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# Linguistic quantifiers modeled by interval-valued intuitionistic Sugeno integrals1

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## Abstract

Ying's model of linguistic quantifiers based on Sugeno integral is generalized to interval-valued intuitionistic Sugeno integral, the truth value of a quantified proposition is evaluated by using interval-valued intuitionistic Sugeno integral. Some logical properties of linguistic quantifiers in this model are discussed, and some application examples in uncertainty decision making and linguistic summarization of data are presented.

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... Definition 1 [21,22] Let U be an ordinary set, F (U ) denote the set of all fuzzy sets on U , A, B ⊆ U , and S: Let U be an nonempty finite set, and A, B ⊆ U . Then, we can prove that ...
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... The concept of an intuitionistic fuzzy (IF for short) set, initiated by Atanassov [15][16][17], is another important tool for dealing with imperfect and imprecise information. Compared with Zadeh's fuzzy set, an IF set is more objective than a fuzzy set to describe the vagueness of data, because IF set gives both a membership and a non-membership degree of which an element belongs to a set [18][19][20][21]. As an important generalization of IF set, Atanassov and Stoeva defined intuitionistic L-fuzzy (ILF for short ) set in 1984, which actually is an IF set based on residuated lattice L. ...
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... Many extensions of Zadeh's fuzzy set, such as vague set, intuitionistic fuzzy, hesitant fuzzy set, etc., have been proposed and been utilized management decision and engineering science problems [6][7][8][9][10][11][12]. Fuzzy integral, first introduced by Sugeno in 1974, is an important analytical tool to measure uncertain information [13][14][15][16][17][18]. ...
... Fuzzy measurements and fuzzy integrals, which were originally introduced by Sugeno in 1974 [1], are important analytical methods of measuring uncertain information [2][3][4]. The Sugeno integral has been applied to many fields, such as management decision-making and control engineering [5][6][7][8][9]. Because of the special integral operator of the Sugeno integral, it is limited in many practical problems. ...
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... Among many applications of the Sugeno integral we shall mention only few. Chen et al. [9] proposed a fusion recognition scheme based on nonlinear decision fusion, Seyedzadeh et al. [31] presented a new RGB color image encryption using keystream generator, Zhang and Zheng [37] generalized Ying's model of linguistic quantifiers, Nemmour and Chibani [19] proposed a new support vector mixture, used to evaluate the interaction of scale factors and to compare the energy performance of buildings in different scale factors [16]. Wang and Klir [35] and Pap [20] have given a general overview on fuzzy measures and fuzzy integration theory. ...
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Model of linguistic quantifiers based on general Sugeno integrals
• Zheng
The first-order fuzzy logic (I)
• Ying