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By Deng-Feng Li

The concentration of this publication is on setting up theories and strategies of either choice and video game research in administration utilizing intuitionistic fuzzy units. It proposes a chain of leading edge theories, versions and strategies resembling the illustration theorem and extension precept of intuitionistic fuzzy units, score equipment of intuitionistic fuzzy numbers, non-linear and linear programming equipment for intuitionistic fuzzy multi-attribute selection making and (interval-valued) intuitionistic fuzzy matrix video games. those theories and techniques shape the speculation process of intuitionistic fuzzy choice making and video games, which isn't purely remarkably diversified from these of the normal, Bayes and/or fuzzy choice idea yet may also offer a good and effective instrument for fixing complicated administration difficulties. considering the fact that there's a sure measure of inherent hesitancy in real-life administration, which can't consistently be defined via the normal mathematical equipment and/or fuzzy set thought, 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 fascinated by theoretical study and sensible functions from various fields/disciplines: choice technology, video game thought, administration technology, fuzzy units, operational learn, utilized arithmetic, platforms engineering, commercial engineering, economics, etc.

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3), the weighted Euclidean similarity degree between two ~ and B ~ is obtained as follows: intuitionistic fuzzy sets A vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u X h i u n ~ BÞ ~ ¼ 1 À t1 "s2 ðA; xj ðlA~ ðxj Þ À lB~ ðxj ÞÞ2 þ ðtA~ ðxj Þ À tB~ ðxj ÞÞ2 þ ðpA~ ðxj Þ À pB~ ðxj ÞÞ2 : 2 j¼1 ð1:3wÞ According to Eq. 4), the weighted Chebyshev similarity degree between two ~ and B ~ is obtained as follows: intuitionistic fuzzy sets A ~ BÞ ~ ¼ 1 À max "sþ1 ðA; 1 j & n ' xj ðjlA~ ðxj Þ À lB~ ðxj Þj þ jtA~ ðxj Þ À tB~ ðxj Þj þ jpA~ ðxj Þ À pB~ ðxj ÞjÞ : 2 ð1:4wÞ Obviously, if all weights xj ¼ 1=n (j ¼ 1; 2; .

2 Triangular Intuitionistic Fuzzy Numbers and Algebraic Operations It is easy to see from the above Sect. 1 that the most possible values of the trapezoidal intuitionistic fuzzy number ~a ¼ hða; a1 ; a2 ; "aÞ; w~a ; u~a i form the closed interval ½a1 ; a2 Š. , a1 ¼ a2 , then the trapezoidal intuitionistic fuzzy number is reduced to the triangular intuitionistic fuzzy number [33, 36]. 6 Definitions of Intuitionistic Fuzzy Numbers and Algebraic Operations Fig. 7 A triangular intuitionistic fuzzy number ~a ¼ hða; a; "aÞ; w~a ; u~a i 41 μ a ( x ) υa ( x ) 1 υa ( x ) wa ua μ a ( x) 0 a 8 1 > > > > < ½a À x þ u~a ðx À aފ=ða À aÞ t~a ðxÞ ¼ u~a > > ½x À a þ u~a ð"a À xފ=ð"a À aÞ > > : 1 a a x ðx\aÞ ða x\aÞ ðx ¼ aÞ ða\x "aÞ ðx [ "aÞ; respectively, depicted as in Fig.

1=2 1 ð0:12 þ 0:12 þ 0:22 þ 0:12 þ 0:12 þ 0 þ 0:12 þ 0:22 þ 0:32 Þ 6 ¼ 0:8085: According to Eq. 4), Chebyshev similarity degree between the intuitionistic ~ 0 and B ~ 0 is obtained as follows: fuzzy sets A & j0:3 À 0:2j þ j0:5 À 0:4j þ j0:2 À 0:4j ~ ~ ; sþ1 ðA0 ; B0 Þ ¼ 1 À max 2Â3 j0:4 À 0:5j þ j0:5 À 0:4j þ j0:1 À 0:1j ; 2Â3 ' j0:6 À 0:5j þ j0:3 À 0:1j þ j0:1 À 0:4j 2Â3 & ' 0:1 þ 0:1 þ 0:2 0:1 þ 0:1 þ 0 0:1 þ 0:2 þ 0:3 ; ; ¼ 1 À max 6 6 6 0:1 þ 0:2 þ 0:3 ¼1 À 6 ¼ 0:9: In the same way, according to Eq.

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