45 research outputs found

    Neutrosophic Sets and Systems, Vol. 36, 2020

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    2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings

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    The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a commutative Γ-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ-ideals of Γ-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ-ideals and 2-absorbing Γ-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ-ideal of a Γ-ring and 2-absorbing K-vague Γ-ideal of a Γ-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ-ring of R induced by a 2-absorbing vague weakly complete Γ-ideal of a 2-absorbing Γ-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ-ideal

    The Encyclopedia of Neutrosophic Researchers - vol. 3

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    This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

    History and new possible research directions of hyperstructures

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    We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research

    Neutrosophic Theory and its Applications : Collected Papers - vol. 1

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    Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel\u27s dialectics (the last one is based on and only). According to this theory every entity tends to be neutralized and balanced by and entities - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Hence, in one hand, the Neutrosophic Theory is based on the triad , , and . In the other hand, Neutrosophic Theory studies the indeterminacy, labelled as I, with In = I for n ≥ 1, and mI + nI = (m+n)I, in neutrosophic structures developed in algebra, geometry, topology etc. The most developed fields of the Neutrosophic Theory are Neutrosophic Set, Neutrosophic Logic, Neutrosophic Probability, and Neutrosophic Statistics - that started in 1995, and recently Neutrosophic Precalculus and Neutrosophic Calculus, together with their applications in practice. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic). In neutrosophic logic a proposition has a degree of truth (T), a degree of indeterminacy (I), and a degree of falsity (F), where T, I, F are standard or non-standard subsets of ]-0, 1+[. Neutrosophic Probability is a generalization of the classical probability and imprecise probability. Neutrosophic Statistics is a generalization of the classical statistics. What distinguishes the neutrosophics from other fields is the , which means neither nor . And , which of course depends on , can be indeterminacy, neutrality, tie (game), unknown, contradiction, vagueness, ignorance, incompleteness, imprecision, etc

    Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor

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    In this paper, we combined entropy with linguisti neutrosophic cubic numbers and used it in daily life problems related to a corporation that is going to choose an area supervisor, which is the main target of our proposed model

    Innovative types of fuzzy gamma ideals in ordered gamma semigroups

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    The fuzzification of algebraic structures plays an important role in handling many areas of multi-disciplinary research, such as computer science, control theory, information science, topological spaces and fuzzy automata to handle many real world problems. For instance, algebraic structures are particularly useful in detecting permanent faults on sequential machine behaviour. However, the idea of ordered T-semigroup as a generalization of ordered semigroup in algebraic structures has rarely been studied. In this research, a new form of fuzzy subsystem in ordered T-semigroup is defined. Specifically, a developmental platform of further characterizations on ordered T-semigroups using fuzzy subsystems properties and new fuzzified ideal structures of ordered semigroups is developed based on a detailed study of ordered T-semigroups in terms of the idea of belongs to (E) and quasicoincidence with (q) relation. This idea of quasi-coincidence of a fuzzy point with a fuzzy set played a remarkable role in obtaining several types of fuzzy subgroups and subsystems based on three contributions. One, a new form of generalization of fuzzy generalized bi T-ideal is developed, and the notion of fuzzy bi T-ideal of the form (E,E Vqk) in an ordered T-semigroup is also introduced. In addition, a necessary and sufficient condition for an ordered T-semigroup to be simple T-ideals in terms of this new form is stated. Two, the concept of (E,E Vqk)-fuzzy quasi T-ideals, fuzzy semiprime T-ideals, and other characterization in terms of regular (left, right, completely, intra) in ordered T-semigroup are developed. Three, a new fuzzified T-ideal in terms of interior T-ideal of ordered T-semigroups in many classes are determined. Thus, this thesis provides the characterizations of innovative types of fuzzy T-ideals in ordered T-semigroups with classifications in terms of completely regular, intra-regular, for fuzzy generalized bi T-ideals, fuzzy bi T-ideals, fuzzy quasi and fuzzy semiprime T-ideals, and fuzzy interior T-ideals. These findings constitute a platform for further advancement of ordered T-semigroups and their applications to other concepts and branches of algebra

    Characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals

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    In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals (resp. (∈, ∈ ∨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨q)-fuzzy ideals and (∈, ∈ ∨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy ideals (resp. (∈, ∈ ∨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed
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