{ "paper_id": "2020", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T07:24:10.087674Z" }, "title": "Fuzzy Logic for Vagueness Management in Referring Expression Generation 1", "authors": [ { "first": "N", "middle": [], "last": "Mar\u00edn", "suffix": "", "affiliation": { "laboratory": "", "institution": "UGR University of Granada", "location": { "postCode": "18071", "settlement": "Granada", "country": "Spain" } }, "email": "" }, { "first": "G", "middle": [], "last": "Rivas-Gervilla", "suffix": "", "affiliation": { "laboratory": "", "institution": "UGR University of Granada", "location": { "postCode": "18071", "settlement": "Granada", "country": "Spain" } }, "email": "" }, { "first": "D", "middle": [], "last": "S\u00e1nchez", "suffix": "", "affiliation": { "laboratory": "", "institution": "UGR University of Granada", "location": { "postCode": "18071", "settlement": "Granada", "country": "Spain" } }, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "In this work we overview some of the contributions regarding the use of Fuzzy Logic in referring expression generation. We also discuss recent advances that can help to overcome the arguments in the literature against the use of Fuzzy Logic in Natural Language Generation.", "pdf_parse": { "paper_id": "2020", "_pdf_hash": "", "abstract": [ { "text": "In this work we overview some of the contributions regarding the use of Fuzzy Logic in referring expression generation. We also discuss recent advances that can help to overcome the arguments in the literature against the use of Fuzzy Logic in Natural Language Generation.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "Different types of vagueness are present in natural language employed for human communication (van Deemter, 2010) . In this paper we are concerned with the kind of vagueness related to concepts, words, and linguistic expressions that allow for borderline cases in which fulfilment is not clear (van Deemter, 2010) . This kind of vagueness cannot be properly represented and managed using classical logics, hence alternative tools are necessary (van Deemter, 2010) . A widely employed tool for dealing with this kind of vagueness is Fuzzy Logic (Kacprzyk and Zadrozny, 2010) .", "cite_spans": [ { "start": 94, "end": 113, "text": "(van Deemter, 2010)", "ref_id": "BIBREF38" }, { "start": 294, "end": 313, "text": "(van Deemter, 2010)", "ref_id": "BIBREF38" }, { "start": 444, "end": 463, "text": "(van Deemter, 2010)", "ref_id": "BIBREF38" }, { "start": 544, "end": 573, "text": "(Kacprzyk and Zadrozny, 2010)", "ref_id": "BIBREF19" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "Fuzzy Logic has been used in Natural Language Generation (NLG) for different purposes Ramos-Soto et al., 2016) : modeling the semantics of concepts and expressions, uncertainty representation and quality measurement, among others. In this paper we focus on the use of Fuzzy Logic for the aforementioned purposes in the setting of referring expression generation (REG), one of the crucial tasks of NLG (Gatt and Krahmer, 2018) . We also briefly discuss recent contributions that enlarge the available Fuzzy Logic toolbox with new capabilities, solving some issues 1 Corresponding author: Gustavo Rivas-Gervilla. Authors appear in alphabetical order. This work has been partially supported by the Spanish Ministry of Science, Innovation and Universities and the European Regional Development Fund -ERDF (Fondo Europeo de Desarrollo Regional -FEDER) under project PGC2018-096156-B-I00, and by the Spanish Ministry of Education, Culture and Sports grant FPU16/05199. that have been argued in order to disregard the use of Fuzzy Logic in NLG.", "cite_spans": [ { "start": 86, "end": 110, "text": "Ramos-Soto et al., 2016)", "ref_id": "BIBREF32" }, { "start": 401, "end": 425, "text": "(Gatt and Krahmer, 2018)", "ref_id": "BIBREF14" }, { "start": 563, "end": 564, "text": "1", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "Given a set of objects O with properties in P, and given o \u2208 O, the objective of the REG task is to provide a linguistic expression able to identify o within O. It is usual to distinguish two steps in REG: extraction and expression . In the first one, the semantics of the referring expression is represented by means of some knowledge representation formalism, typically a formal logic. In the second one, an appropriate sentence in natural language is provided.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Referring expression generation", "sec_num": "2" }, { "text": "In this paper we are concerned only with the extraction phase in which, in its most basic form, a referring expression is a conjunction of properties in P, usually represented by the set of properties that appear in that conjunction. More general structures can be employed involving negation and disjunction, as well as generalized quantifiers. Other generalizations to the problem are the reference to sets of objects, the use of relational properties represented by mathematical relations between objects, the use of collective properties defined for sets of objects, and the use of gradual concepts (Krahmer and Van Deemter, 2012) . The latter are the object of our interest here.", "cite_spans": [ { "start": 603, "end": 634, "text": "(Krahmer and Van Deemter, 2012)", "ref_id": "BIBREF20" } ], "ref_spans": [], "eq_spans": [], "section": "Referring expression generation", "sec_num": "2" }, { "text": "Vagueness due to borderline/intermediate cases appears typically because of the use of gradual concepts in language 2 . One example is the concept large regarding the size of an object since, within the set of all possible sizes, some values match the concept large, some others do not match the concept at all, whilst the rest are intermediate cases that match the concept to a certain extent. Hence, fulfilment of a concept becomes a matter of degree.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Gradual concepts are products of the human mind and abound in human language and communication. As a consequence, they are of primary interest in Artificial Intelligence, particularly when it comes to developing systems for linguistic interaction with humans. One crucial problem is how to represent the semantics of such concepts. It is well known that crisp sets are not well suited for that purpose, since elements either fully belong to the set or to its complement. The only way to represent the semantics of large using a crisp set is by giving a size threshold above which large holds. However, this solution gives counterintuitive results, since a small variation in size near the threshold is enough to turn a large size into a non-large one when, in fact, both sizes may be even indistinguishable. Indeed, when asked about whether something is large, humans do not always provide a yes/no answer, but expressions like \"more or less\", \"so-so\", etc. that cannot be represented by a crisp set. Another example is the definition of the concept heap, leading to the classical Sorites Paradox (van Deemter, 2010).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Fuzzy Logic is recognized as a suitable tool for representing the semantics of gradual concepts (Rosch, 2013) . A fuzzy set F assigns a fulfilment degree in [0, 1] to each value of the domain X where the concept is defined, by means of a membership function \u00b5 F : X \u2192 [0, 1]. This way, the semantics of large can be represented by means of a continuous function on the set of sizes, in which \"small\" differences in size produce \"small\" differences in membership. That is, the transition from being large (1) to not being large (0) becomes gradual, allowing to represent intermediate cases intuitively by assigning them degrees in (0, 1).", "cite_spans": [ { "start": 96, "end": 109, "text": "(Rosch, 2013)", "ref_id": "BIBREF34" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Atomic gradual concepts like large can be combined to form derived gradual concepts, by means of logical connectives. One of the particularities of Fuzzy Logic is that different operators can be used in order to compute the membership function of derived properties: a wide range of t-norms for intersection, t-conorms for union, and fuzzy negations for complement are available. Other kind of derived gradual concepts can be obtained from the application of linguistic hedges that modify the semantics of concepts. The semantics of such derived concepts (like very large) are obtained by means of a composition of a function associated to the hedge (very, a typical function being very(x) = x 2 ) and the membership function representing the semantics of the concept being modified (large).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Gradual concepts can be also employed to form more complex expressions called protoforms, that are one of the main objects of study of the Computing with Words (CW) area (Zadeh, 1999; Kacprzyk and Zadrozny, 2010) . Fulfilment of protoforms is also gradual, degrees in [0, 1] being \"computed\" from the semantics of the concepts involved.", "cite_spans": [ { "start": 170, "end": 183, "text": "(Zadeh, 1999;", "ref_id": "BIBREF40" }, { "start": 184, "end": 212, "text": "Kacprzyk and Zadrozny, 2010)", "ref_id": "BIBREF19" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Protoforms can be expressed linguistically, a paradigmatic example being quantified statements like \"most of the large animals are slow\", which is a particular instantiation of the protoform \"Q of D are A\". In this protoform, Q is a gradual quantifier (most in our previous example) with semantics represented by a fuzzy set \u00b5 Q : [0, 1] \u2192 [0, 1] assigning fulfilment degrees of the quantifier to percentages in [0, 1]. For instance, a particular semantics of most is given by the following continuous and piecewise-linear function:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "EQUATION", "cite_spans": [], "ref_spans": [], "eq_spans": [ { "start": 0, "end": 8, "text": "EQUATION", "ref_id": "EQREF", "raw_str": "Q(x) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 0 x \u2264 0.5 4x \u2212 2 0.5 \u2264 x \u2264 0.75 1 0.75 \u2264 x", "eq_num": "(1)" } ], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "On its turn, both D and A are fuzzy subsets of the same set X (animals), induced by gradual concepts (large and slow, respectively). Techniques for computing the fulfilment degree of such sentences, including more complex sentences involving generalized quantifiers, are available (Delgado et al., 2014; D\u00edaz-Hermida et al., 2018) .", "cite_spans": [ { "start": 281, "end": 303, "text": "(Delgado et al., 2014;", "ref_id": "BIBREF10" }, { "start": 304, "end": 330, "text": "D\u00edaz-Hermida et al., 2018)", "ref_id": "BIBREF11" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Graduality can appear in combination with other sources of uncertainty in protoforms, like probability (Zadeh, 1999) . Besides, gradual concepts can be used for different purposes in protoforms. A particular case is the possibilistic use, in which gradual concepts are employed as restrictions representing the available knowledge. An example of instantiation of such protoforms is \"John is old\", where we lack some knowledge about the actual age of John, but we know it to be restricted to the set of ages that match the gradual concept old, membership degrees representing our preference for some ages against others if we had to guess. Note the difference with \"I like old cars\", in which the same gradual concept appears under a veristic use and, contrary to the previous case, there is no uncertainty (the expression claims that I like every old car, membership degrees corresponding to the degree to which I like every car because of its age).", "cite_spans": [ { "start": 103, "end": 116, "text": "(Zadeh, 1999)", "ref_id": "BIBREF40" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Let us remark that fulfilment of certain protoforms can be computed from other protoforms using rule-based inference, among other kind of reasoning, like in granular linguistic models of phenomena (Trivi\u00f1o and Sugeno, 2013) .", "cite_spans": [ { "start": 197, "end": 223, "text": "(Trivi\u00f1o and Sugeno, 2013)", "ref_id": "BIBREF37" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "The use of fuzzy sets has been discussed specifically for REG in , where some of the properties in P are assumed to be gradual. As a consequence, features like referential success of referring expressions become gradual, as we shall discuss in the next section. Though in only conjunctions of atomic properties are considered, it is immediate to extend the discussion to both derived properties and protoforms like those discussed before, for instance under a possibilistic use of gradual concepts Mar\u00edn et al., 2019) . The case of quantified statements is also particularly interesting in REG, as it has been shown by using crisp generalized quantification in (Ren et al., 2010).", "cite_spans": [ { "start": 498, "end": 517, "text": "Mar\u00edn et al., 2019)", "ref_id": "BIBREF25" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness in words and linguistic expressions", "sec_num": "3" }, { "text": "Quality assessment is a fundamental question in any intelligent system, Data2text systems (including REG approaches) not being an exception. Quality assessment models are necessary for two fundamental reasons: (i) they must guide searching processes and (ii) they must allow the results obtained to be evaluated and compared (Bugar\u00edn et al., 2015b,a) .", "cite_spans": [ { "start": 325, "end": 350, "text": "(Bugar\u00edn et al., 2015b,a)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "The look for quality models is not trivial because they are usually context-dependent and combine aspects that, in many cases, turn out to be subjective and interdependent/conflicting: it is necessary to obey the user's preferences in the context the system is executed . In general, it is a multidimensional problem that requires multi-objective optimization algorithms (Castillo-Ortega et al., 2012) .", "cite_spans": [ { "start": 371, "end": 401, "text": "(Castillo-Ortega et al., 2012)", "ref_id": "BIBREF6" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "An important part of the mentioned quality models focuses on the definition of measures that allow to assess different aspects of quality with values in [0, 1], even when gradual concepts are not involved. For example we can consider:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "\u2022 The accuracy, that is, the degree of fulfillment of the expression by the target object set. We have discussed about accuracy of gradual concepts and protoforms in the previous section.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "\u2022 The brevity, that is, minimizing the length of the expression. Brevity can be measured in [0, 1] when length is divided by the maximum possible length.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "\u2022 The salience, related to how easy is to perceive the properties employed in the expression. In general, more salient expressions are preferred by users.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "As can be seen in these three examples, measures can be gradual, particularly -but not necessarilyin the presence of gradual properties. Fuzzy Logic provides both mechanisms to solve the problem of symbol grounding and an extensive prior knowledge in the form of a wide variety of well known fuzzy measures, which can be used as a basis for measuring such quality related aspects.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "In the case of referring expressions, the case of referential success deserves special mention. In a crisp environment, referential success can be considered as an inherent quality of a referring expression since it makes no sense to use a referring expression lacking referential success. However, in the presence of gradual properties, determining the referential success is also a matter of degree : referring expressions with a high degree of referential success are then searched, preferably the best for each target set.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "As we have previusly mentioned, Fuzzy Logic permits defining gradual measures of referential success. For example, in , a definition of referential success based on accuracy is proposed, measuring to what extent the accuracy occurs in the target set whilst it does not occur in the other distractors. Referential success measurement is also a clear example of how the broad background in measures of Fuzzy Logic can be useful for solving problems in the REG field. For example, studies can be found in the literature (Mar\u00edn et al., 2016b (Mar\u00edn et al., , 2017a (Mar\u00edn et al., , 2018b ) which show that referential success can be assessed using the well-known measures of specificity of Fuzzy Logic (Yager, 1982) . In interested readers can find an experimental analysis with users regarding a variety of specificity based measures of referential success.", "cite_spans": [ { "start": 517, "end": 537, "text": "(Mar\u00edn et al., 2016b", "ref_id": "BIBREF22" }, { "start": 538, "end": 560, "text": "(Mar\u00edn et al., , 2017a", "ref_id": "BIBREF23" }, { "start": 561, "end": 583, "text": "(Mar\u00edn et al., , 2018b", "ref_id": "BIBREF27" }, { "start": 698, "end": 711, "text": "(Yager, 1982)", "ref_id": "BIBREF39" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "Additional measures have to be considered in the possibilistic setting mentioned in the previous section. Consider, for example, datasets in which we find objects satisfying a property among a given set of properties, but not knowing exactly which one. The presence of this type of uncertainty in the information is usually translated into uncertainty in the set of objects that satisfy a given expression. In (Mar\u00edn et al., 2019) a novel fuzzy set based approach to this problem can be found, where innovative notions like possible referent and necessary referent of an expression are defined and used as basis for a gradual measure of referential success.", "cite_spans": [ { "start": 410, "end": 430, "text": "(Mar\u00edn et al., 2019)", "ref_id": "BIBREF25" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "In addition to quality measures of final referring expressions, other fuzzy measures have been proposed for guiding the REG process, such as measures of discriminatory power, for example by means of index-type specificity measures (Mar\u00edn et al., 2017b) , among others.", "cite_spans": [ { "start": 231, "end": 252, "text": "(Mar\u00edn et al., 2017b)", "ref_id": "BIBREF26" } ], "ref_spans": [], "eq_spans": [], "section": "Vagueness and measures", "sec_num": "4" }, { "text": "Different arguments have been put forward against the use of Fuzzy Logic in modeling and reasoning with concepts in REG and NLG in general.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "Fuzzy Logic was deemed unsuitable for representing and dealing with gradual concepts (Osherson and Smith, 1981) . Recent work has shown that such claims are erroneous, mainly due to misunderstandings and misconceptions such as using a set theory as a theory of concepts, (Belohl\u00e1vek et al., 2009; Belohl\u00e1vek and Klir, 2011; Rosch, 2013) . Such use is wrong since, though derived concepts can be obtained by using Fuzzy Logic operations, not every complex concept allows to obtain its semantics by operations on sets, requiring specific modeling of their membership functions instead.", "cite_spans": [ { "start": 85, "end": 111, "text": "(Osherson and Smith, 1981)", "ref_id": "BIBREF30" }, { "start": 271, "end": 296, "text": "(Belohl\u00e1vek et al., 2009;", "ref_id": "BIBREF1" }, { "start": 297, "end": 323, "text": "Belohl\u00e1vek and Klir, 2011;", "ref_id": null }, { "start": 324, "end": 336, "text": "Rosch, 2013)", "ref_id": "BIBREF34" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "Defining appropriate membership functions representing the semantics of gradual concepts is a complex problem because of subjectivity and context-dependence (Cadenas et al., 2014) , among other reasons (van Deemter, 2010) . This has been employed as an argument against using Fuzzy Logic as well. However, the same can be said of using crisp sets; for instance, the definition of concepts like large using crisp sets requires to define subjective and context-dependent thresholds, the semantics of such models being much more sensitive to small changes on thresholds than when using Fuzzy Logic. In general, the symbol grounding problem is shared by every knowledge representation formalism (Harnad, 1990) .", "cite_spans": [ { "start": 157, "end": 179, "text": "(Cadenas et al., 2014)", "ref_id": "BIBREF5" }, { "start": 202, "end": 221, "text": "(van Deemter, 2010)", "ref_id": "BIBREF38" }, { "start": 691, "end": 705, "text": "(Harnad, 1990)", "ref_id": "BIBREF18" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "Fortunately, more and more techniques for appropriately solving this problem in different settings are available in the literature, see (Chamorro-Mart\u00ednez et al., 2017; Ramos-Soto et al., 2019) for recent proposals, the second one in relation to REG. Also related to REG is the proposal in (Mar\u00edn et al., 2018a) , in which the context-dependent semantics of terms like large, medium, and small -interpreted as the largest, etc. (van Deemter, 2006) -are automatically calculated according to the collection of size values of the objects in the context, without requiring the intervention of humans beyond fixing once and for all the axioms that the models must satisfy. A similar idea has been employed for modeling the semantics of crisp contextual properties in (Fern\u00e1ndez, 2009) .", "cite_spans": [ { "start": 136, "end": 168, "text": "(Chamorro-Mart\u00ednez et al., 2017;", "ref_id": "BIBREF7" }, { "start": 169, "end": 193, "text": "Ramos-Soto et al., 2019)", "ref_id": "BIBREF31" }, { "start": 290, "end": 311, "text": "(Mar\u00edn et al., 2018a)", "ref_id": "BIBREF24" }, { "start": 763, "end": 780, "text": "(Fern\u00e1ndez, 2009)", "ref_id": "BIBREF13" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "Regarding operations and reasoning, the availability of different ways for performing usual set operations with fuzzy sets and the fact that they are truth-functional (which imply that no Fuzzy Set Theory is a Boolean algebra) has been pointed out as a disadvantage (van Deemter, 2010). The recent development of level-based representations (RLs) as an alternative to fuzzy sets can solve this problem (Dubois and Prade, 2008; S\u00e1nchez et al., 2008 Martin, 2015) . RLs have been used in REG (Mar\u00edn et al., 2016a) .", "cite_spans": [ { "start": 402, "end": 426, "text": "(Dubois and Prade, 2008;", "ref_id": "BIBREF12" }, { "start": 427, "end": 447, "text": "S\u00e1nchez et al., 2008", "ref_id": "BIBREF35" }, { "start": 448, "end": 461, "text": "Martin, 2015)", "ref_id": "BIBREF29" }, { "start": 490, "end": 511, "text": "(Mar\u00edn et al., 2016a)", "ref_id": "BIBREF21" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "The approach in represents gradual concepts by means of functions \u03c1 : (0, 1] \u2192 2 X instead of fuzzy sets, going beyond Fuzzy Logic in several respects:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "\u2022 Every classical set operation is extended to the gradual case uniquely in a non-truth functional way by performing the operation in each level of (0, 1] independently, keeping all Boolean properties.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "\u2022 Fuzzy sets are employed as input (by using \u03b1-cuts) and output (measuring membership) only. This way, the understandability and modeling resources of fuzzy sets and the algebraic properties of RLs operations are combined into RL-systems that solve some of the drawbacks associated to fuzzy reasoning.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "This discussion leads us to believe that Fuzzy Logic, Computing with Words, and RL-systems can help in dealing with graduality/uncertainty in REG and other NLG tasks.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "5" }, { "text": "The terms gradual or fuzzy are the usual ones in the Soft Computing area for this kind of properties. The term gradable is also common in the literature(van Deemter, 2016).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "Concepts and fuzzy logic", "authors": [], "year": 2011, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Radim Belohl\u00e1vek and George J. Klir, editors. 2011. Concepts and fuzzy logic. 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