{ "item_title" : "Transforms of Undefined Sets, Undefined Structures, and Undefined β", "item_author" : [" Serpente Divo Rex "], "item_description" : "The concept proposed by Zadeh.L.A.[82] defining a fuzzy subset A of a given universe X characterizing the membership of an element x of X belonging to A by means of a membership functionA etc., in handling the imprecise real life situations mathematically. Now, several branches of fuzzy mathematics like fuzzy algebra, fuzzy topology, fuzzy control theory, fuzzy measure the- ory etc. have emerged. But in the decision making, the fuzzy theory takes care of membership of an element x only, that is the evidence of x belonging to A. It does not take care of the evidence against x belonging to A. It is felt by several decision makers and researchers that in proper decision making, the evidence of x belonging to A and evidence not belonging to A are both necessary, and how much x belongs to A or how much x does not belong to A are necessary. This is the problem with fuzzy sets. To counter this problem Gau.W.L. and Buehrer.D.J[28] introduced the concept of Vague Set Theory.", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/9/79/823/030/9798230306139_b.jpg", "price_data" : { "retail_price" : "32.00", "online_price" : "32.00", "our_price" : "32.00", "club_price" : "32.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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