(M, N)-soft intersection BL-algebras and their congruences

Area of Science:

• Algebraic structures
• Set theory
• Uncertainty quantification

Background:

• Traditional algebraic tools struggle with inherent uncertainties in data.
• Soft set theory offers a flexible framework for modeling vagueness.
• BL-algebras are a significant class of algebraic structures with applications in logic and computer science.

Purpose of the Study:

• To introduce a new soft algebraic tool for handling uncertainty.
• To generalize existing soft intersection set concepts.
• To explore the properties of (M, N)-SI filters and (M, N)-soft congruences in BL-algebras.

Main Methods:

• Definition and exploration of the (M, N)-soft intersection set.
• Introduction of (M, N)-SI filters within the context of BL-algebras.
• Investigation of characterizations for these new filter structures.
• Focus on (M, N)-soft congruences in BL-algebras.

Main Results:

• A novel generalization of soft intersection sets, termed (M, N)-soft intersection sets, is presented.
• The concept of (M, N)-SI filters in BL-algebras is formally introduced.
• Key characterizations of these filters are established.
• The study specifically addresses (M, N)-soft congruences within BL-algebras.

Conclusions:

• The proposed (M, N)-soft intersection set provides a foundational soft algebraic tool for uncertainty.
• The introduced (M, N)-SI filters and their characterizations offer new insights into BL-algebras.
• This work extends the applicability of soft set theory to algebraic structures for uncertainty modeling.