Deductive systems and filters of Sheffer stroke Hilbert algebras based on the bipolar-valued fuzzy set environment

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Keywords:

Sheffer stroke Hilbert algebra, filter, (bipolar-valued fuzzy) deductive system, (normal) bipolar-valued fuzzy filter.

Abstract

The notion of bipolar-valued fuzzy set is used to treat the filter and deductive system in Sheffer stroke Hilbert algebras. The concepts of bipolar valued fuzzy filter and bipolar-valued fuzzy deductive system are introduced and related properties are investigated. Conditions under which the bipolar-valued fuzzy set can be a bipolar-valued fuzzy filter are explored. Characterizations of the bipolar-valued fuzzy filter are examined. A bipolar-valued fuzzy filter is built using a filter. To consider the nomality of bipolar-valued fuzzy filter, the notion of normal bipolar-valued fuzzy filter is introduced and related properties are investigated. The method of normalizing the bipolar-valued fuzzy filter is addressed, and we will see what the normal bipolar-valued fuzzy filter looks like.

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Published

2024-01-25

How to Cite

Hee Sik Kim, Seok-Zun Song, Sun Shin Ahn, & Young Bae Jun. (2024). Deductive systems and filters of Sheffer stroke Hilbert algebras based on the bipolar-valued fuzzy set environment. Journal of Computational Analysis and Applications (JoCAAA), 32(1), 192–210. Retrieved from http://eudoxuspress.com/index.php/pub/article/view/52

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