Bisimulations in fuzzy social network analysis

Ignjatović, Jelena; Ćirić, Miroslav; Stanković, Ivan

doi:10.2991/ifsa-eusflat-15.2015.59

Cited by 15 publications

(15 citation statements)

References 28 publications

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“…Following [8], Ignjatović et at. [16] gave an algorithm with the complexity O(ln 5 ) for computing the greatest fuzzy bisimulation between two fuzzy social networks, where n is the number of nodes in the networks and l is the number of different fuzzy values appearing during the computation. Later Micić et at.…”

Section: Related Workmentioning

confidence: 99%

“…For example, in the terminology of FLTSs, vertices, edges, edge labels and vertex labels represent states, transitions, actions and atomic properties of states, respectively. Recall that fuzzy bisimulations have been defined and studied for fuzzy automata [7,8], weighted/fuzzy social networks [12,16], fuzzy modal logics [13,20] and fuzzy description logics [21,22,24]. We give below their definition, which is based on [21,20] and equivalent to the one in [13] when |Σ E | = 1 and the graphs are image-finite.…”

Section: Fuzzy Bisimulationsmentioning

confidence: 99%

“…Crisp bisimulations have been defined and studied for fuzzy transition systems [3,4,31,29,30], weighted automata [9], fuzzy modal logics [11,13,17,10] and fuzzy description logics [21]. Fuzzy bisimulations have been defined and studied for fuzzy automata [7,8], weighted/fuzzy social networks [12,16], fuzzy modal logics [13,20] and fuzzy description logics [21,22,24].…”

Section: Introductionmentioning

confidence: 99%

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Computing the Fuzzy Partition Corresponding to the Greatest Fuzzy Auto-Bisimulation of a Fuzzy Graph-Based Structure

Nguyen¹

2021

Preprint

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Fuzzy graph-based structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models, fuzzy social networks and fuzzy interpretations in fuzzy description logics are useful in various applications. Given two states, two actors or two individuals x and x ′ in such structures G and G ′ , respectively, the similarity degree between them can be defined to be Z(x, x ′ ), where Z is the greatest fuzzy bisimulation between G and G ′ with respect to some t-norm-based fuzzy logic. Such a similarity measure has the Hennessy-Milner property of fuzzy bisimulations as a strong logical foundation. A fuzzy bisimulation between a fuzzy structure G and itself is called a fuzzy auto-bisimulation of G. The greatest fuzzy auto-bisimulation of an image-finite fuzzy graph-based structure is a fuzzy equivalence relation. It is useful for classification and clustering.In this paper, we design an efficient algorithm with the complexity O((m log l + n) log n) for computing the fuzzy partition corresponding to the greatest fuzzy auto-bisimulation of a finite fuzzy labeled graph G under the Gödel semantics, where n, m and l are the number of vertices, the number of non-zero edges and the number of different fuzzy degrees of edges of G, respectively. Our notion of fuzzy partition is novel, defined only for finite sets with respect to the Gödel t-norm, with the aim to facilitate the computation of the greatest fuzzy auto-bisimulation. By using that algorithm, we also provide an algorithm with the complexity O(m • log l • log n + n 2 ) for computing the greatest fuzzy bisimulation between two finite fuzzy labeled graphs under the Gödel semantics. This latter algorithm is better (has a lower complexity order) than the previously known algorithms for the considered problem. Our algorithms can be restated for the other mentioned fuzzy graphbased structures.

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Section: Related Workmentioning

confidence: 99%

Section: Fuzzy Bisimulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computing the Fuzzy Partition Corresponding to the Greatest Fuzzy Auto-Bisimulation of a Fuzzy Graph-Based Structure

Nguyen¹

2021

Preprint

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“…Ignjatović et at. [13] introduced and studied fuzzy simulations and bisimulations between fuzzy social networks in a way similar to [5]. In [10] Fan introduced fuzzy bisimulations and crisp bisimulations for some fuzzy modal logics under the Gödel semantics.…”

Section: Introductionmentioning

confidence: 99%

Computing Fuzzy Bisimulations for Fuzzy Structures Under the Gödel Semantics

Nguyen

Tran

2021

IEEE Trans. Fuzzy Syst.

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Fuzzy structures such as fuzzy automata, fuzzy transition systems, weighted social networks and fuzzy interpretations in fuzzy description logics have been widely studied. For such structures, bisimulation is a natural notion for characterizing indiscernibility between states or individuals. There are two kinds of bisimulations for fuzzy structures: crisp bisimulations and fuzzy bisimulations. While the latter fits to the fuzzy paradigm, the former has also attracted attention due to the application of crisp equivalence relations, for example, in minimizing structures. Bisimulations can be formulated for fuzzy labeled graphs and then adapted to other fuzzy structures. In this article, we present an efficient algorithm for computing the partition corresponding to the largest crisp bisimulation of a given finite fuzzy labeled graph. Its complexity is of order O((m log l + n) log n), where n, m and l are the number of vertices, the number of nonzero edges and the number of different fuzzy degrees of edges of the input graph, respectively. We also study a similar problem for the setting with counting successors, which corresponds to the case with qualified number restrictions in description logics and graded modalities in modal logics. In particular, we provide an efficient algorithm with the complexity O((m log m + n) log n) for the considered problem in that setting.

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“…For fuzzy structures like fuzzy automata and fuzzy labeled transition systems (FLTSs), researchers have studied both crisp simulations [7]- [11] and fuzzy simulations [8], [12]- [15]. Crisp/fuzzy bisimulations have also been studied for fuzzy structures by a considerable number of researchers [7], [9], [12], [14], [16]- [26]. However, as far as we know, only the work [11] has concerned crisp directed simulations for fuzzy structures.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Crisp Simulations and Crisp Directed Simulations between Fuzzy Labeled Transition Systems by Using Fuzzy Modal Logics

Nguyen¹,

Nguyen²

2021

Preprint

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We formulate and prove logical characterizations of crisp simulations and crisp directed simulations between fuzzy labeled transition systems with respect to fuzzy modal logics that use a general t-norm-based semantics. The considered logics are fragments of the fuzzy propositional dynamic logic with the Baaz projection operator. The logical characterizations concern preservation of positive existential (respectively, positive) modal formulas under crisp simulations (respectively, crisp directed simulations), as well as the Hennessy-Milner property of such simulations.

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Bisimulations in fuzzy social network analysis

Cited by 15 publications

References 28 publications

Computing the Fuzzy Partition Corresponding to the Greatest Fuzzy Auto-Bisimulation of a Fuzzy Graph-Based Structure

Computing the Fuzzy Partition Corresponding to the Greatest Fuzzy Auto-Bisimulation of a Fuzzy Graph-Based Structure

Computing Fuzzy Bisimulations for Fuzzy Structures Under the Gödel Semantics

Characterizing Crisp Simulations and Crisp Directed Simulations between Fuzzy Labeled Transition Systems by Using Fuzzy Modal Logics

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