The classical sets are also called clear sets, as opposed to vague, and by the same token classical logic is also. Furthermore, the interval s i, s j includes any virtual terms s. If l is a fuzzy linguistic space, l is a fuzzy linguistic lattice if l is a partially ordered set and with one and only one greatest element for 0 is always assumed to be the least element provided negative fuzzy linguistic terms are not used in l. During reasoning the variables are referred to by the linguistic terms so defined, and the fuzzy sets determine the correspondence with the numerical values. Afterwards, an inference is made based on a set of rules. For example, in the case of the composite term very tall man, the operator very acts on the fuzzy meaning of the term tall. Fuzzy representation systems in linguistic semantics an empirical approach to the reconstruction of lexical meanings from east and westgerman newspapers. Fuzzy sets, linguistic variables and fuzzy ifthen rules by means of example 1, it will be shown first how the formal concepts of a linguistic variable with their linguistic terms and membership functions and of a fuzzy rule are used to represent the available knowledge. Fuzzy linguistic protoforms to summarize heart rate streams.
The fuzzy set a may be written by the set of pairs as follows. By abuse of language, following the habits of the literature, we will use the terms fuzzy sets instead of fuzzy subsets. Linguistic intuitionistic fuzzy sets and application in magdm. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element hfle and define hesitant probabilistic fuzzy linguistic set hpfls for ill structured and complex decision making problem. In talking about fuzzy representation systems in linguistic semantics i will con. Borovicka fuzzy weight estimation method based on the linguistic expression of criterion relevance 15 real interval 0,1. Pdf hesitant fuzzy linguistic term sets for decision making.
Figure 4 scale of fuzzy numbers expressing linguistic meanings in this illustrative case, we have a linguistic variable with three possible terms low, medium and high. Whereas there are many applications of fuzzy set theory, this paper describes one of the first results in the application of ar and linguistic synthesis. The trapezoidal fuzzy twodimensional linguistic power. Fuzzy logic is based on fuzzy set theory, which is a generalization of the classical set theory zadeh, 1965. Pdf a model for representing vague linguistic terms and. In this stage, a fuzzy model is proposed to monitor the heart rate under a linguistic approach in real time by means of three representative terms and their membership functions, low, adequate, and high, as well as shortterm fuzzy temporal windows ftws. A novel linguistic group decisionmaking model based on. The basic operational laws, the score function, and the accuracy function of fermatean fuzzy linguistic numbers are provided. Mining time series data by a fuzzy linguistic summary system.
In this paper, the concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic. Uncertain linguistic terms and extended hesitant fuzzy linguistic term sets. A new similarity measure between ffltss is constructed, which not only includes the linguistic scale function but also combines the cosine similarity measure and euclidean distance measure, and then the related properties of the similarity measure are proven. The axiomatic definition of a linguistic scale fuzziness degree, its major properties and applications.
Fuzzy control strategies involve a large number of inputs, most of which are relevant only for some special conditions. Firstly, a crisp set of input data are gathered and converted to a fuzzy set using fuzzy linguistic variables, fuzzy linguistic terms and membership functions. The closer the value of a x is to 1, the more x belongs to a. In terms of this variable, a linguistic value such as young may be interpreted as a label for a fuzzy restriction on the values of the base. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. Hesitant fuzzy sets, linguistic information, fuzzy linguistic approach, contextfree grammar, com puting with words. Fuzzy control strategies come from experience and experiments rather than from mathematical models and, therefore, linguistic implementations are much faster accomplished. Interpretation of middleaged as a linguistic value. Fermatean fuzzy linguistic set and its application in.
In fuzzy logic, propositional expressions have a numerical value between 0 and 1 as their meaning, and negation and conjunction are interpreted as functions mapping a sin. To determine the membership function of the rule, let t and h be universe of discourse of temperature and humidity, respectively, and let us define variables t. A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. Define the linguistic terms used by decisionmakers table 4. In concrete, we study the l fuzzy concepts obtained from a departure set represented by means of these linguistic labels applied to the set of objects or attributes. Hesitant fuzzy linguistic term sets for decision making. Second, the logic allows logical categories to overlap in contrast to boolean logic, where the two possible logical categories, true and false, are sharply distinct. Zadeh extended the work on possibility theory into a formal system of mathematical logic, and introduced a new concept for applying natural language terms.
First, the formal apparatus of fuzzy logic has been made more general since the 1970s, speci. The process of fuzzy logic is explained in algorithm 1. In concrete, we study the lfuzzy concepts obtained from a departure set represented by means of these linguistic labels applied to the set of objects or attributes. Linguistic fuzzy ifthen rule can be represented in a general form. On the other hand, what we mean by a qualitative model is a generalized fuzzy model consisting of linguistic explanations about system behavior. Distance measure for fermatean fuzzy linguistic term sets. It has a definite meaning, which can be made more precise only through further elaboration. A study in meaning criteria and the logic of fuzzy. Approaches based on computing with words find good applicability in decision making systems. Fuzzy logic is a tool for embedding human knowledge experience, expertise, heuristics the university of iowa intelligent systems laboratory human knowledge is fuzzy.
Pdf hesitant fuzzy linguistic term sets researchgate. Hesitant fuzzy information processing based on the. The generalized form has wider applications in linguistic group. A model for representing vague linguistic terms and fuzzy rules for classification in ontologies. Linguistic fuzzylogic game theory badredine arfi, 2006. In this paper, we propose the concept of fermatean fuzzy linguistic term sets based on linguistic term sets and fermatean fuzzy sets. If the above mapping is from x to a closed interval o,i then we have a fuzzy subset. Fuzzy linguistic protoforms to summarize heart rate. By contrast, in boolean logic, the truth values of variables may only be the integer values 0 or 1. The value a x characterizes the grade of membership of x in a. Zadehs idea of control realized on the basis of the description using genuine natural language. Fuzzy representation systems in linguistic semantics.
Type2 fuzzy set based hesitant fuzzy linguistic term sets. Fuzzy statistics and computation on the lexical semantics. The preference ratios of alternatives are expressed by fuzzy linguistic variables in triangular fuzzy numbers. Given a subset a of x acx a can be represented by a characteristic function. To better deal with imprecise and uncertain information in decision making, the definition of linguistic intuitionistic fuzzy sets lifss is introduced, which is characterized by a linguistic membership degree and a linguistic nonmembership degree, respectively. Fuzzy set theoryand its applications, fourth edition. Predominantly finding their basis in type1 fuzzy sets, computing with words approaches employ type1 fuzzy sets as semantics of the linguistic terms. It is assumed that we have already defined a fuzzy set to describe a late completion date. In this article i use linguistic fuzzyset theory to analyze the process of decision making in politics. Hesitant fuzzy linguistic term sets for decision making article pdf available in ieee transactions on fuzzy systems 201. A decision framework under a linguistic hesitant fuzzy set. When the fuzzy numbers represent linguistic concepts, e. These linguistic values are expressed as fuzzy subsets of the universes.
For example, it is easier for an expert to evaluate a transport company by the criterion of insurance level of cargo in a fuzzy form with the help of linguistic estimates terms, for example, the level of cargo insurance. Pdf hesitant probabilistic fuzzy linguistic sets with. Lfsa deals with qualitative aspects that are represented in qualitative terms by means of. First, the truth values of logical propositions span a set of linguistic terms such as true, very true, almost false, very false, and false. Linguistic variables are central to fuzzy logic manipulations, but are often ignored in the.
Therefore, the fuzzy linguistic scaling used for measuring the meaning of terms measurement is necessary to be mathematically defined with membership. For example, in the case of the composite term very tall man, the operator very acts on the fuzzy meaning of the term tall man. This chapter explains the principles of fuzzy control and fuzzy decision. Hesitant fuzzy linguistic term sets for linguistic.
Pdf hesitant fuzzy linguistic terms sets for decision. In a standard fuzzy partition, each fuzzy set corresponds to a linguistic concept, for instance very low, low, average, high, very high. An integrated approach of fuzzy linguistic preference. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether. Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. The fuzzy variable terms along with a set of fuzzy modifiers such as very or slightly, the operators and and or fuzzy set intersection and union respectively and the left and right parentheses provide the basis for a grammar that allows one to write fuzzy linguistic expressions that describe fuzzy concepts in an englishlike manner. In this paper, we propose the fermatean fuzzy linguistic term set fflts based on the linguistic scale function. A study in meaning criteria and the logic of fuzzy concepts george lakoff journal of philosophical logic volume 2, pages 458 508 1973 cite this article. A linguistic hedge is an operation that modifies the meaning of a fuzzy set, which can be understood as terms that modify the shapes of fuzzy sets by using adverbs such as very, quite, more, less and slightly. Abstract dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Hesitant fuzzy linguistic term set hflts is a set with ordered consecutive linguistic terms, and is very useful in addressing the situations where people are hesitant in providing their linguistic assessments. A fuzzysettheoretic interpretation of linguistic hedges. The ftws are described straightforwardly according to the distance of the current time to a given time stamp as. This new logic for representing and manipulating fuzzy terms was called fuzzy logic, and zadeh became the masterfather of fuzzy logic.
Linguistic terms representing approximate values of base. In this contribution the aim is to introduce the concept of hesitant fuzzy linguistic term sets hflts that will provide a linguistic elicitation based on the fuzzy. Measuring the intellectual capital performance based on 2. Feb 26, 2020 approaches based on computing with words find good applicability in decision making systems.
We also illustrate the results by means of an example. Mining time series data by a fuzzy linguistic summary. Recently, a new model that is based on hesitant fuzzy sets has been presented to manage situations in which experts hesitate. Taboo words change from generation to generation, e. Fuzzy weights estimation method based on the linguistic. A basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially. For instance, i propose a situation depicted in the following picture figure 4. Applications of fuzzy set theory 9 9 fuzzy logic and approximate reasoning 141 9. The concept of a linguistic variable and its application. If x is ai then y is bi, where x is the antecedent variable input. If l is a fuzzy linguistic space, l is a fuzzy linguistic lattice if l is a partially ordered set and with one and only one greatest element for 0 is always assumed to be the least element. If the linguistic fuzzy relation is simplified into a crisp twovalued logic, the linguistic fuzzy game reduces to the conventional game. Fuzzy logic is a form of manyvalued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive.
North american fuzzy logic proceeding society nafips92. Lfuzzy concepts and linguistic variables in knowledge. It can be implemented in systems with various sizes and capabilities ranging from small microcontrollers to large, networked, workstationbased control systems. Third, a fuzzy temporal window 28, 29 to model the hrs was proposed in order to weight fuzzy linguistic terms based on fuzzy temporal linguistic terms and provide flexibility in the presence of eventual signal loss or variance in the sample rate. For example, if s contains five linguistic terms then g 4 and.
The linguistic terms are computed in real time within the wristworn device in order to. A fuzzy linguistic summary for concentrating on presenting our fuzzy linguistic summary function in the data mining agent of the system, we assume that all relevant attributes and data have been extracted according to the corresponding domain knowledge. A new similarity measure between ffltss is constructed, which not only includes the linguistic scale function but also combines the cosine similarity measure and euclidean distance measure, and then the related properties of the. Artificial intelligence fuzzy logic systems tutorialspoint. Linguistic variable an overview sciencedirect topics. Pdf linguistic fuzzylogic game theory researchgate.
Jul 31, 2008 a basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially. However, type2 fuzzy sets have been proven to be scientifically more appropriate to represent linguistic information in practical systems. To compare any two linguistic intuitionistic fuzzy values lifvs, the score function and accuracy function are defined. The case against fuzzy logic revisited 187 of kamp 8 and to a lesser extent that of fine 4. Hesitant fuzzy linguistic term sets for linguistic decision. Wang, extended hesitant fuzzy linguistic term sets and their aggregation in group decision making, international journal of computational intelligence systems81 2015 1433. The author develops a new gametheoretic approach, anchored not in boolean twovalued logic but instead in linguistic fuzzy logic. In this perspective, fl flu, and fln is merely a branch of fl. In this pa per, the concept of a hesitant fuzzy linguistic term set is introduced to provide a. The fuzzy logic works on the levels of possibilities of input to achieve the definite output.
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