Towards probabilistic partial metric spaces: Diagonals between distance distributions

Jialiang He; Hongliang Lai; Lili Shen

doi:10.1016/j.fss.2018.07.011

Towards probabilistic partial metric spaces: Diagonals between distance distributions

Jialiang He, Hongliang Lai, Lili Shen

Sichuan University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the quantaloid of diagonals between distance distributions, which is expected to establish the categorical foundation of probabilistic partial metric spaces. Observing that the quantale of distance distributions w.r.t. an arbitrary continuous t-norm is non-divisible, we precisely characterize diagonals between distance distributions, and prove that one-step functions are the only distance distributions on which the set of diagonals coincides with the generated down set.

Original language	English
Pages (from-to)	99-119
Number of pages	21
Journal	Fuzzy Sets and Systems
Volume	370
DOIs	https://doi.org/10.1016/j.fss.2018.07.011
State	Published - 1 Sep 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Funding

The first author acknowledges the support of National Natural Science Foundation of China (No. 11771311 ). The second author acknowledges the support of National Natural Science Foundation of China (No. 11771310 ). The third author acknowledges the support of National Natural Science Foundation of China (No. 11701396 ) and the Fundamental Research Funds for the Central Universities (No. YJ201644 ). The first author acknowledges the support of National Natural Science Foundation of China (No. 11771311). The second author acknowledges the support of National Natural Science Foundation of China (No. 11771310). The third author acknowledges the support of National Natural Science Foundation of China (No. 11701396) and the Fundamental Research Funds for the Central Universities (No. YJ201644). The authors are grateful to the anonymous referees for their helpful remarks and suggestions.

Funders	Funder number
National Natural Science Foundation of China	11771311, 11771310, 11701396
Fundamental Research Funds for the Central Universities	YJ201644

Keywords

Continuous t-norm
Enriched category
Partial metric space
Probabilistic partial metric space
Quantale
Quantaloid

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abstract = "The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the quantaloid of diagonals between distance distributions, which is expected to establish the categorical foundation of probabilistic partial metric spaces. Observing that the quantale of distance distributions w.r.t. an arbitrary continuous t-norm is non-divisible, we precisely characterize diagonals between distance distributions, and prove that one-step functions are the only distance distributions on which the set of diagonals coincides with the generated down set.",

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Towards probabilistic partial metric spaces: Diagonals between distance distributions

Abstract

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Keywords

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