Fuzzy Engineering and Operations Research by S. H. Nasseri, Z. Alizadeh, B. Khabiri (auth.), Bing-Yuan

By S. H. Nasseri, Z. Alizadeh, B. Khabiri (auth.), Bing-Yuan Cao, Xiang-Jun Xie (eds.)

“Fuzzy Engineering and Operations examine” is the edited final result of the fifth overseas convention on Fuzzy info and Engineering (ICFIE2011) held in the course of Oct. 15-17, 2011 in Chengdu, China and via the first educational convention in institution of Guangdong Province Operations examine Society (GDORSC) hung on Oct. 20, 2011 in Guangzhou, China. The fifth ICFIE2011, equipped at the luck of past meetings, and the GDORC, first held, are significant Symposiums, respectively, for scientists, engineers practitioners and Operation learn (OR) researchers offering their up to date effects, advancements and functions in all parts of fuzzy details and engineering and OR. It goals to bolster kinfolk among learn laboratories and universities, and to create a chief symposium for international scientists in Fuzziology and OR fields. The ebook includes sixty two papers and is split into 5 major elements: “Fuzzy Optimization, good judgment and Information”, “The mathematical concept of Fuzzy Systems”, “Fuzzy Engineering purposes and gentle Computing Methods”, “OR and Fuzziology” and “Guess and Review”.

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Thanks to the support by National Natural Science Foundation of China (No. 60873042). References 1. : For the first time in nearly a decade violent crime growth in China. China News Service (2010) 2. : Intelligent data analysis: developing new methodologies through pattern discovery and recovery. -q. -m. -x. Liu 3. : Crime investigation and analysis using neural nets. In: 7th International Multi Topic Conference, INMIC, pp. 346–350 (2003) 4. : On the application of fuzzy clustering for crime hot spot detection.

3. Corresponding to given a real number t, there is a trapezoidal fuzzy number t˜ such that CM2λ (t˜) = t. Proof. Similar to previous theorem, given a real number λ (0 ≤ λ ≤ 1), there α . Hence, if we let aL = t − 2α are two real numbers α and β, such that λ = α+β 3 and aU = t + α 2β 3 . CM2α+β (t˜)=t − From (10) we have 2α 3 α α+β 2β 3 t+ −t+ 2α 3 α+β 3 α − α3 =t − 2α 3 +α− 3 =t Therefore, in this case we have a trapezoidal fuzzy number t˜ as (t− 2α , t+ 2β , α, β). H. Nasseri and A. Ebrahimnejad We are now in a position to naturally extend the usual definition of a linear programming problem to the problem with fuzzy variables.

Corresponding to given a real number t, there is a trapezoidal fuzzy number t˜ such that CM1λ (t˜) = t. Proof. Clearly, for given a real number λ (0 ≤ λ ≤ 1), there are two real numα . Hence, if we let aL = t − α2 and aU = t + β2 in bers α and β such that λ = α+β (9), thus we have α CM1α+β (t˜) = t − α 2 α α+β β 2 t+ −t+ α 2 α+β 2 = t − α2 + α − α2 = t Therefore, in this case we have a trapezoidal fuzzy number t˜ as (t − α2 , t + β2 , α, β), where α and β obtain from definition of λ. 3. Corresponding to given a real number t, there is a trapezoidal fuzzy number t˜ such that CM2λ (t˜) = t.

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