By Deng-Feng Li
The concentration of this ebook is on constructing theories and strategies of either determination and online game research in administration utilizing intuitionistic fuzzy units. It proposes a sequence of cutting edge theories, versions and strategies resembling the illustration theorem and extension precept of intuitionistic fuzzy units, rating tools of intuitionistic fuzzy numbers, non-linear and linear programming tools for intuitionistic fuzzy multi-attribute choice making and (interval-valued) intuitionistic fuzzy matrix video games. those theories and techniques shape the speculation approach of intuitionistic fuzzy determination making and video games, which isn't merely remarkably various from these of the conventional, Bayes and/or fuzzy choice idea yet may also offer an efficient and effective instrument for fixing complicated administration difficulties. on the grounds that there's a convinced measure of inherent hesitancy in real-life administration, which can't continuously be defined through the normal mathematical tools and/or fuzzy set idea, this ebook deals a good method of utilizing the intuitionistic fuzzy set expressed with club and non-membership functions.
This publication is addressed to all these occupied with theoretical learn and sensible functions from quite a few fields/disciplines: selection technological know-how, video game thought, administration technology, fuzzy units, operational study, utilized arithmetic, structures engineering, business engineering, economics, etc.
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Extra resources for Decision and Game Theory in Management With Intuitionistic Fuzzy Sets
It is obvious that k power of ‘‘approximately 2’’ is equal to ‘‘approximately 2k . According to Eq. 28), we have: ~ 00 Ä~ B ~ 00 ¼ fh1=4; 0:7; 0:2i; h1=3; 0:8; 0:1i; h1=2; 1; 0i; h2=3; 0:8; 0:1i; h1; 0:8; 0:1i; h2; 0:8; 0:1ig; A which means ‘‘approximately 1/2’’. It is reasonable that the quotient (or ratio) of ‘‘approximately 1’’ and ‘‘approximately 2’’ is equal to ‘‘approximately 1/2’’. Using Eq. 29), we obtain: ~ 00 ¼ fhc; 0:8; 0:1i; h2c; 1; 0i; h3c; 0:8; 0:1i; h4c; 0:7; 0:2ig; c Â~ B ð1:35Þ which means ‘‘approximately 2c’’, where c 6¼ 0.
6. , Eq. 24)], we can define algebraic operations over the trapezoidal intuitionistic fuzzy numbers such as the addition, subtraction, multiplication and division operations2 as follows. Let ~ a ¼ hða; a1 ; a2 ; "aÞ; w~a ; u~a i and ~b ¼ hðb; b1 ; b2 ; "bÞ; w~b ; u~b i be any trapezoidal intuitionistic fuzzy numbers and c 6¼ 0 be any real number. Then, the algebraic (or arithmetical) operations are stipulated as follows: ~ ð1:36Þ aþ~ b ¼ ða þ b; a1 þ b1 ; a2 þ b2 ; "a þ "bÞ; w~a ^ w~b ; u~a _ u~b ; ~ aÀ~ b ¼ ða À "b; a1 À b2 ; a2 À b1 ; "a À bÞ; w~a ^ w~b ; u~a _ u~b ; 2 ð1:37Þ According to the notations in Sect.
If H : FðXÞ ! FðYÞ is a mapping so that [ È É ~ 2 FðXÞ 7! 5 Extension Principles of Intuitionistic Fuzzy Sets and Algebraic Operations 29 ~ 2 FðXÞ, where FðXÞ and FðYÞ are the sets of image of the intuitionistic fuzzy set A the intuitionistic fuzzy sets on the universal sets X and Y, respectively. Similarly, if H À1 : FðYÞ ! FðXÞ is a mapping so that [ È É ~ 2 FðYÞ 7! H À1 ðBÞ ~ ¼ ~ hc;gi Þ 2 FðXÞ; B hc; gihÀ1 ðB ^ hc;gi2D ~ is then H À1 is called the mapping induced by hÀ1 from FðYÞ to FðXÞ, H À1 ðBÞ ~ 2 FðYÞ, where called the inverse image of the intuitionistic fuzzy set B S ~ ~ ~ ~ ^ B¼ fhc; giBhc;gi g and Bhc;gi is the hc; gi-cut set of B, D is the set of the ^ hc;gi2D ordered pairs of the minimum membership degrees and maximum nonmembership ^ M ^ is the set of the distinct ordered pairs of degrees for all subsets ^S of M.