Pith Number

pith:Z54CRAAI

pith:2026:Z54CRAAI2UHZ2JS2R3IX7JDDYG

not attested not anchored not stored refs pending

Roughness and entropy measures of a soft set

Sankar K. Pal, Santanu Acharjee

Soft sets receive two roughness measures and six entropy measures defined within their native framework.

arxiv:2605.14560 v1 · 2026-05-14 · math.GM

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\usepackage{pith}
\pithnumber{Z54CRAAI2UHZ2JS2R3IX7JDDYG}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We introduce two distinct roughness measures and six entropy measures for soft sets and systematically investigate their properties using both theoretical analysis and computational techniques. The proposed framework is shown to be novel with respect to roughness characterization.

C2weakest assumption

The new measures preserve the foundational principles of soft set theory as established by Molodtsov and provide a genuinely novel roughness characterization distinct from classical rough sets.

C3one line summary

Two roughness measures and six entropy measures are introduced for soft sets, with properties analyzed theoretically and computationally, and compared to classical rough sets.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:05.603700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf78288008d50f9d265a8ed17fa463c18757a808bd9f80dcd605ccf2351d0558

Aliases

arxiv: 2605.14560 · arxiv_version: 2605.14560v1 · doi: 10.48550/arxiv.2605.14560 · pith_short_12: Z54CRAAI2UHZ · pith_short_16: Z54CRAAI2UHZ2JS2 · pith_short_8: Z54CRAAI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z54CRAAI2UHZ2JS2R3IX7JDDYG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cf78288008d50f9d265a8ed17fa463c18757a808bd9f80dcd605ccf2351d0558

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e8faf66c87040984e264dc67a43f3a5964bc7c909ac55d69e74c32c0a8f6e19",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-05-14T08:33:37Z",
    "title_canon_sha256": "ce43e9c474614f798f6b40cc6aeecf77f5a386771ec84573f9dee8becc468e12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14560",
    "kind": "arxiv",
    "version": 1
  }
}