Lattice-valued convergence associated with CNS spaces

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

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“…(2) The convergence theory associated with STrL-Top is given in [14]. (3) The convergence theory associated with CNS is developed in [29].…”

Section: Definition 3 ([14])mentioning

confidence: 99%

Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Jin

Jiang

2019

Mathematics

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“…Since the most common feature in decision information is the ambiguity of the information. Therefore, some related researches based on fuzzy information have been proposed [4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Multi-Attribute Decision Making Based on Probabilistic Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators

2019

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Take the third-party logistics providers (3PLs) as an example, according to the characteristics of correlation between attributes in multi-attribute decision-making, two Choquet aggregation operators adoping probabilistic neutrosophic hesitation fuzzy elements (PNHFEs) are proposed to cope with the situations of correlation among criterions. This measure not only provides support for the correlation phenomenon between internal attributes, but also fully concerns the incidental uncertainty of the external space. Our goal is to make it easier for decision makers to cope with this uncertainty, thus we establish the notion of probabilistic neutrosophic hesitant fuzzy Choquet averaging (geometric) (PNHFCOA, PNHFCOG) operator. Based on this foundation, a method for aggregating decision makers’ information is proposed, and then the optimal decision scheme is obtained. Finally, an example of selecting optimal 3PL is given to demonstrate the objectivity of the above-mentioned standpoint.

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“…Since Chang [1] introduced fuzzy set theory to topology, fuzzy topology and its related theories have been widely investigated such as [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The degree approach that equips fuzzy topology and its related structures with some degree description is also an essential character of fuzzy set theory.…”

Section: Introductionmentioning

confidence: 99%

Degrees of L-Continuity for Mappings between L-Topological Spaces

Xiu

2019

Mathematics

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By means of the residual implication on a frame L, a degree approach to L-continuity and L-closedness for mappings between L-cotopological spaces are defined and their properties are investigated systematically. In addition, in the situation of L-topological spaces, degrees of L-continuity and of L-openness for mappings are proposed and their connections are studied. Moreover, if L is a frame with an order-reversing involution , where b = b → ⊥ for b ∈ L, then degrees of L-continuity for mappings between L-cotopological spaces and degrees of L-continuity for mappings between L-topological spaces are equivalent.

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Lattice-valued convergence associated with CNS spaces

Cited by 34 publications

References 29 publications

Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Multi-Attribute Decision Making Based on Probabilistic Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators

Degrees of L-Continuity for Mappings between L-Topological Spaces

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