A new pattern of interval-valued fuzzy interior ideals in semigroups. | [Science International • 2014]

Author(s):

1. Hidayat Ullah Khan: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia; Department of Mathematics, University of Malakand, Chakdara, Dir (L), Khyber Pakhtoonkhwa, Pakistan

2. Nor Haniza Sarmin: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia

3. Asghar Khan: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtoonkhwa, Pakistan

4. Faiz Muhammad Khan: Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtoonkhwa, Pakistan

Abstract:

Interval-valued fuzzy sets (advanced generalization of Zadeh`s fuzzy sets) with new type of generalizations can deal with real world problem more precisely then ordinary fuzzy sets in several applied disciplines like Robotics, Fuzzy Control Theory, Computer Science and Error Correcting Cods. In this regard, a more general form of interval-valued fuzzy interior ideals called interval-valued fuzzy interior ideals of types (∈,∈∨ q) and (, qk~) ∈ ∈∨ of semigroups by using the idea of interval-valued generalised quasi-coincidence (qk~) of an interval-valued fuzzy point with an interval-valued fuzzy set is introduced. These new concepts are generalisations of both ordinary interval-valued fuzzy interior ideals and (∈,∈∨ q) -fuzzy interior ideals. Since level sets play a key role in the aforementioned disciplines, therefore level sets are used to link ordinary interior ideals with interval-valued fuzzy interior ideals of types (∈,∈∨ q) and (, qk~) ∈ ∈∨ . It is also investigated that every interval-valued fuzzy interior ideal of a semigroup is an interval-valued (, qk~) ∈ ∈∨ -fuzzy interior ideal and a condition is provided for its converse.

Page(s): 527-535

DOI: DOI not available

Published: Journal: Science International, Volume: 26, Issue: 2, Year: 2014

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