13 found
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  1. Soft Neutrosophic Ring and Soft Neutrosophic Field.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Munazza Naz - 2014 - Neutrosophic Sets and Systems 3:53-59.
    In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper we (...)
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  2.  99
    Neutrosophic Bi-LA-Semigroup and Neutrosophic N-LASemigroup.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Munazza Naz - 2014 - Neutrosophic Sets and Systems 4:19-24.
    In this paper we define neutrosophic bi-LAsemigroup and neutrosophic N-LA-semigroup. Infact this paper is an extension of our previous paper neutrosophic left almost semigroup shortly neutrosophic LAsemigroup. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic bi-LA-semigroup, neutrosophic N-LAsemigroup and display many properties of them (...)
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  3. Generalization of Neutrosophic Rings and Neutrosophic Fields.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Luige Vladareanu - 2014 - Neutrosophic Sets and Systems 5:9-14.
    In this paper we present the generalization of neutrosophic rings and neutrosophic fields. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of notions which are related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic birings, neutrosophic N-rings with neutrosophic bifields and neutrosophic N-fields and display many properties of them in this paper.
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  4. Soft Neutrosophic Group.Muhammad Shabir, Mumtaz Ali, Munazza Naz & Florentin Smarandache - 2013 - Neutrosophic Sets and Systems 1:13-25.
    In this paper we extend the neutrosophic group and subgroup to soft neutrosophic group and soft neutrosophic subgroup respectively. Properties and theorems related to them are proved and many examples are given.
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  5. A New Approach to Multi-Spaces Through the Application of Soft Sets.Mumtaz Ali, Florentin Smarandache, Said Broumi & Muhammad Shabir - 2015 - Neutrosophic Sets and Systems 7:34-39.
    Multi-space is the notion combining different fields in to a unifying field, which is more applicable in our daily life. In this paper, we introduced the notion of multi-soft space which is the approximated collection of the multi-subspaces of a multi-space . Further, we defined some basic operations such as union, intersection, AND, OR etc. We also investigated some properties of multi-soft spaces.
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  6. Neutrosophic Left Almost Semigroup.Mumtaz Ali, Muhammad Shabir, Munazza Naz & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 3:18-28.
    In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties (...)
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  7. Soft Neutrosophic Loops and Their Generalization.Mumtaz Ali, Christopher Dyer, Muhammad Shabir & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 4:55-75.
    Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic loop,soft neutosophic biloop, soft neutrosophic N -loop with the discuission of some of their characteristics. We also introduced a new type of soft neutrophic loop, the so called soft strong neutrosophic loop which is of pure neutrosophic character. This notion also found in all the other corresponding notions of soft neutrosophic thoery. We also given some of (...)
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  8. Soft Neutrosophic Bi-LA-semigroup and Soft Neutrosophic N-LA-semigroup.Mumtaz Ali, Florentin Smarandache & Muhammad Shabir - 2014 - Neutrosophic Sets and Systems 5:45-58.
    Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic biLA-semigroup,soft neutosophic sub bi-LA-semigroup, soft neutrosophic N -LA-semigroup with the discuission of some of their characteristics. We also introduced a new type of soft neutrophic bi-LAsemigroup, the so called soft strong neutrosophic bi-LAsemigoup which is of pure neutrosophic character. This is also extend to soft neutrosophic strong N-LA-semigroup. We also given some of their properties of this (...)
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  9.  98
    Soft Neutrosophic Bigroup and Soft Neutrosophic N-Group.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Munazza Naz - 2014 - Neutrosophic Sets and Systems 2:55-81.
    Soft neutrosophic group and soft neutrosophic subgroup are generalized to soft neutrosophic bigroup and soft neutrosophic N-group respectively in this paper. Different kinds of soft neutrosophic bigroup and soft neutrosophic N-group are given. The structural properties and theorems have been discussed with a lot of examples to disclose many aspects of this beautiful man made structure.
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  10.  86
    Generalization of Soft Neutrosophic Rings and Soft Neutrosophic Fields.Mumtaz Ali, Florentin Smarandache, Luige Vladareanu & Muhammad Shabir - 2014 - Neutrosophic Sets and Systems 6:35-41.
    In this paper we extend soft neutrosophic rings and soft neutrosophic fields to soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic bifields and soft neutrosophic N-fields. We also extend soft neutrosophic ideal theory to form soft neutrosophic biideal and soft neutrosophic N-ideals over a neutrosophic biring and soft neutrosophic N-ring . We have given examples to illustrate the theory of soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic fields and soft neutrosophic N-fields and display many properties of these.
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  11.  16
    Soft Relations Applied to the Substructures of Quantale Module and Their Approximation.Saqib Mazher Qurashi, Khushboo Zahra Gilani, Muhammad Shabir, Muhammad Gulzar & Ashraful Alam - 2022 - Complexity 2022:1-12.
    This research article offers a study on a new relation of rough sets and soft sets with an algebraic structure quantale module by using soft reflexive and soft compatible relations. The lower approximation and upper approximation of subsets of quantale module are utilized by aftersets and foresets. As a sequel of this relation, different characterizations of rough soft substructures of quantale modules are obtained. To ensure the results, soft reflective and soft compatible relations are focused and these are interpreted by (...)
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  12. SOFT NEUTROSOPHIC ALGEBRAIC STRUCTURES AND THEIR GENERALIZATION, Vol. 1.Florentin Smarandache, Mumtaz Ali & Muhammad Shabir - 2014 - Columbus, OH, USA: Educational Publisher.
    In this book the authors introduced the notions of soft neutrosophic algebraic structures. These soft neutrosophic algebraic structures are basically defined over the neutrosophic algebraic structures which means a parameterized collection of subsets of the neutrosophic algebraic structure. For instance, the existence of a soft neutrosophic group over a neutrosophic group or a soft neutrosophic semigroup over a neutrosophic semigroup, or a soft neutrosophic field over a neutrosophic field, or a soft neutrosophic LA-semigroup over a neutrosophic LAsemigroup, or a soft (...)
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  13.  96
    SOFT NEUTROSOPHIC ALGEBRAIC STRUCTURES AND THEIR GENERALIZATION, Vol. 2.Florentin Smarandache, Mumtaz Ali & Muhammad Shabir - 2014 - Columbus, OH, USA: Educational Publisher.
    In this book we define some new notions of soft neutrosophic algebraic structures over neutrosophic algebraic structures. We define some different soft neutrosophic algebraic structures but the main motivation is two-fold. Firstly the classes of soft neutrosophic group ring and soft neutrosophic semigroup ring defined in this book is basically the generalization of two classes of rings: neutrosophic group rings and neutrosophic semigroup rings. These soft neutrosophic group rings and soft neutrosophic semigroup rings are defined over neutrosophic group rings and (...)
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