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Cardinal Numbers of Fuzzy Sets 被引量:8
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作者 李洪兴 罗承忠 +1 位作者 汪培庄 袁学海 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第3期101-107,共7页
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ... Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers. 展开更多
关键词 Fuzzy relations Fuzzy mappings the cardinal numbers of fuzzy sets
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The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers 被引量:2
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作者 张诚一 党平安 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第1期78-81, ,共4页
In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.
关键词 Fuzzy mappings the cardinal numbers of fuzzy sets
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Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers 被引量:1
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作者 Ramon Carbó-Dorca 《Applied Mathematics》 2022年第6期538-543,共6页
A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the preci... A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;M<sub>N</sub>]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers. 展开更多
关键词 Mersenne numbers Recursive Generation of Natural numbers Mersenne Natural number Intervals Counting the number of Prime numbers in Mersenne Natural Intervals Correlation between Prime number Set Cardinalities and Mersenne numbers Extended Twin Prime number Conjecture
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P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees
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作者 Mailing Zhao Jun Ye 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第9期1219-1230,共12页
In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrate... In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting. 展开更多
关键词 Orthopair neutrosophic number set p-indeterminate vector similarity measure p-indeterminate cosine measure p-indeterminate Dice measure p-indeterminate Jaccard measure decision making
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Polysurfacic Tori or Kideas Inspired by the Möbius Strip Topology
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作者 Emmanuel Cadier Anaxhaoza 《Advances in Pure Mathematics》 2023年第9期543-551,共9页
Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the n... Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the number of sides or surfaces separated by edges, can vary in a non-trivial manner depending on the degree of twisting during the revolution. We use the term “Kideas” to specifically denote these polysurfacic tori, and we represent the number of sides (referred to as “facets”) of the original polygon followed by a point, while the number of facets from which the torus is twisted during its revolution is indicated. We then explore the use of concave regular polygons to generate Kideas. We finally give acceleration for the algorithm for calculating the set of prime numbers. 展开更多
关键词 Heavenly Things Topology Euclidian Geometry Möbius Strip Emmanuel’s Tori YiBoLong’s Tori Cadier’s Tori Möbius Tori Polysurfacic Tori Kideas The Keys KideaCross KideaStar Churros Algorithm for Calculating the Set of Prime numbers P The Last Found Element of P
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Binding Numbers for Fractional ID-k-factor-critical Graphs
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作者 Si Zhong ZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第1期181-186,共6页
LetG be a graph,and k≥2 be a positive integer.A graph G is fractional independentset-deletable k-factor-critical(in short,fractional ID-k-factor-critical),if G I has a fractional k-factor for every independent set ... LetG be a graph,and k≥2 be a positive integer.A graph G is fractional independentset-deletable k-factor-critical(in short,fractional ID-k-factor-critical),if G I has a fractional k-factor for every independent set I of G.The binding number bind(G)of a graph G is defined as bind(G)=min|NG(X)||X|:=X V(G),NG(X)=V(G).In this paper,it is proved that a graph G is fractional ID-k-factor-critical if n≥6k 9 and bind(G)〉(3k 1)(n 1)kn 2k+2. 展开更多
关键词 Graph binding number independent set fractionalk-factor fractional ID-k-factor-criti-cal
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Matching Preclusion for Augmented k-ary n-cubes
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作者 ZHANG Xinyuan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2015年第1期15-24,共10页
The (conditional) matching preclusion number of a graph is the minimum number of edges whose deletion leaves a resulting graph (with no isolated vertices) that has neither perfect matchings nor almost perfect matc... The (conditional) matching preclusion number of a graph is the minimum number of edges whose deletion leaves a resulting graph (with no isolated vertices) that has neither perfect matchings nor almost perfect matchings. In this paper, we find this number and classify all optimal sets for the augmented k-ary n-cubes with even k ≥ 4. 展开更多
关键词 perfect matching augmented k-ary n-cubes (conditional) matching preclusion set/number
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