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This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special... more
This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special cases and also handels diverse situations in multiset rewriting transformations. Specifically, this paper unifies and generalizes the works of Parikh(1966), Hickman(1980), Khomenko(2003) and Nazmul(2013).
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Some basic results concerning closure, interior, semi-closure and semi-interior of fuzzy sets are contributed. Fuzzy s-open and fuzzy s-closed mappings are studied further.
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Different notions of Classical Topology which are defined through a -open sets resist a straightforward fuzzification due to the fact that unlike classical counterpart the collection of fuzzy a -open sets does not make a fuzzy topology in... more
Different notions of Classical Topology which are defined through a -open sets resist a straightforward fuzzification due to the fact that unlike classical counterpart the collection of fuzzy a -open sets does not make a fuzzy topology in the sense of Chang. Expecting such interesting deviations, in this paper we study the notion of fuzzy a - continuous mappings. We first give several fundamental properties of fuzzy a -open sets. Using these results different characterizations of fuzzy a -continuous, fuzzy almost a -continuous and fuzzy semi-weakly continuous mappings have been obtained.
In this paper, we define and present several properties of fuzzy a -semiopen, fuzzy a -semiclosed sets; fuzzy a -semiopen and fuzzy a -semiclosed mappings. We also study characterizations of fuzzy a -semicontinuous, fuzzy almost a... more
In this paper, we define and present several properties of fuzzy a -semiopen, fuzzy a -semiclosed sets; fuzzy a -semiopen and fuzzy a -semiclosed mappings. We also study characterizations of fuzzy a -semicontinuous, fuzzy almost a -continuous and fuzzy semiweaky continuous mappings. Moreover, we establish necessary (resp. sufficient) conditions for fuzzy a -semiopen and fuzzy a -semiclosed (resp. fuzzy a -semiclosed, fuzzy a -irresolute) mappings. Keywords: Fuzzy a -semiopen (fuzzy a -semiclosed) sets, Fuzzy a -semicontinuous mappings; Fuzzy a -semiopen (fuzzy a -semiclosed) mappings; fuzzy semiweakly continuous, fuzzy almost a -continuous mappings.
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This work presents a method of multi-criteria decision making (MCDM) using neutrosophic sets. Besides studying some interesting mathematical properties of the method, algorithm viz neut-MCDM is presented. The work also furnishes the... more
This work presents a method of multi-criteria decision making (MCDM) using neutrosophic sets. Besides studying some interesting mathematical properties of the method, algorithm viz neut-MCDM is presented. The work also furnishes the fundamentals of neutrosophic set theory succinctly, to provide a first introduction of neutrosophic sets for the MCDM community. To illustrate the computational details, neut-MCDM has been applied to the problem of university faculty selection against a given set of criteria.
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Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between... more
Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms.
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Notions of core, support, and inversion of a soft set have been defined and studied. Soft approximations are soft sets developed through core and support and are used for granulating the soft space. Membership structure of a soft set has... more
Notions of core, support, and inversion of a soft set have been defined and studied. Soft approximations are soft sets developed through core and support and are used for granulating the soft space. Membership structure of a soft set has been probed in and many interesting properties are presented. We present a new conjecture to solve an optimum choice problem. Our Example 31 presents a case where the new conjecture solves the problem correctly.
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We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four... more
We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton’s method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.
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In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain... more
In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.
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In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of... more
In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of medical diagnosis in medical expert systems.
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We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in... more
We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in product-related spaces. We give necessary conditions for fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions. Moreover, fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions have been characterized via fuzzy-derived (resp., fuzzy-semiderived) sets.
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We define the concept of a mapping on classes of fuzzy soft sets and study the properties of fuzzy soft images and fuzzy soft inverse images of fuzzy soft sets, and support them with examples and counterexamples.
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We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition... more
We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.
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Using intuitionistic fuzzy set theory, Sanchez's approach to medical diagnosis has been applied to the problem of selection of single remedy from homeopathic repertorization. Two types of Intuitionistic Fuzzy Relations... more
Using intuitionistic fuzzy set theory, Sanchez's approach to medical diagnosis has been applied to the problem of selection of single remedy from homeopathic repertorization. Two types of Intuitionistic Fuzzy Relations (IFRs) and three types of selection indices are discussed. I also propose a new repertory exploiting the benefits of soft-intelligence.