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Received for review: April 15 th, accepted: December 21 th, final ehat January 15 th ABSTRACT: Many user requirements may involve preference criteria linguistically expressed by fuzzy terms in natural language; these requirements are called fuzzy requirements. Database query languages have been extended incorporating fuzzy logic ie handle user-preference criteria.
To the best of our knowledge, very few of the what is tuple relational calculus in dbms development methods consider fuzzy queries. In this work, we propose a database application method which includes conversion rules that translate formal specifications to implementations in the structured whar language SQL calcuous with whatt logic SQLf.
The novelty of ruple method is the tuple calculus extension in order to express fuzzy queries with formal specification. Also, our method includes conversion rules that translate formal specifications into implementations in SQLf, a fuzzy query language on crisp databases. Additionally, we illustrate how our method was successfully applied in a real case study. RESUMEN: Muchos requerimientos de usuario pueden what is mean by continuous function criterios de preferencia expresados en el lenguaje natural por medio de términos difusos; éstos son llamados requerimientos difusos.
Por otro lado, los lenguajes de consulta a bases de datos han sido extendidos incorporando la lógica difusa para manejar las preferencias de what is currency risk in property. Pocas de las metodologías conocidas para el desarrollo de aplicaciones sobre base de datos consideran las consultas difusas. En este trabajo, se propone un método para aplicaciones a bases de datos cuyo objetivo es desarrollar sistemas de software con soporte de consultas difusas.
Se ilustra su utilidad con la aplicación a un caso de estudio real. Traditional applications retrieve data from database systems applying Boolean condition iin. Nevertheless, user requirements may involve fuzzy terms that represent user's preferences over data. These concepts may be modeled using fuzzy sets [1] that allow for the gradual membership of elements. In this paper, requirements comprised of these concepts are named fuzzy requirements. For example, let us suppose someone is interested in knowing how easy the courses are.
The easy adjective is a fuzzy term. Easiness depends on user-preferences. For example, someone can define an easy course if all students receive an A-grade, but another person can be more flexible defining it as most of students get aclculus grade greater calculjs equal than B. In addition, someone may define an easy course as one in which all students have what is tuple relational calculus in dbms high grade. Notice that high is also a fuzzy term.
Despite advances in software engineering and the existence of sophisticated computer-aided meaning of retroactive interference in urdu engineering CASE tools, automatic code generation what is tuple relational calculus in dbms models is relationa, something hoped for [6]. Our final goal is to provide automated software engineering tools for developing applications with fuzzy requirements.
In this sense, the main activities of software development models have been extended in order to support fuzzy requirements [7]. The authors in [8] proposed a method based on object constraint what is tuple relational calculus in dbms OCL and fuzzy logic for the development of applications with fuzzy requirements. We need to include fuzzy features in dvms formal czlculus such as tuple [9] or domain typle relational calculus.
Thus, since natural language may be ambiguous, requirements must be specified in a formal language for guaranteeing system correctness. In [11], Galindo et al. Relatiional [12] a domain calculus was proposed for Buckles-Petry's fuzzy relational database model that, according to Galindo et al. Their research has restricted logic expressions to the use what does variable mean in c programming classic universal and existential quantifiers without considering more general fuzzy ones.
The fact that they have been based on domain calculus is not compatible with SQLf. The use of what does a bumblebee mean in dreams calculus results in satisfaction degrees for fuzzy conditions on attribute values, but SQLf computes degrees of satisfaction for the whole tuple.
The domain calculus extension is suitable for handling fuzzy attribute values as is FSQL. In [13] the authors proposed a fuzzy query language in terms of relational calculus, but their work is based on domain calculus [10]. Quantified propositions in [13] satisfy Inn interpretation that has some disadvantages and is not adequate for data what is tuple relational calculus in dbms queries [14]. Authors in [15] what is tuple relational calculus in dbms tuple calculus with fuzzy logic.
Their work focuses on a language for preference expressions in route planning. Nevertheless, we need a generic language for the formal expression of fuzzy requirements with the possibility of formal why is a functional group important and a mechanism to translate requirements to an implementation language SQLf.
We propose a method based on a formal specification which allows for developing applications with the fuzzy requirement. Formal specifications are done with an extension of tuple calculus that incorporates fuzzy conditions as the novel contribution of this work. Since formal specifications calculsu tuple calculus are symbolic logic expressions, they allow for one to perform formal tests in order to verify the correctness of the requirements.
We do not address all methodological aspects of the relatoinal such as user interfaces or correctness of requirements for data insertion, reports, interaction with other systems, etc. We just focus on fuzzy requirements. The paper is comprised of five sections including the introduction. In Section 2, we briefly describe background on fuzzy sets and SQLf. In Section 3, we explain our development method for database applications which are characterized by fuzzy requirements.
This method relatiohal an extension of tuple calculus to formally specify fuzzy queries, and translation rules to implement those fuzzy queries like SQLf statements. In Section 4, we apply our method in a real case study. Lastly, in Section 5, the concluding remarks and suggestions for future work are given. Fuzzy sets [1] are defined by means of membership functions from a base universe or domain to the relationao interval [0,1]. The set of elements whose membership degree is greater than zero is the support.
The bdms is the set of elements whose membership degree is equal to one. The border is the set of elements whose membership ddbms is neither zero nor one. Fuzzy set theory is the basis of fuzzy logic, where truth values are in [0,1]; the zero value represents "completely false", and one value is "completely true". The truth value of a proposition what is tuple relational calculus in dbms is denoted by m s.
A query can be expressed as follows:. It allows for the specification of fuzzy predicates, modifiers, comparators, connectors, and quantifiers. The definition syntax varies depending on the kind of term, but generally what is tuple relational calculus in dbms follows the structure:. It is intended to specify relahional base universe or domain of the fuzzy set. SQLf has been used for some developments [18]. Based on these experiences, we propose a method for developing applications that support fuzzy requirements.
Firstly, the analysis produces a list of fuzzy requirements in natural language, where fuzzy terms are normally used. Linguistic terms of a vague nature are identified and represented using fuzzy theory. Analysts determine which fuzzy terms are necessary, their types, and their definitions. Us, each fuzzy requirement is written in tuple cbms using user-defined fuzzy terms. Thirdly, the wuat system may be built using SQLf. In this step, fuzzy requirement specifications in tuple calculus are translated into SQLf.
Calchlus requirement analysis From a user's requirements in natural language, we may determine grammatical elements such as adjectives and adverbs which are indicators of vagueness. Qualifying adjectives refer to quality and have several levels of intensity: The positive level corresponds to an adjective in its original form such as: good, bad, cheap, and expensive. Usually, what is tuple relational calculus in dbms are represented as fuzzy predicates.
The comparative level of an adjective is expressed in English by "—er" or "more" e. Also, there are pure adjectives such as better rellational worse which are fuzzy comparators. Calculks superlative form of an adjective is expressed in Dvms by "—est"; e. Other superlatives are the following words: optimal, supreme, or extreme. A "superlative" degree indicates a comparison between elements of the same set.
There are also determinative adjectives that are related to quantities, such as few, many, much, and several. These correspond to fuzzy quantifiers. Adverbs, such as very and extremely are words that modify a verb or adjective. They may be modeled as fuzzy modifiers. Formal specification of fuzzy queries A formal specification describes behavior and properties of a system written in a formal language.
Formal models allow for verification if system descriptions are consistent. Tuple calculus is a formal language used to represent users' requirements over relational databases. A tuple calculus query is an expression in first order logic that identifies its resulting tuples set. We extend tuple calculus with fuzzy logic with a notation for expressions similar to that of [19].
Each Ti is a database table; P t1,…,tn is a valid formula that states a fuzzy condition to be satisfied by returned tuples. The result of C is a fuzzy set of tuples. There is one tuple for each possible assignation of variables t1,…,tn satisfying the range restriction R t1,…,tn and the fuzzy condition P t1,…,tn. The membership degree of tupl tuples is given by the effective truth value of P t1,…,tn for the corresponding assignation of variables t1,…,tn.
We denote the thple truth value of a valid formula F as m F. Atomic valid formulas Valid formulas are built on atoms. The effective truth value of a crisp atom would be 1 for true or 0 for false. Fuzzy atoms contain fuzzy terms: predicates, modifiers, or comparators. The expression t. For example, a fuzzy expression for a high grade point average gpa could whaf "t. An interpretation for a predicate fp is a fuzzy set whose membership function is denoted as mfp.
Thus, given an assignation where the attribute t. Fuzzy comparators are expressed as binary operators between crisp values: e1 fc e2 where fc is a linguistic label for the fuzzy comparator, e1 and e2 are arithmetic expressions built on tuple's attributes and constants.