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Guan X. Comparison of two types of separation axioms in soft topological spaces1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-212432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Soft separation axioms and their properties are popular topic in the research of soft topological spaces. Two types of separation axioms Ti-I and Ti-II (i = 0, 1, ⋯ , 4) which take single point soft sets and soft points as separated objects have been given in [18] and [30] respectively. In this paper we show that a soft T0-II(T1-II, T2-II, and T4-II respectively) space is a soft T0-I(T1-I, T2-I, and T4-I respectively) space, if the initial universe set X and the parameter set E are sets of two elements. Some examples are given to explain that a soft Ti-I may not to be a soft Ti-II space (i = 0, 1, ⋯ , 4).
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Affiliation(s)
- Xuechong Guan
- College of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, The People’s Republic of China
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Mobini M, Ahn S, Borzooei R. A short note on the category of soft sets. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-220762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Molodtsov, initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. In the paper entitled “The Category of Soft Sets”, we studied the category of soft sets, and we proved that the category of soft sets does not necessarily have products. But, there is a mistake in the proof of this result. In this short note, we give a correct proof for this result.
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Affiliation(s)
- M. Mobini
- Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
| | - S.S. Ahn
- Department of Mathematics Education, Dongguk University, Seoul, Korea
| | - R.A. Borzooei
- Department of Mathematics, Shahid Beheshti University, Tehran, Iran
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Abstract
In this paper, we generalize the concept of extended order algebras in order to get a new algebraic structure called “extended implicative groupoid”. First, we define the notions of pre-weak extended, weak extended, right extended and left extended implicative groupoid. Then we introduce the concept of extended implicative groupoid by using these notions. In addition, the special properties of these structures, such as the existence of MacNeille completion and adjoint product are studied. Finally, we prove that the class of symmetrical associative complete distributive extended implicative groupoids, coincides with complete residuated lattices.
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Affiliation(s)
- E. Sameri
- Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
| | - R.A. Borzooei
- Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
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Category of soft Lie algebra. Soft comput 2020. [DOI: 10.1007/s00500-019-04583-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Khameneh AZ, Kilicman A, Salleh AR. Application of a preference relationship in decision-making based on intuitionistic fuzzy soft sets. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018. [DOI: 10.3233/jifs-17089] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
| | - Adem Kilicman
- Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia
- Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia
| | - Abdul Razak Salleh
- School of Mathematical Sciences, Universiti Kebangsaan Malaysia, Selangor, Malaysia
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Guan X. On central soft sets: Definitions and basic operations1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017. [DOI: 10.3233/jifs-162011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Xuechong Guan
- College of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, The People’s Republic of China
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