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Create a set of membership functions for each input. A membership function is simply a graphical representation of the fuzzy variable sets. For this example, use three fuzzy sets, COLD, WARM, and HOT. We will then create a membership function for each of three sets of temperature as shown in the cold-normal-hot graphic, Figure 1.

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Fuzzy sets, logic, numbers; intuitionistic fuzzy sets, fuzzy linguis.

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The list below attempts to disambiguate these various types. match query + fuzziness option: Adding the fuzziness parameter to a match query turns a plain match query into a fuzzy one. Analyzes the query text before performing the search. fuzzy query: The elasticsearch fuzzy query type should generally be avoided. Acts much like a term query.

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For example the use of transistors instead of vacuum tubes is a paradigm shift - likewise the development of Fuzzy Set Theory from conventional bivalent set theory is a paradigm shift. Bivalent Set Theory can be somewhat limiting if.

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A fuzzy set A is normal if its maximal degree of membership is unity (i.e., there must exist at least one x for which µA( x) =1). Of course, non-normal fuzzy sets have maximum degree of membership less than one. Definition 5. (Convex fuzzy set) A fuzzy set A is convex if and only if it satisfies the following property:.

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We identify the set of positive as well as the set of negative examples which are not necessarily complementary. Taking this into account we introduce new quality measures comprising the existing ones. ... The power of a fuzzy set A in a ˜nite universe X was introduced as a generalization of the classical concept of cardinality of a crisp set.

Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional. In these cases, type-2 fuzzy sets provide the necessary framework to formalize and work with this information. This post will look at the basic concepts behind type-2 fuzzy sets. We will base this discussion on "Type-2 Fuzzy Sets made Simple" by Robert John and Jerry Mendel, possibly the best paper to learn about type-2 fuzzy sets and logic.

A fuzzy set operation is an operation on fuzzy sets. These operations are generalization of crisp set operations. There is more than one possible generalization. The most widely used operations are called standard fuzzy set operations. There are three operations: fuzzy complements, fuzzy intersections, and fuzzy unions.

With the example of * 0, the fuzzy set represents only one point in one way or another.The letter 5/25 indicates a single horizontal line (with a membership value of.000).All x values are counted as five.You don’t need to read this to realize this is not a single sentence.If, for example, 0 equals such singletons, the result will be 0000.5 1.

The notion of a fuzzy set proposed by Lotfi Zadeh  is the first very successful approach to vagueness. In this approach sets are defined by partial membership, in contrast to ... notion of a set is a crisp (precise) one. For example, the set of odd numbers is crisp because every number is either odd or even. In mathematics we have to use.

The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics. Examples of fuzzy sets include: {'Tall people'}, {'Nice day'}, {'Round object'} If a person's height is 1.88 meters is he considered 'tall'? What if we also know that he is an NBA player? 3.

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Fuzzy set: Fuzzy set is a set having degrees of membership between 1 and 0. Fuzzy sets are represented with tilde character(~). For example, Number of cars following traffic signals at a particular time out of all cars present will have membership value between [0,1].

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fuzzy sets, and to set the stage for potential applications of the local homotopy theory of simplicial presheaves in topological data analysis. ... Example 6. Suppose that a nite set XˆRn is a data cloud, and suppose that X! ˘= N is a listing of the members of X, where N = f0;1;:::;Ng. Choose.

This natural phenomenon can be described more accurately by Fuzzy Set Theory. Fig.2 below shows how fuzzy sets quantifying the same information can describe this natural drift. Figure 3: Example of a Fuzzy set Properties of Fuzzy sets Fuzzy sets follow the same properties as crisp sets. Since membership values of crisp sets are a subset of.

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Fuzzy Logic Example Fuzzy Logic Example Steps Fuzzification: determines an input's % membership in overlapping sets. Rules: determine outputs based on inputs and rules. ... May use centroid of weighted sets. Fuzzy Logic Example Note there would be a total of 95 different rules for all combinations of inputs of 1, 2, or 3 at a time. ( 5x3x3.

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Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al. ... Fuzzy controller is a knowledge-based controller in which fuzzy logic is used to. Mar 15, 2016 · Interval type-2 fuzzy logic controller (IT2FLC) method for controlling the speed with a direct.

A fuzzy set is determined by its indeterminate boundaries, there exists an uncertainty about the set boundaries. On the other hand, a crisp set is defined by crisp boundaries, and contain the precise location of the set boundaries. Fuzzy set elements are permitted to be partly accommodated by the set (exhibiting gradual membership degrees).

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5. For example, fuzzy sets A and B are defined by the function : for 2 ≤x≤ 10 A(x) = 1-(|x-61/4) 0 for x<2 and X>10 B(x) = 1-(|x-81/4) 0 for 4 ≤ x ≤ 12 for x<4 and x>12 a.

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Fuzzy Logic: A mathematical logic that attempts to solve problems by assigning values to an imprecise spectrum of data in order to arrive at the most accurate conclusion possible. Fuzzy logic is.

Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al. ... Fuzzy controller is a knowledge-based controller in which fuzzy logic is used to. Mar 15, 2016 · Interval type-2 fuzzy logic controller (IT2FLC) method for controlling the speed with a direct.

When there is “=”, we obtain the ordinary fuzzy sets, in the opposite case, the new objects must be used – the intuitionistic fuzzy sets. Let us discuss one example. Let E = f0,1,2,...,10g, M = f0,1gˆR, A = fnjn2E& the equation x3 y2 = n has more than 2 solutionsg. For example, m) = A (0 1, m A. Examples for fuzzy intersection/union pairs with standard negator can be derived from samples provided in the article about t-norms. The fuzzy intersection is not idempotent in general, because the standard t-norm min is the only one which has this property.

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A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

The classical example in fuzzy sets is tall men. The elements of the fuzzy set “tall men” are all men, but their degrees of membership depend on their height. D e gree o f M e mbe rs hip F uzzy M ark John To m Bob B ill 1 1 1 0 0 1.00 1.00 0.98 0.82 0.78 P eter S teve n M ike D a vid C hris C risp 1 0 0 0 0 0.24 0.15 0.06 0.01 0.00 N ame H.

Fuzzy set is a set having degrees of membership between 1 and 0. Partial membership exists when member of one fuzzy set can also be a part of other fuzzy sets in the same universe. The degree of membership or truth is not same as probability, fuzzy truth represents membership in vaguely defined sets. A fuzzy set A on a universe of discourse U is characterized by a membership function that takes values in the interval . Fuzzy sets represent commonsense linguistic labels like slow, fast, small, large, heavy, low, medium, high, tall, etc. A given element can be a member of more than one fuzzy set at a time. A fuzzy set A in U may be.

A novel three-way decision method is presented for solving decision-making problems by means of hesitant fuzzy sets and canonical soft sets. Finally, a numerical example regarding peer review of research articles is given to illustrate the validity and efficacy of the proposed method. Keywords:.

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A novel three-way decision method is presented for solving decision-making problems by means of hesitant fuzzy sets and canonical soft sets. Finally, a numerical example regarding peer review of research articles is given to illustrate the validity and efficacy of the proposed method. Keywords:.

Fuzzy sets. Examples of fuzzy sets Fuzzy sets can be discrete or continuous The interval [0,1] can be extended to [0,k], where k > 0 It is possible to deﬁne fuzzy sets on more complex structures than intervals or real numbers, e.g. L-fuzzy sets, where Lis a partially ordered set (see chapter 3, Extensions of fuzzy sets).

Figure 2-3 Union and intersection of fuzzy sets. 18 Figure 3-1 Fuzzy sets vs. probabilistic sets. 26 Figure 3-2 Mapping of t-norms, t-conorms, and averaging operators. 38 ... Figure 11-4 Rule consequences in the heating system example. 232 Figure 11-5 Extreme Value Strategies. 234 Figure 11-6 COA Defuzzification. 235.

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Description. fis = mamfistype2 creates a type-2 Mamdani FIS with default property values. To modify the properties of the fuzzy system , use dot notation. fis = mamfistype2 (Name,Value) specifies FIS configuration information or sets object properties using name-value pair arguments.

In this paper, we use membership function matrices associated with fuzzy c -partitions of X, together with their values in the Euclidean (matrix) norm, to formulate an a posteriori method for evaluating algorithmically suggested clusterings of X. Several numerical examples are offered in support of the proposed technique.

Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al. ... Fuzzy controller is a knowledge-based controller in which fuzzy logic is used to. Mar 15, 2016 · Interval type-2 fuzzy logic controller (IT2FLC) method for controlling the speed with a direct.

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The process of fuzzy logic is explained in Algorithm 1: 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. This step is known as fuzzi cation. Afterwards, an inference is made based on a set of rules. Lastly,.

For example, if X is a set of colored objects, ... In this approach fuzzy sets are built ab initio, without viewing them as a superstructure of a predetermined theory of ordinary sets. The only primitive relation used in the theory is a ternary relation, interpreted as a membership relation. There are 14 axioms, some of which have a strongest.

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Rough Approximations on Hesitant Fuzzy Sets: 10.4018/978-1-4666-9798-0.ch013: Introduction of hesitant fuzzy rough sets would facilitate the use of rough set based techniques to hesitant fuzzy environment. ... It may be the lack of knowledge or for example in decision making problems; situations may arise where the decision makers are not able.

The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed between theory and practice.

So a given person's height might be described by more than one set. If one was, for example, 74 inches he would be in the "tall" and "very tall" set. The other thing about fuzzy sets is that set membership is not binary. In classical logic, an element is either in or our of the set. In fuzzy logic membership in a set is a continuum, so one can.

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The ‘tipping problem’ is commonly used to illustrate the power of fuzzy logic principles to generate complex behavior from a compact, intuitive set of expert rules. If you’re new to the world of fuzzy control systems, you might want to check out the Fuzzy Control Primer before reading through this worked example.

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Each term in the term-set is a fuzzy set and comprises one or more primary terms, whose meaning is defined a prior, which serves as a basis for the computation of the non-primary terms in the term-set. The meaning of a primary term is a primary fuzzy set. In the above example of age, the primary terms are young and old.

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EXAMPLE OF MAMDANI METHOD Let the fuzzy rule base consist of one rule: R: If u is A then v is B where A=(0, 2, 4) and B=(3, 4, 5) are triangular fuzzy sets Question 1: What is the output B’ if the input is a crisp value u 0=3?.

Fuzzy control methods and algorithms, including many specialized software and hardware available on the market today, may be classified as one type of intelligent control. This is because fuzzy systems modeling, analysis, and control incorporate a certain amount of human knowledge into its components (fuzzy sets, fuzzy logic, and fuzzy rule base).

of fuzzy set extensions in the fuzzy set theory, for example, intuitionistic fuzzy sets, interval-valued fuzzy sets, vague sets, bipolar-valued fuzzy sets etc. The notion of bipolar-valued fuzzy sets was rst introduced by Lee  in 2000, is an extension of fuzzy sets whose membership degree range is enlarged from the interval [0;1] to [ 1;0.

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The list below attempts to disambiguate these various types. match query + fuzziness option: Adding the fuzziness parameter to a match query turns a plain match query into a fuzzy one. Analyzes the query text before performing the search. fuzzy query: The elasticsearch fuzzy query type should generally be avoided. Acts much like a term query.

In this article you will get very preliminary concepts of fuzzy set theory. You will be able to learn about alpha-cut, strong alpha-cut, support, core, normality fuzzy set, sub normality, cardinality and nucleus of a fuzzy set. Also, you will find the very basic operation union, intersection and complement of fuzzy sets and explained with examples.

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The classical example in fuzzy sets is tall men. The elements of the fuzzy set “tall men” are all men, but their degrees of membership depend on their height. D e gree o f M e mbe rs hip F uzzy M ark John To m Bob B ill 1 1 1 0 0 1.00 1.00 0.98 0.82 0.78 P eter S teve n M ike D a vid C hris C risp 1 0 0 0 0 0.24 0.15 0.06 0.01 0.00 N ame H.

The defuzzified value X ∗ is defined as : Here, n is the number of fuzzy sets, N is the number of fuzzy variables, μAk(xi) is the membership function for the k-th fuzzy set. Example Center of gravity (COG) / Centroid of Area (COA) Method This method provides a crisp value based on the center of gravity of the fuzzy set. Fuzzy sets, logic, numbers; intuitionistic fuzzy sets, fuzzy linguis.

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Sums and a negative of fuzzy numbers fuzzy numbers look at Fig. 2.7 with the fuzzy numbers A 0 , B 0 shown there. Then one has A 0 ⊕ B 0 , A 0 ⊕ A 0 and − A 0 as shown in Fig. 2.7.

Consider the following two fuzzy sets: A = { 0.3 x 1 + 0.7 x 2 + 1 x 3 } B = { 0.4 y 1 + 0.9 y 2 } Perform the Cartesian product over three given fuzzy sets. Solution: The fuzzy Cartesian product performed over fuzzy sets A and B results in fuzzy relation R given by, R = A X B.

A Type 1 Purge Set Represented by a Type 2 Fuzzy Set. A type 1 fuzzy set can be interpreted as a type 2 fuzzy set with all of the second ranks being single (i.e. all flags being 1). In fact, a type 1 fuzzy set is an instance of a type 2 fuzzy set. This is a clear version of the type 2 fuzzy set.

A Fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair (A; ... 2.2.1 Examples of Fuzzy Logic In a Fuzzy Logic washing machine, Fuzzy Logic detects the type and amount of laundry in the.

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Soft Computing: Fuzzy Sets 7 Membership Functions (MFs) Characteristics of MFs: • Subjective measures • Not probability functions MFs 5’10’’ Heights.5.8.1 “t“tall” Ain Asia “t“tall” in the US “t“tall” in NBA Soft Computing: Fuzzy Sets 8 Fuzzy Sets Formal definition: A fuzzy set A in X is expressed as a set of ordered.

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A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of.

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In this paper, we use membership function matrices associated with fuzzy c -partitions of X, together with their values in the Euclidean (matrix) norm, to formulate an a posteriori method for evaluating algorithmically suggested clusterings of X. Several numerical examples are offered in support of the proposed technique.

conorm operators defined on type-1 and type-2 fuzzy sets. The remaining part of the paper is organised as follows; the next section concerns the preliminaries materials and methods needed in section 3 where we discuss the operators on type-1 fuzzy sets with examples and in section 4 we extend our examples to type-2 fuzzy sets.

Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible.  fuzzy set theory Then I used Fuzzy Set Theory to analyze the membership degree of key elements to verify my.

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Neutrosophic Set – A Generalization of the Intuitionistic Fuzzy Set Florentin Smarandache, University of New Mexico, Gallup, NM 87301, USA, E-mail: [email protected] Abstract: In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented.

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Fuzzy Systems samples. Fuzzy Sets Sample This sample application demonstrates the basics of fuzzy sets - how to define fuzzy sets and linguistic variables and check membership of an arbitrary value to a certain fuzzy set. The application demonstrates graphically such variable like temperature and shows values' membership to different sets like.

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and.

Examples for fuzzy intersection/union pairs with standard negator can be derived from samples provided in the article about t-norms. The fuzzy intersection is not idempotent in general, because the standard t-norm min is the only one which has this property.

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11. When I think of "Fuzzy logic" the first thing that comes to mind is engineering, where is it used in control systems, and information processing. For example, "fuzzy logic" is used in control systems for washing machines. I think it was a hot topic in 1980s and 1990s, and one article from that time is "Designing with Fuzzy Logic" by Kevin. A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

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Download Fuzzy sets for Ada for free. Fuzzy sets, logic, numbers; intuitionistic fuzzy sets, fuzzy linguis. Fuzzy sets for Ada is a library providing implementations of confidence factors with the operations not, and, or, xor, +, and *, classical fuzzy sets with the set-theoretic operations and the operations of the possibility theory, intuitionistic fuzzy sets with the.

"Intuitionistic Fuzzy Sets", subtitle: "Theory and Applications" is the title of a book by Krassimir Atanassov, published in Springer Physica-Verlag Publishing house in November 1999 under ISBN 3-7908-1228-5.It is featured in the series "Studies in Fuzziness and Soft Computing" under Volume 35. The book introduces the basic definitions and properties of the intuitionistic fuzzy sets, which are.

In particular, it is demonstrated how fuzzy sets can induce shadowed sets. Subsequently, shadowed sets reveal interesting conceptual and algorithmic relationships existing between rough sets and fuzzy sets. Detailed computational aspects of shadowed sets are discussed. Several illustrative examples are provided.

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Fuzzy Sets (Continue) Example • Let X = {g1, g2, g3, g4, g5} be the reference set of students. • Let Ã be the fuzzy set of "smart" students, where "smart" is fuzzy term. Ã = { (g1,0.4) (g2,0.5) (g3,1) (g4,0.9) (g5,0.8)} Here Ã indicates that the smartness of g1 is 0.4 and so on 13.

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Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible.  fuzzy set theory Then I used Fuzzy Set Theory to analyze the membership degree of key elements to verify my.

Consider the following two fuzzy sets: A = { 0.3 x 1 + 0.7 x 2 + 1 x 3 } B = { 0.4 y 1 + 0.9 y 2 } Perform the Cartesian product over three given fuzzy sets. Solution: The fuzzy Cartesian product performed over fuzzy sets A and B results in fuzzy relation R given by, R = A X B.

Following are the examples of set in Roster or Tabular Form − Set of vowels in English alphabet, A = {a,e,i,o,u} Set of odd numbers less than 10, B = {1,3,5,7,9} Set Builder Notation In this form, the set is defined by specifying a property that elements of the set have in common. The set is described as A = {x:p (x)}.

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A fuzzy set is an extension of a classical set. If X is the sample space and its elements are denoted by x, then a fuzzy set A in X is defined as a set of ordered pairs. A = {x, µA(x) | x ∊ X} µA(x) is called the membership function (or MF) of x in A. The membership function maps each element of X to a membership value between 0 and 1.

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Fuzzy SetsFuzzy sets theory is an extension of classical set theory. • Elements have varying degree of membership. A logic based on two truth values, • True and False is sometimes insufficient when describing human reasoning. • Fuzzy Logic uses the whole interval between 0 (false) and 1 (true) to describe human reasoning.

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console table entryway  • i |i I} The family of sets is also called an indexed set. For example: A A {A 1 ,A 2 ,...,A n •A is a subset of B: •AandBare equal sets: ,, A B A B A B and B A •Aand Bare not equal: •Ais proper subset of B: •Ais included in B: A B A B andA B Crisp sets: an overview
• Note: This is a discontinued product. Archival documentation » Fuzzy Logic is a Mathematica application package that brings you an essential set of tools for creating, modifying, and visualizing fuzzy sets and fuzzy logic-based systems. Ideal for engineers, researchers, and educators, the practical examples provided introduce you to basic concepts of fuzzy logic and
• This natural phenomenon can be described more accurately by Fuzzy Set Theory. Fig.2 below shows how fuzzy sets quantifying the same information can describe this natural drift. Figure 3: Example of a Fuzzy set Properties of Fuzzy sets Fuzzy sets follow the same properties as crisp sets. Since membership values of crisp sets are a subset of
• Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible.  fuzzy set theory Then I used Fuzzy Set Theory to analyze the membership degree of key elements to verify my ...