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

“Fuzzy Engineering and Operations learn” is the edited end result of the fifth foreign convention on Fuzzy info and Engineering (ICFIE2011) held in the course of Oct. 15-17, 2011 in Chengdu, China and by means of 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 study (OR) researchers offering their up-to-date effects, advancements and functions in all components of fuzzy info and engineering and OR. It goals to reinforce kin among learn laboratories and universities, and to create a main symposium for international scientists in Fuzziology and OR fields. The ebook includes sixty two papers and is split into 5 major components: “Fuzzy Optimization, common sense and Information”, “The mathematical idea of Fuzzy Systems”, “Fuzzy Engineering purposes and smooth Computing Methods”, “OR and Fuzziology” and “Guess and Review”.

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**Extra resources for Fuzzy Engineering and Operations Research**

**Example text**

Now, let z˜j = c˜B B −1 aj = w ˜∗ aj be the fuzzy number corresponding to real −1 number zj = cB B aj with respect to a linear ranking function, where aj is the jth column of the coefficient matrix [A I] in (10). , m. , n, that is, wA ˜ c˜. , m, we have, z˜n+i − c˜n+i = c˜B B −1 ei − ˜0 = w ˜ ∗ ei = w ˜i∗ and A New Approach to Duality in Fuzzy Linear Programming 27 hence, w ˜∗ ˜ 0. , n + m implies ∗ ˜∗ ˜ 0, where w ˜∗ = c˜B B −1 . That is w ˜ ∗ is a feasible solution to that w ˜ A c˜ and w (6).

T. , n, where [ M , M ] and [l0 , l0 ] are constant. M is the pessimistic affordable risk level of investors, and M is the optimistic affordable risk level. l0 is pessimistic l0 is optimistic affordable liquidity level. The interval numbers of objective function in (LIPM ) represents portfolio affordable liquidity level, and uncertain profits, the left of (1) is risks of portfolio described by interval numbers of standard variance, the right represents affordable risk interval. The left of (2) represents uncertainty of liquidity, the right is affordable liquidity interval.

0100. 0145. 0147. ） 5 （ Conclusion These factors in securities investment all are uncertain. It is very consistent with real condition to describe the uncertainty by interval numbers. The author has converted the fuzzy portfolio selection problem with liquidity constraints into a linear programming problem with parameters. The numerical examples have shown the method for solving this problem is valid. By the results, we know that it has an obvious influence on investment whether or not to consider liquidity constraints, and different levels of liquidity have also significant implications.