New Forms of Fuzzy Filters in Sheffer Stroke Hilbert Algebras

For the purpose of studying the fuzzy version of the filter in Sheffer stroke Hilbert algebra using the concept of fuzzy point, the concept of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo>∈</mml:mo> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>∈</mml:mo> <mml:mo>∨</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -fuzzy filters in the Sheffer stroke Hilbert algebra is introduced and several properties are investigated. The relationship between fuzzy filters and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo>∈</mml:mo> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>∈</mml:mo> <mml:mo>∨</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -fuzzy filters is considered, and characterizations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo>∈</mml:mo> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>∈</mml:mo> <mml:mo>∨</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -fuzzy filters are discussed. The conditions under which <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo>∈</mml:mo> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>∈</mml:mo> <mml:mo>∨</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -fuzzy filters can become fuzzy filters are explored, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo>∈</mml:mo> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>∈</mml:mo> <mml:mo>∨</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -fuzzy filters associated with homomorphisms are studied.