An isomorphic approach of fuzzy soft lattices to fuzzy soft Priestley spaces
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An isomorphic approach of fuzzy soft lattices to fuzzy soft Priestley spaces Muhammad Shabir1 · Shakreen Kanwal1 · Shahida Bashir2 · Rabia Mazhar2 Received: 14 May 2020 / Revised: 4 September 2020 / Accepted: 7 October 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract The main purpose of this paper is to establish a relation between fuzzy soft lattices and fuzzy soft Priestley spaces. We have proved that each bounded distributive lattice of fuzzy soft sets is isomorphic to the lattice of all clopen upsets of a Priestley space. For this reason, we have defined fuzzy soft upsets, fuzzy soft downsets, fuzzy soft filters, fuzzy soft ideals and fuzzy soft Priestley space. To endorse the above relation, we have proved some related results. Keywords Fuzzy soft topological spaces · Fuzzy soft Priestley spaces · Fuzzy soft lattices Mathematics Subject Classification 54A10 · 54G12
1 Introduction The theory of fuzzy sets was developed by Zadeh (1965) in 1965. It is an appropriate theory for dealing with uncertainties occurring while solving complicated problems of real world, with which classical methods become unable to work. It was specifically designed to represent mathematical uncertainty and vagueness to provide tools for dealing with intrinsic imprecision of many problems. This theory is applied on logic, set theory, groupoids, semigroup theory, group theory, ring theory, semiring theory etc. Extensive applications of fuzzy set theory have been found in artificial intelligence, computer science, control engineering,
Communicated by Regivan Hugo Nunes Santiago.
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Shahida Bashir [email protected]; [email protected] Muhammad Shabir [email protected]; [email protected] Shakreen Kanwal [email protected] Rabia Mazhar [email protected]
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Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
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Department of Mathematics, University of Gujrat, Gujrat, Pakistan 0123456789().: V,-vol
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expert system, management science, operation research and many others (Masulli et al. 2007; Tamir et al. 2015). As time passes, some researchers became aware about fuzzy set theory that there is nonexistence of parameterization tool. In 1999, Molodtsov removed this inadequacy by the development of soft set theory (Molodtsov 1999). He presented parameterization tools to handle several unsureness occurring in decision making and medical diagnosis problems. It has opened new horizons for researchers to work in diverse areas. A lot of work has been done on soft set theory because of using parameterization tools. Soft set theory has many applications in many fields; for example, the smoothness of functions, game theory, Riemann integration, Perron integration (Molodtsov 1999; Molodtsov et al. 2006; Naz and Shabir 2013; Shabir and Naz 2011; Tripathy et al. 2018; Yuksel et al. 2013). Maji et al. (2003) defined several operations on soft sets. In 2009, Ali et al. (2009) also defined some operations on soft
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