Families of Fuzzy Sets and Lattice Isomorphisms Preparation

Subject Areas : Transactions on Fuzzy Sets and Systems

John  Mordeson ¹ (Department of Mathematics, Creighton University, Omaha, Nebraska USA. )
Sunil  Mathew ² (Department of Mathematics, National Institute of Technology Calicut, Calicut, India.)

Received: 2024-03-12 Accepted : 2024-05-07 Published : 2024-05-07

Keywords: Modern slavery, Government response, Vulnerability, Lattice isomorphisms, Fuzzy sets.,

Abstract :

In this paper, we discuss how theoretical results from one family of fuzzy sets can be carried over immediately to another family of fuzzy sets by the use of lattice isomorphisms. We also show that these families can occur naturally and that applications may not necessarily be carried over using these isomorphisms. We illustrate this using techniques from the study of human trafficking and its analysis using mathematics of uncertainty. We also consider the new definition of fuzzy set provided by Trillas and de Soto.

References:

[1] Atannasov KT. Intuitionistic Fuzzy Sets, Theory and Applications. Springer; 1999.
[2] Ibrahim HZ, Alshammari I. n,m-rung orthopair fuzzy sets with applications to multicritera decision making. IEEE Access. 2022; 10: 99562-99572. DOI: 10.1109/ACCESS.2022.3207184
[3] Klement EP, Mesiar R. L-fuzzy sets and isomorphic lattices: Are the new results really new?. Mathematics. 2018; 6(9): 146. DOI: https://doi.org/10.3390/math6090146
[4] Mordeson JN, Mathew S. Mathematics of Uncertainty for Coping with World Challenges: Climate Change, World Hunger, Modern Slavery, Coronavirus, Human Trafficking. Springer; 2021.
[5] Mordeson JN, Mathew S. Sustainable Development Goals: Analysis by Mathematics of Uncertainty. Springer; 2021.
[6] Saaty TL. Relative measurement and its generalization in decision making: Why pairwise comparisons are central in mathematics for the measurement of intangible factors; the analytic hierarchy process. RACSAM-Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas.
2008; 102 (2): 251-318. DOI: https://doi.org/10.1007/BF03191825
[7] SDG Index and Dashboard Report 2017. Global Responsibilities, International Spillovers in Achieving the Goals, Bertelsmann Stiftung. Sustainable Development Solutions Network.
[8] Smarandach F. Neutrosophy: Neutrosophic Probability, Set and Logic: Analytic Synthesis and Synthetic Analysis. American Research Press; 1998.
[9] The Walk Free Foundation. Global Slavery Index 2018. https://reliefweb.int/report [Accessed 16th April 2024].
[10] Trafficking in Persons: Global Patterns, The United Nations Office for Drugs and Crime, Trafficking Persons Citation Index. https://www.unodc.org/unodc/data-and-analysis/glotip.html
[11] Trillas E, De Soto AR. On the search for speculations. New Mathematics and Natural Computation. 2022; 18(01): 9-18. DOI: https://doi.org/10.1142/S1793005722500028
[12] Trillas E, De Soto AR. On a new view of a fuzzy set. Transactions on Fuzzy Sets and Systems. 2023; 2(1): 92-100. DOI: 10.30495/tfss.2022.1971064.1051
[13] Trillas E, Garcia-Honrado I. A reflection on dialectic synthesis. New Mathematics and Natural Computation. 2019; 15(01): 31-46. DOI: https://doi.org/10.1142/S1793005719500029
[14] Yager RR. Pythagorean membership grades in multi-criteria decision making. IEEE Transactions on fuzzy systems. 2014; 22(4): 958-965. DOI: 10.1109/TFUZZ.2013.2278989