Abstract

We introduce the notion of soft filters in residuated lattices and investigate their basic properties. We investigate relations between soft residuated lattices and soft filter residuated lattices. The restricted and extended intersection (union), ∨ and ∧-intersection, cartesian product, and restricted and extended difference of the family of soft filters residuated lattices are established. Also, we consider the set of all soft sets over a universe set U and the set of parameters P with respect to U, SoftP(U), and we study its structure.

Highlights

  • In economics, engineering, environmental science, medical science, and social science, there are complicated problems which to solve them methods in classical mathematics may not be successfully used because of various uncertainties arising in these problems

  • Mathematical theories such as probability theory, fuzzy set theory [1], rough set theory [2, 3], vague set theory [4], and the interval mathematics [5] were established by researchers to modelling uncertainties appearing in the above fields

  • ISRN Algebra lattices and some basic notions relevant to soft set theory will be used and we prove that SoftP(U) is a bounded commutative BCK-algebra with respect to suitable operations

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Summary

Introduction

In economics, engineering, environmental science, medical science, and social science, there are complicated problems which to solve them methods in classical mathematics may not be successfully used because of various uncertainties arising in these problems. Soft set relations are defined and studied in [12] and some new operations are introduced in [13]. Zhan and Jun [15] studied soft BL-algebras on fuzzy sets. Residuated lattices were introduced in 1924 by Krull in [19] who discussed decomposition into isolated component ideals After him, they were investigated by Ward and Dilworth in 1930s, as the main tool in the abstract study of ideal theory in rings. ISRN Algebra lattices and some basic notions relevant to soft set theory will be used and we prove that SoftP(U) is a bounded commutative BCK-algebra with respect to suitable operations.

A Brief Excursion into Residuated Lattices and Soft Sets
Soft Residuated Lattices and Soft Filters
Conclusion
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