11,533 research outputs found

    Ideal Theory in BCK/BCI-algebras in the Frame Of Hesitant Fuzzy Set Theory

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    Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov’s intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra’s hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed

    Himpunan Kabur Hesitant Ganda yang Diperluas (Expanded Dual Hesitant Fuzzy Sets)

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    Konsep Expanded Dual Hesitant Fuzzy Sets merupakan suatu pengembangan dari konsep Hesitant Fuzzy Sets. Berdasarkan konsep Hesitant Fuzzy Sets telah diperoleh beberapa konsep seperti Dual Hesitant Fuzzy Sets, Expanded Hesitant Fuzzy Sets, dan Extended Hesitant Fuzzy Sets yang menjadi konsep dasar pengembangan Expanded Dual Hesitant Fuzzy Sets. Kemudian akan dikaji beberapa operasi-operasi terkait Expanded Dual Hesitant Fuzzy Sets, skor pada Expanded Dual Hesitant Fuzzy Sets, hukum perbandingan, dan penerapan konsep Expanded Dual Hesitant Fuzzy Sets dalam masalah pengambilan keputusan

    Partial orderings for hesitant fuzzy sets

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    New partial orderings =o=o, =p=p and =H=H are defined, studied and compared on the set HH of finite subsets of the unit interval with special emphasis on the last one. Since comparing two sets of the same cardinality is a simple issue, the idea for comparing two sets A and B of different cardinalities n and m respectively using =H=H is repeating their elements in order to obtain two series with the same length. If lcm(n,m)lcm(n,m) is the least common multiple of n and m we can repeat every element of A lcm(n,m)/mlcm(n,m)/m times and every element of B lcm(n,m)/nlcm(n,m)/n times to obtain such series and compare them (Definition 2.2). (H,=H)(H,=H) is a bounded partially ordered set but not a lattice. Nevertheless, it will be shown that some interesting subsets of (H,=H)(H,=H) have a lattice structure. Moreover in the set BB of finite bags or multisets (i.e. allowing repetition of objects) of the unit interval a preorder =B=B can be defined in a similar way as =H=H in HH and considering the quotient set View the MathML sourceBÂż=B/~ of BB by the equivalence relation ~ defined by A~BA~B when A=BBA=BB and B=BAB=BA, View the MathML source(BÂż,=B) is a lattice and (H,=H)(H,=H) can be naturally embedded into it.Peer ReviewedPostprint (author's final draft

    Expanded hesitant fuzzy sets and group decision making: slides for FUZZ-IEEE 2017

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    [EN]We define expanded hesitant fuzzy sets, which incorporate all available information of the decision makers that provide the membership degrees that define a hesitant fuzzy set. We show how this notion relates to hesitant fuzzy set and extended hesitant fuzzy set. We define various scores for this setting, which generalize popular scores for hesitant fuzzy elements. Finally, a group decision making procedure is presented and illustrated with an example

    Modeling group assessments by means of hesitant fuzzy linguistic term sets

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    Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.Peer ReviewedPostprint (author's final draft

    Dual Hesitant Fuzzy Set

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    Konsep dual hesitant fuzzy set merupakan suatu pengembangan dari konsep fuzzy set. Berdasarkan konsep fuzzy sets telah diperoleh beberapa konsep seperti Intuitionistic fuzzy sets dan Hesitant Fuzzy Sets yang menjadi konsep dasar pengembangan dual hesitant fuzzy set. Kemudian akan dikaji beberapa operasi-operasi terkait dual hesitant fuzzy set, pembuktian teorema-teorema yang ada dan dikaji juga tentang penerapan konsep dual hesitant fuzzy set dalam masalah pengambilan keputusan

    Intuitionistic Hesitant Fuzzy Filters in BE-Algebras

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    The notions of hesitant fuzzy filters and hesitant implicative filter was introduced. In this paper, we introduce the notion of intuitionistic hesitant fuzzy filters (IHFF) and intuitionistic hesitant implicative filters (IHIFB) and several properties are investigated. Also, we defined ?-level sets, and we show the relation between IHFF, IHIFF and ?-Level

    The generalized dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic information

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    In this paper, we shall present some novel Dice similarity measures of hesitant fuzzy linguistic term sets and the generalized Dice similarity measures of hesitant fuzzy linguistic term sets and indicate that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute decision making models with hesitant fuzzy linguistic term sets. Finally, a practical example concerning the evaluation of the quality of movies is given to illustrate the applicability and advantage of the proposed generalized Dice similarity measure

    The generalized dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic information

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    In this paper, we shall present some novel Dice similarity measures of hesitant fuzzy linguistic term sets and the generalized Dice similarity measures of hesitant fuzzy linguistic term sets and indicate that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute decision making models with hesitant fuzzy linguistic term sets. Finally, a practical example concerning the evaluation of the quality of movies is given to illustrate the applicability and advantage of the proposed generalized Dice similarity measure
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