. Fuzzy Inf. Eng. 2017, 9, 93–116. [Google Scholar] [CrossRef]
- Khan, M.; Gulistan, M.; Yaqoob, N.; Hussain, F. General cubic hyperideals of LA-semihypergroups. Afr. Mat. 2016, 27, 731–751. [Google Scholar] [CrossRef]
- Yaqoob, N.; Gulistan, M.; Leoreanu-Fotea, V.; Hila, K. Cubic hyperideals in LA-semihypergroups. J. Intell. Fuzzy Syst. 2018, 34, 2707–2721. [Google Scholar] [CrossRef]
- Khan, M.; Jun, Y.B.; Gulistan, M.; Yaqoob, N. The generalized version of Jun’s cubic sets in semigroups. J. Intell. Fuzzy Syst. 2015, 28, 947–960. [Google Scholar]
- Khan, M.; Gulistan, M.; Yaqoob, N.; Shabir, M. Neutrosophic cubic (α,β)-ideals in semigroups with application. J. Intell. Fuzzy Syst. 2018, 35, 2469–2483. [Google Scholar] [CrossRef]
- Ma, X.L.; Zhan, J.; Khan, M.; Gulistan, M.; Yaqoob, N. Generalized cubic relations in Hv-LA-semigroups. J. Discret. Math. Sci. Cryptgr. 2018, 21, 607–630. [Google Scholar] [CrossRef]
- Gulistan, M.; Khan, M.; Yaqoob, N.; Shahzad, M.; Ashraf, U. Direct product of generalized cubic sets in Hv-LA-semigroups. Sci. Int. 2016, 28, 767–779. [Google Scholar]
- Smarandache, F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability; American Research Press: Rehoboth, NM, USA, 1999. [Google Scholar]
- Smarandache, F. Neutrosophic set, a generalization of the intuitionistic fuzzy set. Int. J. Pure Appl. Math. 2005, 24, 287–297. [Google Scholar]
- Wang, H.; Smarandache, F.; Zhang, Q.Y.; Sunderraman, R. Single Valued Neutrosophic Sets; Infinite Study: New Delhi, India, 2010. [Google Scholar]
- De, S.K.; Beg, I. Triangular dense fuzzy neutrosophic sets. Neutrosophic Sets Syst. 2016, 13, 25–38. [Google Scholar]
- Gulistan, M.; Khan, A.; Abdullah, A.; Yaqoob, N. Complex neutrosophic subsemigroups and ideals. Int. J. Anal. Appl. 2018, 16, 97–116. [Google Scholar]
- Jun, Y.B.; Smarandache, F.; Kim, C.S. Neutrosophic cubic sets. New Math. Nat. Comput. 2017, 13, 41–54. [Google Scholar] [CrossRef]
- Jun, Y.B.; Smarandache, F.; Kim, C.S. P-union and P-intersection of neutrosophic cubic sets. Anal. Univ. Ovidius Constanta 2017, 25, 99–115. [Google Scholar] [CrossRef] [Green Version]
- Gulistan, M.; Yaqoob, N.; Rashid, Z.; Smarandache, F.; Wahab, H. A study on neutrosophic cubic graphs with real life applications in industries. Symmetry 2018, 10, 203. [Google Scholar] [CrossRef]
- Zhan, J.; Khan, M.; Gulistan, M.; Ali, A. Applications of neutrosophic cubic sets in multi-criteria decision-making. Int. J. Uncertain. Quantif. 2017, 7, 377–394. [Google Scholar] [CrossRef]
- Hashim, R.M.; Gulistan, M.; Smrandache, F. Applications of neutrosophic bipolar fuzzy sets in HOPE foundation for planning to build a children hospital with different types of similarity measures. Symmetry 2018, 10, 331. [Google Scholar] [CrossRef]
- Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning Part I. Inf. Sci. 1975, 8, 199–249. [Google Scholar] [CrossRef]
- Herrera, F.; Herrera-Viedma, E.; Verdegay, L. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 1996, 79, 73–87. [Google Scholar] [CrossRef]
- Herrera, F.; Herrera-Viedma, E. linguistic decision analysis: Steps for solving decision problems under linguistic information. Fuzzy Sets Syst. 2000, 115, 67–82. [Google Scholar] [CrossRef]
- Xu, Z.S. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 2004, 166, 19–30. [Google Scholar] [CrossRef]
- Chen, Z.C.; Liu, P.H.; Pei, Z. An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int. J. Comput. Intell. Syst. 2015, 8, 747–760. [Google Scholar] [CrossRef] [Green Version]
- Zhang, H. Linguistic intuitionistic fuzzy sets and application in MAGDM. J. Appl. Math. 2014. [Google Scholar] [CrossRef]
- Fang, Z.B.; Ye, J. Multiple attribute group decision-making method based on linguistic neutrosophic numbers. Symmetry 2017, 9, 111. [Google Scholar] [CrossRef]
- Peng, H.G.; Wang, J.Q.; Cheng, P.F. A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety. Int. J. Mach. Learn. Cybern. 2017, 9, 1053–1068. [Google Scholar] [CrossRef]
- Ye, J. Aggregation operators of neutrosophic linguistic numbers for multiple attribute group decision making. SpringerPlus 2016, 5, 1691. [Google Scholar] [CrossRef] [PubMed]
- Li, Y.Y.; Zhang, H.; Wang, J.Q. Linguistic neutrosophic sets and their application in multicriteria decision-making problems. Int. J. Uncertain. Quantif. 2017, 7. [Google Scholar] [CrossRef]
- Hara, T.; Uchiyama, M.; Takahasi, S.E. A refinement of various mean inequalities. J. Inequal. Appl. 1998, 4, 932025. [Google Scholar] [CrossRef]
- Zadeh, L.A. Fuzzy sets and systems. Int. J. Gen. Syst. 1990, 17, 129–138. [Google Scholar] [CrossRef]
- De Luca, A.; Termini, S. A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 1972, 20, 301–312. [Google Scholar] [CrossRef]
- Kaufmann, A.; Bonaert, A.P. Introduction to the theory of fuzzy subsets-vol. 1: Fundamental theoretical elements. IEEE Trans. Syst. Man Cybern. 1977, 7, 495–496. [Google Scholar] [CrossRef]
- Kosoko, B. Fuzzy entropy and conditioning. Inf. Sci. 1986, 40, 165–174. [Google Scholar] [CrossRef]
- Majumdar, P.; Samanta, S.K. Softness of a soft set: Soft set entropy. Ann. Fuzzy Math. Inf. 2013, 6, 59–68. [Google Scholar]
- Szmidt, E.; Kacprzyk, J. Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 2001, 118, 467–477. [Google Scholar] [CrossRef]
- Yager, R.R. On the measure of fuzziness and negation, Part I: Membership in the unit interval. Int. J. Gen. Syst. 1979, 5, 189–200. [Google Scholar] [CrossRef]
- Ye, J. An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. J. Intell. Fuzzy Syst. 2015, 28, 247–255. [Google Scholar]
- Patrascu, V. The neutrosophic entropy and its five components. Neutrosophic Sets Syst. 2015, 7, 40–46. [Google Scholar]
- Liu, P.; You, X. Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making. PLoS ONE 2018, 13, e0193027. [Google Scholar] [CrossRef] [PubMed]
- Ye, J. Linguistic neutrosophic cubic numbers and their multiple attribute decision-making method. Information 2017, 8, 110. [Google Scholar] [CrossRef]
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Gulistan, M.; Wahab, H.A.; Smarandache, F.; Khan, S.; Shah, S.I.A. Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor. Symmetry 2018, 10, 428. https://doi.org/10.3390/sym10100428
Gulistan M, Wahab HA, Smarandache F, Khan S, Shah SIA. Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor. Symmetry. 2018; 10(10):428. https://doi.org/10.3390/sym10100428
Chicago/Turabian StyleGulistan, Muhammad, Hafiz Abdul Wahab, Florentin Smarandache, Salma Khan, and Sayed Inayat Ali Shah. 2018. "Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor" Symmetry 10, no. 10: 428. https://doi.org/10.3390/sym10100428