By Deng-Feng Li
The concentration of this booklet is on setting up theories and techniques of either determination and online game research in administration utilizing intuitionistic fuzzy units. It proposes a sequence of cutting edge theories, types and techniques equivalent to the illustration theorem and extension precept of intuitionistic fuzzy units, score tools of intuitionistic fuzzy numbers, non-linear and linear programming equipment for intuitionistic fuzzy multi-attribute choice making and (interval-valued) intuitionistic fuzzy matrix video games. those theories and strategies shape the speculation method of intuitionistic fuzzy choice making and video games, which isn't in basic terms remarkably varied from these of the normal, Bayes and/or fuzzy determination concept yet may also supply an efficient and effective instrument for fixing complicated administration difficulties. in view that there's a convinced measure of inherent hesitancy in real-life administration, which can't consistently be defined via the conventional mathematical equipment and/or fuzzy set idea, this e-book bargains a good method of utilizing the intuitionistic fuzzy set expressed with club and non-membership functions.
This publication is addressed to all these all for theoretical learn and useful functions from a number of fields/disciplines: choice technological know-how, video game idea, administration technological know-how, fuzzy units, operational examine, utilized arithmetic, platforms engineering, commercial engineering, economics, etc.
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Additional resources for Decision and Game Theory in Management With Intuitionistic Fuzzy Sets
B ‘‘approximately 2c’’. , Eqs. 31)]. They have to be cautiously chosen for applications to solving real management and decision problems [30, 31]. 6 Definitions of Intuitionistic Fuzzy Numbers and Algebraic Operations The intuitionistic fuzzy number is a very important concept of the intuitionistic fuzzy modeling and optimization, which may be used to quantify an ill-known quantity in some real management situations [15, 16]. In this section, we will firstly introduce the concept of an intuitionistic fuzzy number.
1), Minkowski normalized distance ~ and B ~ is obtained as follows: between any intuitionistic fuzzy sets A vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u X Ã u 1 n Â q ~ BÞ ~ ¼t dq ðA; ðlA~ ðxj Þ À lB~ ðxj ÞÞq þ ðtA~ ðxj Þ À tB~ ðxj ÞÞq þ ðpA~ ðxj Þ À pB~ ðxj ÞÞq : 2n j¼1 ð1:5Þ Analogously, according to Eq. 2), Hamming normalized distance between ~ and B ~ is obtained as follows: any intuitionistic fuzzy sets A ~ BÞ ~ ¼ d1 ðA; n À Á 1 X jlA~ ðxj Þ À lB~ ðxj Þj þ jtA~ ðxj Þ À tB~ ðxj Þj þ jpA~ ðxj Þ À pB~ ðxj Þj : 2n j¼1 ð1:6Þ 20 1 Intuitionistic Fuzzy Set Theories According to Eq.
4), respectively. 3 Let A hx1 ; 0:2; 0:4i þ hx2 ; 0:5; 0:4i þ hx3 ; 0:5; 0:1i be two intuitionistic fuzzy sets on the universal set X0 ¼ fx1 ; x2 ; x3 g. Assume that weights of the elements x1 , x2 and x3 are given as follows: x1 ¼ 0:5, x2 ¼ 0:2, x1 ¼ 0:3. , s1 ðA ~ 0 Þ, s2 ðA ~ 0 Þ, sþ1 ðA ~ 0 Þ, "s1 ðA ~ 0 Þ, fuzzy sets A ~0; B ~0; B ~ 0 Þ, and "sþ1 ðA ~ 0 Þ. "s2 ðA ~ 0 and B ~ 0, Solving According to Eq. 3 Distances and Similarity Degrees Between Intuitionistic Fuzzy Sets 17 1 ½ðj0:3 À 0:2j þ j0:5 À 0:4j þ j0:2 À 0:4jÞ þ ðj0:4 À 0:5j 2Â3 þj0:5 À 0:4j þ j0:1 À 0:1jÞ þ ðj0:6 À 0:5j þ j0:3 À 0:1j þ j0:1 À 0:4jÞ 1 ¼ 1 À ð0:1 þ 0:1 þ 0:2 þ 0:1 þ 0:1 þ 0 þ 0:1 þ 0:2 þ 0:3Þ 6 ¼ 0:8: ~0; B ~0Þ ¼ 1 À s1 ðA Likewise, according to Eq.