FuzzyVis: Fuzzy Ontology Exploration

• FuzzyVis is an interactive ontology exploration system that leverages fuzzy ontology embeddings to interpret composite queries approximately.
• It offers a visual interface enabling users to build queries with logical operators and navigate complex structures using treemaps and network graphs.
• The system computes graded, vector-based representations of ontology concepts, allowing intuitive retrieval even when exact matches are absent.

Searching arXiv for the named system and closely related visualization work to ground the article in current papers. arXiv_search(query="FuzzyVis ontology exploration fuzzy ontology embeddings visual query building", max_results=5) FuzzyVis is a proof-of-concept system for interactive ontology exploration that combines a visual interface for browsing and building queries without formal syntax with a fuzzy ontology embedding model that interprets user-built concepts approximately rather than only exactly (Zhurov et al., 11 Aug 2025). It is designed for large, complex ontologies in domains such as biomedicine, where keyword search is often too shallow and formal query languages such as SPARQL require users to understand both ontology structure and query syntax. Its central mechanism is visual concept construction: users select and combine existing ontology concepts with conjunction, disjunction, and negation, and the resulting composite concept is matched against the ontology through fuzzy membership-based embeddings that support graded, concept-level similarity search (Zhurov et al., 11 Aug 2025).

1. Definition and problem setting

FuzzyVis is designed as a web-based ontology exploration system for users who need more expressive querying than keyword search but do not want to write SPARQL or understand the ontology’s internal logical structure in detail (Zhurov et al., 11 Aug 2025). The system targets large ontologies that are difficult to navigate visually and conceptually, particularly in domains such as biomedicine, computational biology, law, and engineering (Zhurov et al., 11 Aug 2025). The motivating claim is that ontology use is often an exploratory learning problem: users need to discover landmarks, routes, and neighborhoods in an ontology rather than merely execute exact formal retrieval (Zhurov et al., 11 Aug 2025).

The system addresses several specific limitations of existing access modes. The data state that large ontologies are hard to navigate, keyword search is too shallow because labels may not match user vocabulary, and formal query languages are too demanding because users must know syntax and structure (Zhurov et al., 11 Aug 2025). The same source also states that users often have vague, evolving, partial, or even internally conflicting information needs, and that the concept sought may not exist explicitly in the ontology as a named class (Zhurov et al., 11 Aug 2025). In response, FuzzyVis allows users to define a new composite concept from existing ontology concepts and retrieve the most similar primitive concepts in the ontology (Zhurov et al., 11 Aug 2025).

A canonical example is the query

$$Q \equiv \texttt{Slurred speech} \sqcap \texttt{Dysphagia} \sqcap \neg \texttt{Abnormality of the immune system}.$$

The data explicitly note that this concept is not explicitly named in HPO, but FuzzyVis can still interpret it as a fuzzy concept and retrieve relevant known concepts such as Pseudobulbar paralysis or Abnormal esophagus physiology (Zhurov et al., 11 Aug 2025). This suggests that the system is intended less as an exact logical reasoner than as an exploratory interface for approximate semantic retrieval.

2. System architecture

FuzzyVis is implemented as a web application with a front-end/back-end split (Zhurov et al., 11 Aug 2025). The front-end is built with HTML5, CSS, JavaScript, and D3.js v7 for interactive visualization (Zhurov et al., 11 Aug 2025). The back-end is implemented in Python and exposed through a Flask API (Zhurov et al., 11 Aug 2025). The architecture includes four major back-end components: an ontology loader, an ontology database, a vector database, and a query resolver (Zhurov et al., 11 Aug 2025).

The ontology loader loads ontologies in .owl or .ttl format, parses them, stores them, and computes metadata such as subtree sizes and number of children (Zhurov et al., 11 Aug 2025). The ontology database is implemented using OwlReady2, while the vector database stores embeddings for primitive concepts and is implemented with Chroma in the prototype (Zhurov et al., 11 Aug 2025). The query resolver receives user-built composite queries, computes a composite concept embedding, compares it with stored primitive concept embeddings, and returns ranked results (Zhurov et al., 11 Aug 2025).

The front-end contains several interface regions. The primary visualization area supports different ontology views such as treemaps, nested lists, and network graphs (Zhurov et al., 11 Aug 2025). A header bar provides keyword search, switching between loaded ontologies, and ontology loading or upload (Zhurov et al., 11 Aug 2025). Visualization controls allow adjustment of depth, tiling ratio, scaling, visibility, normalization, focus mode, and similarity staining (Zhurov et al., 11 Aug 2025). Separate concept panels support collection, pinning, and concept inspection, while query-building panels support assembling concepts and logical operators, submitting composite queries, and inspecting ranked results (Zhurov et al., 11 Aug 2025).

The end-to-end pipeline is described explicitly. Ontology ingestion is followed by embedding preparation, storage of ontology structure and vectors, visual exploration, query construction, query resolution, top-$k$ similarity search, and presentation of ranked results (Zhurov et al., 11 Aug 2025). The data also state that the front-end dynamically loads only the ontology portions needed for current interaction and discards unused ones to reduce memory usage and maintain responsiveness (Zhurov et al., 11 Aug 2025).

3. Fuzzy ontology embedding model

The system’s main technical contribution is a fuzzy ontology embedding model in which ontology concepts are represented by vectors of membership degrees over a fixed interpretation domain (Zhurov et al., 11 Aug 2025). Let $O$ be an ontology and let

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$

be a fuzzy interpretation of $O$, where

$\Delta^\mathcal{I} = \{x_1, \ldots, x_d\}.$

Each concept $C$ is interpreted as a fuzzy membership function

$\mu_C^\mathcal{I} : \Delta^\mathcal{I} \to [0,1].$

The embedding of a primitive concept $C$ is then

$$\mathbf{v}_C = [\mu_C^\mathcal{I}(x_1), \mu_C^\mathcal{I}(x_2), \ldots, \mu_C^\mathcal{I}(x_d)] \in [0,1]^d.$$

The paper characterizes these as fuzzy membership-based embeddings, emphasizing that each coordinate has semantic meaning because it corresponds to a domain element and stores a degree of membership (Zhurov et al., 11 Aug 2025).

The data state that multiple mechanisms may be used to obtain the fuzzy interpretation $k$0, including fuzzyDL, DeLorean, and FALCON (Zhurov et al., 11 Aug 2025). FALCON is singled out because it learns fuzzy interpretations via sampling and optimization and allows control over the sample size, which determines

$k$1

the embedding dimension (Zhurov et al., 11 Aug 2025). The source also notes that the system is agnostic to the particular reasoner, so long as it yields a coherent fuzzy interpretation approximately satisfying ontology axioms (Zhurov et al., 11 Aug 2025).

For hierarchical ontologies, the paper proposes a constructive method called $k$2-embeddings (Zhurov et al., 11 Aug 2025). In this setting, for each new domain element $k$3, a leaf concept $k$4 is chosen uniformly at random and assigned

$k$5

For every other leaf concept $k$6, membership is determined by graph distance to the lowest common ancestor: $k$7 where $k$8 is a decay parameter (Zhurov et al., 11 Aug 2025). For an internal concept $k$9 with children $O$0, membership is defined recursively by fuzzy union: $O$1 The paper argues that this construction satisfies taxonomic subsumption in the fuzzy sense because parent membership is at least child membership under fuzzy union (Zhurov et al., 11 Aug 2025).

This representation differs from standard latent ontology or knowledge graph embeddings in that the coordinates are not arbitrary learned features. A plausible implication is that the model is intended to retain semantic inspectability at the coordinate level, even though the paper does not present a quantitative comparison against latent-only embedding families.

4. Query model and compositional semantics

FuzzyVis supports a query model in which users create new concept expressions by combining primitive ontology concepts with conjunction, disjunction, and negation (Zhurov et al., 11 Aug 2025). The background semantics are given in terms of fuzzy concepts with membership functions. For concepts $O$2 and $O$3 with membership functions $O$4 and $O$5,

$O$6

$O$7

$O$8

where $O$9 is a continuous t-norm, $$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$0 is its corresponding t-conorm, and $$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$1 is a negation function (Zhurov et al., 11 Aug 2025). The paper explicitly mentions product, Gödel, and Łukasiewicz t-norms, and also gives standard negation

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$2

and the probabilistic-sum t-conorm example

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$3

These operators are transferred into embedding space through element-wise vector operations (Zhurov et al., 11 Aug 2025).

For conjunction,

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$4

for disjunction,

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$5

and for negation,

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$6

With the product t-norm,

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$7

and with standard negation,

$$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$8

A query embedding $$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$9 is computed recursively from the syntax tree of the concept expression (Zhurov et al., 11 Aug 2025).

Given a user query $O$0, the system compares $O$1 to primitive concept embeddings using cosine similarity and returns the top-$O$2 concepts (Zhurov et al., 11 Aug 2025). The source does not print the cosine formula explicitly, but states that cosine similarity is the scoring function and that ranking is by descending cosine similarity (Zhurov et al., 11 Aug 2025). It also emphasizes that this is concept-level approximate retrieval rather than exact logical entailment. The paper further notes that the system does not prevent users from constructing logically awkward or classically inconsistent concepts, and presents this as a strength for exploratory search because such queries may still yield meaningful approximate matches in fuzzy embedding space (Zhurov et al., 11 Aug 2025).

5. Visual interface and interaction model

The interface is designed so that users can explore and query without writing formal logic syntax directly (Zhurov et al., 11 Aug 2025). The interaction repertoire described in the data includes browsing ontology structure visually, selecting concepts, dragging concepts into collections, pinning concepts, dragging concepts into the query builder, composing with AND, OR, and NOT, submitting a query, inspecting ranked results, and reusing results in new queries (Zhurov et al., 11 Aug 2025). The query builder thus functions as a concept construction workspace rather than a textual query editor.

The paper emphasizes the nested treemap as the main illustrative primary visualization (Zhurov et al., 11 Aug 2025). The system can display only concepts within adjustable distance of a selected concept, support selection to refocus on subtrees, and mark concepts through pinning (Zhurov et al., 11 Aug 2025). It also offers a focus mode using a discrete Cartesian or fisheye-like distortion: mousing over a concept expands it, its subtree becomes visible in more detail, users can drill down recursively, multiple loci can be locked, and a focus locus can be transformed into another local view (Zhurov et al., 11 Aug 2025). This is intended to reduce clutter while preserving context.

The data explicitly mention “partial search” in two senses: lexical partial label search through the header and semantic approximation through fuzzy query embeddings (Zhurov et al., 11 Aug 2025). Ranked results are displayed with similarity scores and expandable details, and can be dragged back into future queries (Zhurov et al., 11 Aug 2025). The interface also supports a similarity stain mode, in which concepts in the main visualization are colored according to their relevance to the current query (Zhurov et al., 11 Aug 2025). This makes graded relevance visually explicit rather than confining it to a ranked list.

A typical exploration workflow is described as follows: load an ontology; explore visually using treemap, list, or graph; use keyword search to jump to landmarks; inspect details of encountered concepts; pin and collect promising concepts; drag them into the query builder; combine them with fuzzy operators; submit the query; inspect top-ranked similar concepts; navigate to returned concepts in the ontology; and refine the query (Zhurov et al., 11 Aug 2025). In the HPO scenario, the user searches for “speech,” finds Slurred speech, browses toward Abnormality of the nervous system, finds Dysphagia, collects Abnormality of the immune system for exclusion, builds

$O$3

and obtains matches including Pseudobulbar paralysis, Pseudobulbar signs, and Abnormal esophagus physiology (Zhurov et al., 11 Aug 2025).

6. Case studies, positioning, and limitations

The paper presents usage scenarios and case studies rather than a large-scale quantitative benchmark (Zhurov et al., 11 Aug 2025). The detailed scenario uses the Human Phenotype Ontology, and the paper also mentions broader applicability to GO, Sequence Ontology, Disease Ontology, MeSH, legal ontologies, and hierarchical ontologies such as the Plant Ontology (Zhurov et al., 11 Aug 2025). The main example uses an $O$4-embedding with

$O$5

and product t-norm for conjunction, the corresponding t-conorm for disjunction, and standard negation (Zhurov et al., 11 Aug 2025). A follow-up query adds a second negation: $O$6 The paper describes this as somewhat illogical in strict terms, but still useful in the fuzzy embedding regime (Zhurov et al., 11 Aug 2025).

The system is positioned between ontology browsers and formal query systems. The paper contrasts FuzzyVis with Protégé/WebProtégé, OWLViz, WebVOWL, OntoGraf, Jambalaya, and OntoTrix, which are described as mainly supporting browsing, inspection, and structure visualization rather than user-defined fuzzy composite concepts and approximate concept-level matching (Zhurov et al., 11 Aug 2025). It also contrasts the approach with prior ontology embedding methods such as translation-based models, RDF2Vec, OWL2Vec, EL Embeddings, BoxE, and ConeE, arguing that these are generally static and not designed for user-defined interactive concept construction with negation and disjunction (Zhurov et al., 11 Aug 2025). This suggests that the paper’s strongest novelty claim lies in runtime compositionality: define a new concept now, compute its vector now, retrieve results now (Zhurov et al., 11 Aug 2025).

The design also emphasizes computational efficiency. Primitive embeddings are precomputed offline, composite query embeddings are built by simple vectorized fuzzy operations, and retrieval is top-$O$7 similarity search over a vector database (Zhurov et al., 11 Aug 2025). The prototype uses Chroma, though the paper notes that vector search can also be delegated to optimized systems such as FAISS or Qdrant (Zhurov et al., 11 Aug 2025). It states that queries resolve nearly instantly in the prototype (Zhurov et al., 11 Aug 2025).

The paper is explicit that FuzzyVis is a prototype. It does not report a formal user study, retrieval accuracy benchmarks, latency benchmarks, ablation experiments, or comparative quantitative evaluation (Zhurov et al., 11 Aug 2025). The stated limitations include scalability for very large ontologies, a limited visual repertoire, limited result triage, restricted ontology expressiveness beyond hierarchical subsumption structures, and the absence of extensive evaluation (Zhurov et al., 11 Aug 2025). Future work includes optimizing performance and scalability, adding more visualizations, improving result organization, testing alternative embedding techniques, and supporting more expressive ontologies with richer axioms (Zhurov et al., 11 Aug 2025).

A potential source of confusion is terminological rather than substantive: several nearby systems in the literature combine “fuzzy” or “fuzz” with “visualization,” but they solve different problems. FMViz visualizes byte-level AFL mutations (Hussain et al., 2021), FuzzSplore provides visual analytics for feedback-driven fuzzing (Fioraldi et al., 2021), FuseVis interprets image fusion CNNs by per-pixel saliency visualization (Kumar et al., 2020), and “A Visual Quality Index for Fuzzy C-Means” proposes a visual aid for choosing cluster counts in fuzzy clustering (Oztürk et al., 2018). FuzzyVis, by contrast, is specifically an ontology exploration system based on fuzzy ontology embeddings and visual query building (Zhurov et al., 11 Aug 2025).