Abstract
In this paper, the concepts of fuzzy translation to fuzzy H-ideals in BCK/BCI-algebras are introduced. The notion of fuzzy extensions and fuzzy mul-tiplications of fuzzy H-ideals with several related properties are investigated. Also,the relationships between fuzzy translations, fuzzy extensions and fuzzy multiplica-tions of fuzzy H-ideals are investigated.DOI : http://dx.doi.org/10.22342/jims.21.1.200.45-58
Highlights
Fuzzy set theory, which was introduced by Zadeh [24], is the oldest and most widely reported component of present day soft computing, allowing the design of more flexible information processing systems [18], with applications in different areas, such as artificial intelligence, multiagent systems, machine learning, knowledge discovery, information processing, statistics and data analysis, system modeling, control system, decision sciences, economics, medicine and engineering, as shown in the recent literature collected by Dubois et al [2, 3]
Routine calculations show that μ is a fuzzy H-ideal of X
If μ is a fuzzy H-ideal of X, the fuzzy α-translation μTα of μ is a fuzzy H-ideal of X, for all α ∈ [0, ⊤]
Summary
Fuzzy set theory, which was introduced by Zadeh [24], is the oldest and most widely reported component of present day soft computing, allowing the design of more flexible information processing systems [18], with applications in different areas, such as artificial intelligence, multiagent systems, machine learning, knowledge discovery, information processing, statistics and data analysis, system modeling, control system, decision sciences, economics, medicine and engineering, as shown in the recent literature collected by Dubois et al [2, 3]. In 1999, Khalid and Ahmad [12] introduced fuzzy H-ideals in BCI-algebras. Lee et al [13] and Jun [11] discussed fuzzy translations, fuzzy extensions and fuzzy multiplications of fuzzy subalgebras and ideals in BCK/BCI-algebras. They investigated relations among fuzzy translations, fuzzy extensions and fuzzy multiplications. Fuzzy translations, fuzzy extensions and fuzzy multiplications of fuzzy H-ideals in BCK/BCI-algebras are discussed. Fuzzy extensions and fuzzy multiplications of fuzzy H-ideals in BCK/BCIalgebras are investigated
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