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Knowledge graph embedding models have gained significant attention in AI research. The aim of knowledge graph embedding is to embed the graphs into a vector space in which the structure of the graph is preserved. Recent works have shown that the inclusion of background knowledge, such as logical rules, can improve the performance of embeddings in downstream machine learning tasks. However, so far, most existing models do not allow the inclusion of rules. We address the challenge of including rules and present a new neural based embedding model (LogicENN). We prove that LogicENN can learn every ground truth of encoded rules in a knowledge graph. To the best of our knowledge, this has not been proved so far for the neural based family of embedding models. Moreover, we derive formulae for the inclusion of various rules, including (anti-)symmetric, inverse, irreflexive and transitive, implication, composition, equivalence, and negation. Our formulation allows avoiding grounding for implication and equivalence relations. Our experiments show that LogicENN outperforms the existing models in link prediction.

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity.

Presently, research and development (R&D) and innovation have been discussed in diverse ways. However, the nexus of subsidy was relatively unexplored in emerging economies. Furthermore, the effects of age are observed to be inconclusive. Considering 1272 selected Chinese manufacturing firms over the period 2007–2017, we employ fixed effect models to examine the effects of Subsidy on R&D and innovation and whether age was a moderating factor. Consistent with the sandwich theoretical proposition, this article found that there exists a significantly transitive relationship between government subsidy, R&D, and innovation. Whereas young firms perform better in the short-term, state-owned firms outweigh the private ones in performance. Subsequently, age alternatively moderates the R&D and innovation relationship from the perspective of subsidy. Though subsidy is a short-term determinant of R&D, it has a long-term relationship with innovation. In contrast, R&D and innovation have short-term effects based on lag computations. Overall, our findings suggest that government subsidy plays a crucial role in R&D and innovation for emerging markets. We discuss our results within the theoretical frameworks of sandwich, the economics of subsidy, and behavioral theory of R&D.

The human action observation network (AON) encompasses brain areas consistently engaged when we observe other's actions. Although the core nodes of the AON are present from childhood, it is not known to what extent they are sensitive to different action features during development. Because social cognitive abilities continue to mature during adolescence, the AON response to socially-oriented actions, but not to object-related actions, may differ in adolescents and adults. To test this hypothesis, we scanned with functional magnetic resonance imaging (fMRI) male and female typically-developing teenagers (n= 28; 13 females) and adults (n= 25; 14 females) while they passively watched videos of manual actions varying along two dimensions: sociality (i.e., directed toward another person or not) and transitivity (i.e., involving an object or not). We found that action observation recruited the same fronto-parietal and occipito-temporal regions in adults and adolescents. The modulation of voxel-wise activity according to the social or transitive nature of the action was similar in both groups of participants. Multivariate pattern analysis, however, revealed that decoding accuracies in intraparietal sulcus (IPS)/superior parietal lobe (SPL) for both sociality and transitivity were lower for adolescents compared with adults. In addition, in the lateral occipital temporal cortex (LOTC), generalization of decoding across the orthogonal dimension was lower for sociality only in adolescents. These findings indicate that the representation of the content of others' actions, and in particular their social dimension, in the adolescent AON is still not as robust as in adults.SIGNIFICANCE STATEMENTThe activity of the action observation network (AON) in the human brain is modulated according to the purpose of the observed action, in particular the extent to which it involves interaction with an object or with another person. How this conceptual representation of actions is implemented during development is largely unknown. Here, using multivoxel pattern analysis (MVPA) of functional magnetic resonance imaging (fMRI) data, we discovered that, while the action observation network is in place in adolescence, the fine-grain organization of its posterior regions is less robust than in adults to decode the abstract social dimensions of an action. This finding highlights the late maturation of social processing in the human brain.

Building on earlier results for regular maps and for orientably regular chiral maps, we classify the non-abelian finite simple groups arising as automorphism groups of maps in each of the 14 Graver–Watkins classes of edge-transitive maps.

In this paper, we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity. Specifically, we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collection of t-norms preserving the transitivity. We characterize them in terms of triangular triplets. Further, the relationship between triangular triplets, the monotonicity of the aggregation function and an appropriate dominance notion is explicitly stated. Special attention is paid to a few classes of transitive fuzzy binary relations that are relevant in the literature. Concretely, we describe, in terms of triangular triplets, those functions that aggregate a collection of fuzzy pre-orders, fuzzy partial orders, relaxed indistinguishability relations, indistinguishability relations and equalities. A surprising relationship between functions that aggregate transitive fuzzy relations into a T M -transitive fuzzy relation and those that aggregate relaxed indistinguishability relations is shown. A few consequences of the new results are also provided for those cases in which all the t-norms of the given collection are the same. Some celebrated results are retrieved as a particular case from the exposed theory.

The Amber rules are well-known and widely used for subtyping iso-recursive types. They were first briefly and informally introduced in 1985 by Cardelli in a manuscript describing the Amber language. Despite their use over many years, important aspects of the metatheory of the iso-recursive style Amber rules have not been studied in depth or turn out to be quite challenging to formalize. This paper aims to revisit the problem of subtyping iso-recursive types. We start by introducing a novel declarative specification that we believe captures the “spirit” of Amber-style iso-recursive subtyping. Informally, the specification states that two recursive types are subtypes if all their finite unfoldings are subtypes . The Amber rules are shown to be sound with respect to this declarative specification. We then derive a sound , complete and decidable algorithmic formulation of subtyping that employs a novel double unfolding rule. Compared to the Amber rules, the double unfolding rule has the advantage of: 1) being modular; 2) not requiring reflexivity to be built in; and 3) leading to an easy proof of transitivity of subtyping. This work sheds new insights on the theory of subtyping iso-recursive types, and the new double unfolding rule has important advantages over the original Amber rules for both implementations and metatheoretical studies involving recursive types. All results are mechanically formalized in the Coq theorem prover. As far as we know, this is the first comprehensive treatment of iso-recursive subtyping dealing with unrestricted recursive types in a theorem prover.

In discussing the strategies of politeness, Brown and lrvinson (1978) claim that treating "the respect for face as norms or values subscribed to by members of a society" (p. 67) is a basic human desire. It seems that all languages have strategies to satisfy this basic human desire. According to Brown & Irvinson, one of the politeness strategies is the use of impersonal constructions, that is, agentless constructions such as passives as in (1). Such impersonal constructions could lead to the assumption that the speaker linguistically indicates his politeness by avoiding expressions which could be interpreted as imposition. Other impersonal constructions involve: dative-agent deletion, as in (2); use of modals with deletion of pronouns to remove traces of person in verbal agreement, as in (3); use of "stativephrasing", i.e. intransitive verbs instead of transitive verbs, as in (a) @rown & Irvinson 1978: 197-L98); and conditionals, as in (5).

Language is undoubtedly the most powerful semiotic resource in every society. Identities, idiosyncrasies, ideologies, and feelings can be evidenced through, and at the same time constructed by, language. Discourse Analysis aims to discover the intentions and meanings in and behind language and how these can (re)construct social structure, relationships, and change. The purpose of this article is to present a Positive Discourse Analysis of the article Que Privaticen toda la Educación by Antonio Morales Riveira. The analysis is based on Systemic Functional Linguistics categories within the appraisal (Martin & White, 2005) and transitivity systems (Martin & Rose, 2007; Goatly, 2000). Conclusions are drawn in terms of the representation of students in the public education system as well as implications for educational and research purposes.

Question Answering Systems (QAS) are rising solutions providing exact and precise answers to natural questions. Duplicate Question Detection (DQD), which aims to reuse previous answers, has shown its ability to improve user experience and reduce significantly the response time. However, few Arabic QAS integrate solutions able to detect duplicate questions in their workflow. In this paper, we build a DQD method based on contextual word representation, question classification and forward/backward structured self attention. First, we extract contextual word representation Embeddings from Language Models (ELMo) to map questions into a vector space. Next, we train two models to classify question embedding according to two taxonomies: Hamza et al. and Li & Roth. Then, we introduce a class label matching step to filter out questions that have different class labels. Finally, we propose a Bidirectional Attention Bidirectional LSTM (BiAttention BiLSTM) model that focuses only on keywords to predict whether a question pair is a duplicate or not. We also apply a data augmentation strategy based on symmetry, reflexivity, and transitivity relations to improve the generalization of our model. Various experimentations are performed to evaluate the impact of question classification and pre-processing step on DQD model. The obtained results show that our model achieves good performances as compared to the baseline results.

Political ideologies and power are shaped by politicians’ manipulation of linguistic features that appeared in their public discourses. Employing transitivity system, this study investigated President Donald Trump’s speech during the 2020 “March for Life†to identify the transitivity processes and to determine how these processes are assimilated in the said discourse. Findings revealed that 126 transitivity processes are dominantly material, relational, and mental. Being the first US president who graced this event, material processes constructed a self-statement of initiatives and efforts in preserving human life and his attack on his political nemesis as threats to the preservation of the value and dignity of life. Relational processes have constructed life-protection ideas by valuing the significance of the children and the unborn. Trump’s feelings toward the dignity of life are shaped by mental processes by his direct association to the public as among the advocates of human life.  Ironically, transitivity processes have shown minimal involvement of women in his speech, contrary to the theme. Data prove that language employed in a public discourse builds power and ideologies that serve as the human framework to understand the mind of the speaker.

We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the shadowing property are expansive in the set of transitive points. This is in contrast with pseudo-Anosov diffeomorphisms of the two-dimensional sphere that are transitive, cw-expansive, satisfy the shadowing property but the dynamical ball in each transitive point contains a Cantor subset. We exhibit examples of countably expansive homeomorphisms that are not finite expansive, satisfy the shadowing property and admits an infinite number of chain-recurrent classes. We further explore the relation between countable and entropy expansivity and prove that for surface homeomorphisms f : S → S f\colon S\to S satisfying the shadowing property and Ω ( f ) = S \Omega (f)=S , both countably expansive and entropy cw-expansive are equivalent to being topologically conjugate to an Anosov diffeomorphism.

Knowledge of transitive relationships between items can contribute to learning the order of a set of stimuli from pairwise comparisons. However, cognitive mechanisms of transitive inferences based on rank order remain unclear, as are relative contributions of reward associations and rule-based inference. To explore these issues, we created a conflict between rule- and reward-based learning during a serial ordering task. Rhesus macaques learned two lists, each containing five stimuli that were trained exclusively with adjacent pairs. Selection of the higher-ranked item resulted in rewards. “Small reward” lists yielded two drops of fluid reward, whereas “large reward” lists yielded five drops. Following training of adjacent pairs, monkeys were tested on novels pairs. One item was selected from each list, such that a ranking rule could conflict with preferences for large rewards. Differences between the corresponding reward magnitudes had a strong influence on accuracy, but we also observed a symbolic distance effect. That provided evidence of a rule-based influence on decisions. RT comparisons suggested a conflict between rule- and reward-based processes. We conclude that performance reflects the contributions of two strategies and that a model-based strategy is employed in the face of a strong countervailing reward incentive.

The join query, which finds matching pairs from two object sets, is a fundamental operation in computer systems and helps to solve many real problems, e.g., entity resolution. In this paper, we address the problem of join queries by leveraging crowdsourcing to obtain matching relationships. The goal is to minimize the monetary cost while maintaining high quality of query results. However, existing approaches focused on finding matching pairs from a single object set and assumed the existence of prior knowledge, which is not applicable in real applications. We propose a cost-effective crowdsourced join query framework that minimizes the overall monetary cost by reducing the monetary cost of labeling single pairs and the amount of comparison pairs. Specifically, we first propose a novel two-level confidence-based labeling model that minimizes the cost for labeling a single pair with confidence guarantee. This model crowdsources easy-judging pairs to ordinary workers, and asks for skilled workers who may charge more than ordinary workers to compare only hard-judging pairs. Statistical estimations are used to aggregate crowdsourcing results with 1 − α confidence. Then, we propose a transitivity-based query scheme that minimizes the number of comparison pairs on the basis of transitive relations. Guided by the principle of eagerly identifying matching pairs, especially matching pairs from a single set, our scheme carefully designs the processing order of pairs in order to make full use of transitivities to infer new labels. The results of our extensive experiments demonstrate that the proposed framework can save much more monetary cost while assuring the accuracy of results.

Woolford (2015) distinguishes two types of ergativity—active and object shift—whereas ergativity is not governed by transitivity in any of the languages she examines. However, several languages remain unclassified in Woolford’s typology, among them two Nakh-Daghestanian languages, Archi and Tsez. Woolford inquires whether they belong to the active or object shift type or whether ergativity in these languages depends on transitivity. This article presents data from another Nakh-Daghestanian language, Tabasaran, and shows that this language is best analyzed as an example of traditional transitivity-based ergativity.

The development of crowdsourcing marketplaces has leveraged the power of human intelligence into tackling computationally challenging problems. Pareto-optimal queries become more and more popular in subtle and comprehensive decision support due to the increasingly complex comparison criteria, e.g., partial orders. However, none of previous work focused on efficient crowdsourced Pareto-optimal queries over partial orders with minimum monetary cost and quality guarantee with a confidence level. In this paper, we propose a cost-efficient framework to find Pareto-optimal objects with minimum monetary cost and quality guarantee with a confidence level. We first propose a dynamic-status judgment model based on Student's t-distribution, which gives a confidence interval of the judgment to ensure the quality of pairwise comparisons while minimizing the number of crowdsourcers required for each pairwise comparison. We then propose a filtering-verification scheme that takes full advantage of transitivity to avoid unnecessary crowdsourcing comparisons, which significantly reduces the number of crowdsourcing pairwise comparisons. The results of our extensive experiments demonstrate that the dynamic-status judgment model requires a small number of crowdsourcers for a pairwise comparison while maintaining the accuracy, and the filtering-verification scheme can reduce the number of pairwise comparisons by 40% in average.

Previous studies on adolescent friendship network formation emphasize the roles played by individual characteristics, structural opportunities, and endogenous tie formation processes. This study extends previous studies in three major aspects: 1) developing and testing theories of status differential (i.e., friendship ties are more likely to run from low status subjects to high status subjects than vice versa) and differential homophily (i.e., homophily is stronger between high status subjects than between low status subjects) through modeling tie-mixing effects of individual characteristics, 2) including qualitative analyses to elaborate selected mechanisms, and 3) comparing selected friendship patterns between China and the U.S. The extended framework is applied to analyzing survey data obtained from 4,094 students in six middle schools in China. The results show that friendship ties are unevenly distributed by individual characteristics (status differential is confirmed for five of the seven characteristics examined), there is significant tie homophily (stronger homophily among high status subjects than among low status subjects is observed for five of the seven characteristics examined with three of them being statistically significant), and endogenous tie formation processes such as reciprocity, transitivity, and preferential attachment are strongly present. Although some of these patterns are common to both China and the U.S., there are also notable differences between the two. Lastly, I discuss the implications and limitations of this study.

The consistency and implication relation of chaotic properties of $ p $-periodic discrete system and its induced autonomous discrete system are obtained. The chaotic properties discussed involve several types of transitivity and some stronger forms of sensitivity in the sense of Furstenberg families.

Despite considerable advancement in the study of network evolution, three basic limitations are common to the data collected: (1) examining a small number of networks, (2) not observing networks from scratch, (3) not collecting time-stamped, continuous records of all interactions among all members of groups. Here, we avoid these limitations by observing all aggressive interactions leading to network formation from the moment of introduction among all members of 45 groups of four individuals each in three species of animals: chickens, cichlid fish, and mice. We apply several recently developed methods for the visualization and analysis of network evolution to these unique datasets. We discover, first, that network evolution is a remarkably dynamic process across all three species: networks do not evolve to specific structures and then remain in those configurations. Instead, we find dynamic stability in which many groups continually return to a general class of structures. Second, we find considerable similarity across species in the pathways that the groups take through different possible network configurations as they evolve. Third, we show that transitive component triads are more stable than intransitive ones. Fourth, we track the evolution of individual ranks within groups and discover that many individuals do not have stable positions. Finally, we discuss fundamental questions that our findings raise for the study of networks in both animals and humans.

We determine for which Coxeter types the associated small quotient of the 2 2 -category of Soergel bimodules is finitary and, for such a small quotient, classify the simple transitive 2 2 -representations (sometimes under the additional assumption of gradability). We also describe the underlying categories of the simple transitive 2 2 -representations. For the small quotients of general Coxeter types, we give a description for the cell 2 2 -representations.

Seymour’s Second Neighborhood Conjecture (SSNC) asserts that every finite oriented graph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood. Such a vertex is called a Seymour vertex. In this paper, we prove that SSNC holds for some particular cases of m -free digraphs (digraphs having no directed cycles with length at most m ). A digraph D = ( V , E ) is k -transitive if for any directed u v -path of length k , we have ( u , v ) ∈ E . For k ≤ 6 , we prove that every k -transitive digraph with no sink (vertex of out-degree zero) has at least two Seymour vertices. A digraph D = ( V , E ) is k -anti-transitive if for any directed u v -path of length k , we have ( u , v ) ∉ E . For k ≤ 4 , we prove that every k -anti-transitive digraph with no sink has at least two Seymour vertices. In k -transitive and k -anti-transitive digraphs, the Seymour vertices found are explicitly identified.

Let H be a digraph possibly with loops and D a digraph without loops with a coloring of its arcs c : A ( D ) → V ( H ) ( D is said to be an H -colored digraph). A directed path W in D is said to be an H -path if and only if the consecutive colors encountered on W form a directed walk in H . A subset N of vertices of D is said to be an H -kernel if (1) for every pair of different vertices in N there is no H -path between them and (2) for every vertex u in V ( D ) ∖ N there exists an H -path in D from u to N . Under this definition an H -kernel is a kernel whenever A ( H ) = 0 ; an H -kernel is a kernel by monochromatic paths whenever A ( H ) = { ( u , u ) : u ∈ V ( H ) } ; an H -kernel is a properly colored kernel whenever H has no loops and an H -kernel is a kernel by rainbow paths whenever H has no directed cycles. Let k be an integer, with k ≥ 2 . D is k -quasi-transitive if for every pair of vertices u and v of D , the existence of a directed path of length k from u to v implies that { ( u , v ) , ( v , u ) } ∩ A ( D ) ≠ 0 . In Galeana-Sanchez and O’Reilly-Regueiro (2013), in Delgado-Escalante et al. (2018) and in Galeana-Sanchez and Rojas-Monroy (2006) the authors establish sufficient conditions to guarantee the existence of kernels by monochromatic paths in 3-quasi-transitive digraphs, the existence of properly colored kernels in 2-quasi-transitive digraphs and the existence of kernels in 2-quasi-transitive digraphs, respectively. In this paper we investigate the problem of the existence of H -kernels in quasi-transitive and in 3-quasi-transitive digraphs by means of a partition of V ( H ) . We give some examples which show that each hypothesis in the main result for quasi-transitive digraphs is tight.

In mass communication, the material process use makes it easy to lay emphasis on the participants’ actions, events, and circumstances of their occurrence, while mental process contributes to insisting on their psychological and emotional states. As for indirect speech, it characterizes the version always used by messengers, public announcers, journalists, and reporters. This study aims to analyze Transitivity and Indirect Speech in clauses ingrained and identified in some passages taken from Helon Habila’s Oil On Water (2011). One of the major principles of Systemic Functional Linguistics is that the exploration of the Transitivity properties (processes, participants, and circumstances) in a text leads to draw conclusions about the question -“who does what to whom, under what circumstances?”? In order to deliver the set objectives, the ongoing study specifically draws on the principles of experiential meaning to get data from the selected extracts and, focuses on describing the clauses containing reported speeches. By following the mixed research methods guiding principles, this research work has generated some data which enable to come up with a conclusion on the psychological and psychosomatic states of the participants as well as on the assigned status adopted by some characters. That correlates them to reporters and journalists. This research work has enabled me to develop another. This paper has made it easy to have another view about Helon Habila’s messages and the way they are conveyed throughout his novel.

In the Post Covid-19 Era, taking the advantage of shaping a true, active, and the positive national image is of strategic significance for China to transform the fake national image constructed by other countries, and also for its development in the future. Based on the corpus of a white paper Fighting Covid-19: China in Action, the paper is intended to focus on the transitivity system to examine how China constructs a positive national image in the fight against the pandemic. The findings show that China has constructed four kinds of national images in the fight, including; the persistent image of solidarity and bravery; the responsible image of duty-shouldering and challenge-facing; the humanism image of respecting human lives and rights; the diplomatic image of dedication and commitment. By virtue of self-constructing national image, it is conducive to telling Chinese stories, spreading Chinese image, and sharing Chinese experience in the battle of fighting the Covid-19 pandemic.

We extend a result on existence of Walrasian equilibria in He and Yannelis (Econ Theory 61:497–513, 2016) by replacing the compactness assumption on consumption sets made there by the standard assumption that these sets are closed and bounded from below. This provides a positive answer to a question explicitly raised in He and Yannelis (Econ Theory 61:497–513, 2016). Our new equilibrium existence theorem generalizes many results in the literature as we do not require any transitivity or completeness or continuity assumption on preferences, initial endowments need not be in the interior of the consumption sets, preferences may be interdependent and price-dependent, and no monotonicity or local non satiation is needed for any of the agents.

We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.

The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. If the Sheffer operation is also commutative, then the induced binary relation is antisymmetric. Moreover, commutative Sheffer groupoids form a congruence distributive variety. We characterize symmetry, antisymmetry and transitivity of binary relations by identities and quasi-identities satisfied by an assigned Sheffer operation. The concepts of twist products of relational systems and of Kleene relational systems are introduced. We prove that every directed relational system can be embedded into a directed relational system with involution via the twist product construction. If the relation in question is even transitive, then the directed relational system can be embedded into a Kleene relational system. Any Sheffer operation assigned to a directed relational system $${\mathbf {A}}$$ A with involution induces a Sheffer operation assigned to the twist product of $${\mathbf {A}}$$ A .

We present a complete description of strongly regular graphs admitting a distance-transitive group of automorphisms. Parts of the list have already appeared in the literature; however, this is the first time that the complete list appears in one place. The description is complemented, where possible, with the discussion of the corresponding distance-transitive groups and some further properties of the graphs. We also point out an open problem.

Recent studies on colonial discourse have demonstrated that the speeches of freedom activists in colonial Africa served as sites of resistance. One key text type that has, however, been neglected in the critical literature on the discourse of emancipation is the national anthem of colonised states. To fill this gap, the present study examines the discursive enactment of resistance in the anthems of former British colonies in Africa, focusing on the transitivity framework in systemic functional linguistics. Semantic and structural parallelisms across the anthems are identified as evidence of a collective memory, a cultural trauma reconfigured and reconstituted to reclaim a positive identity and project a desirable postcolonial future. They also foreground the motif of freedom and legitimise the African as the owner of the reclaimed territory. These procedures articulate an anti-imperialist and anti-establishment stance that provides hope, strength and encouragement to an oppressed group. This paper extends the scholarship on the discursive enactment of resistance by focusing attention on a context underexplored in the literature. It also illustrates the (re)construction of relevant ideologies in national anthems to stimulate desirable, progressive attitudes among citizenry in African states. The paper is furthermore significant to decolonial research and highlights the role of language in political decolonisation processes.

In this paper, we present a complete list of connected arc-transitive graphs of square-free order with valency 11. The list includes the complete bipartite graph [Formula: see text], the normal Cayley graphs of dihedral groups and the graphs associated with the simple group [Formula: see text] and [Formula: see text], where [Formula: see text] is a prime.

In this paper, the notion of a fuzzy geometric space is introduced. Some structures related to it are studied and connections of them are investigated. By using fuzzy blocks of a fuzzy geometric space, the concept of strongly transitivity of fuzzy geometric spaces is defined and studied. Finally, it is proved that the relation [Formula: see text] is transitive on fuzzy hypergroups, by associating strongly transitivity fuzzy geometric spaces to fuzzy hypergroups.