Evaluating new varieties of wheat with the application of Vague optimization methods

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1 Evauatg ew varetes of wheat wth the appcato of Vague optmzato methods Hogxu Wag, FuJ Zhag, Yusheg Xu,3 Coege of scece ad egeerg, Coege of eectroc formato egeerg, Qogzhou Uversty, aya Haa 570, Cha. Abstract. The Vague optmzato method sorted out s a speca case of the patter recogto method of the Vague set. Its specfc appcato steps are as foows: the set-up of characters to determe the evauato; the estabshmet of a coecto of ew varetes of wheat to be optmzed; 3 the extract of the dea set of ew wheat varetes ; 4 the costructo of Vague evromet to coect a varetes of Vague sets; 5 the Vague optmzato: to cacuate smarty measures betwee Vague sets to obta the ew wheat varetes based o umerca smarty measures ad to propose the smarty measures formua betwee the Vague sets. Ths optmzato formua s supported by Vague cass techques. Breedg ew varetes of wheat wth comprehesve quaty trats s oe of the drectos wheat breedg. It s a ew attempt to study the wheat assessmet of the ew wheat varetes wth the appcato of optmzato methods. The wheat assessmet case of the ew wheat varetes shows that both the formua ad the method are practca. Keywords: Vague set; Vague optmzato; Vague evromet; smarty measure; assessmet of ew varetes of wheat Itroducto Vague sets [] were put forward as Fuzzy ets popuato []. Though t was put forward 8 years ater tha Fuzzy set theory, Vague set theory has bee wdey used may feds such as patter recogto, automatc cotro, teget reasog, for t uses the terva umbers of Vague set membershp to dcate degree of membershp, whch ca more fuy refect the fuzzy formato. Ths paper ams to appy the Vague set theory to the evauato of ew varetes of wheat ad to provde the ew research methods to the agrcuture-reated ssues. Basc cocept Defto [] uppose L be a pot of space, ay oe of the eemets ca be dcated wth. L o a Vague set s, t s a membershp fucto wth a true t ad a fase membershp fucto f sad. t () s evdece to support the export of s Ackowedgmets:The Haa Provca Natura cece Fud Project No.604;the Haa Provca oca deveopmet projects for scece ad techoogy deveopmet fud No.00F004 ad aya Cty Coege, 009 speca fud project fudg ssues (YD0907).

2 certa ower boud of the membershp, ad s the evdece from the opposto f () derved the ower boud of the egatve membershp. t () ad f () w be a rea umber the rage of pot of cotact wth the L together. That s, map t : L [0,], f : L [0,], ad satsfes the costrats: t ( ) f ( ).Vague set ca be recorded L pots the membershp or Vague s smpfed by ( ) [ t ( ), f ( )] or [ t, f ]. It ca be see from the defto of [ t, f] [0,]. t f that o the set of eemets pars s ucerta fucto Vague, aso caed the degree of ucertaty or the degree of Vague. If L s a dscrete doma of [ t ( ), f ( )] L {,,, } ad L o Vague set ca be wrtte as, [ t, f ] aso deoted by. 3 Vague evrometa costructo The so-caed costructo of Vague evromet s to tur the raw data to Vague data. Ths step s a prerequste for the appcato of Vague sets. The sge-vaue data are tured to the data defto Vague proposed Referece [3], here aga the formua for turg sge-vaue data to a Vague data s provded the assessmet of ew wheat varetes. Defto Let the doma L {,,, }, L, has a coecto of (,, m), j ( j,, ) data set of characters wth o-egatve sgevaue data j. uppose whe the sge-vaue data whe the o-egatve j Vague data turg to the formua to meet the output of the coverso of ( ) [ t, f ] codtos ad Vague terms, we ca ths formua the formua j j j j for the output type, amog whch: a. Output codtos If 0 kj j, j ad kj sge-vaue data tur to the Vague data respectvey, ( ) [ t, f ] ad ( ) [ t, f ] satsfy the codto: j j j j t t, f f. kj j kj j k j kj kj kj b. Iput codtos If 0 kj j, j ad kj sge-vaue data tur to the Vague data, ( ) [ t, f ] ad ( ) [ t, f ] satsfy the codto: j j j j t t, f f kj j kj j k j kj kj kj

3 c. Vague terms 0 t f. j j Note: Output type trasformato formua for umerca characters takes "the bgger, the better" use; put type trasformato formua for umerca characters takes "the smaer the better" use. Theorem : If j max max{ j, j,, mj}, the j j ( j ) j [ tj, fj ], jmax () jmax s o-egatve sge-vaue data j to the output data type Vague coverso formua. j j ( j ) j [ tj, fj ], () jmax jmax s o-egatve sge-vaue data j to the put data type Vague coverso formua. 4 The ew smarty measures betwee Vague vaues If Lemma [4] s to Vague vaue of [ t, f ], the ( m ) ( m [ ), ( m t f ) ] s Vague vaue. Vague vaue [ t, f ] of the formua s kow as the frst m to ( t, f ) data mg Vague vaue, amog whch: f f ( ), ( m) m ( m) ( t f )( ), m ( m) ( m) ( t f )( ),( m 0,,, ). A smpe ad practca Vague measure of smarty betwee the vaues s defed by Referece [5]. Defto 3 If s [ t, f ], h [ t, f ] s two Vague vaues, the s s h h formua M( s, h ) betwee s ad h s smarty measures of the Vague vaue, f M( s, h ) satsfes the foowg codtos: a. 0- codtos 0 M( s, h) b. ymmetry codtos M( s, h) M( h, s) c. Refexve codtos M( s, s) d. Mmum codto Whe s[0,0], h [,] or s[,], h [0,0], the M( s, h) 0. Vague, whch s aso kow as the umerca vaue of M( s, h) 0 smarty betwee s ad h.

4 Note: the smarty measure of Vague vaue betwee s ad h, meas that the greater the smarty vaues of M( s, h ), s ad h, the more smar Vague vaues betwee s ad h, especay whe the maxmum smarty vaue of M( s, h ) s up to, the vaue of Vague s ad h s the most smar; coversey, the smaer the smarty vaue of M( s, h ), s ad h, ess smar Vague vaues betwee s ad h, especay whe the mmum smarty vaue of M( s, h ) reaches 0, vaue of Vague s ad h s the east smar. Theorem Note m 0,,,, the formua ( m) ( m) ( m) ( m) ( ) ( ) s h s m m h M m ( s, h) fs f h measure of Vague vaue betwee s ad h. (3) s the smarty 5 Vague smarty measures betwee the ew Vague sets of metrcs From the defto of smarty measures betwee Vague ets ad Vague ets smarty betwee the weghted measure, smar to Defto 3, theorem ca aso be obtaed from the foowg theorem. [ t ( ), f ( )] Theorem 3 Let the doma L {,,, }, L o ad [ th ( ), fh ( )] H Vague sets are smpy deoted as [ th, f ] h H respectvey. Ad ote m 0,,,, The formua [ ts, f ] s ad ( m) ( m) ( m) ( m) ( ) ( ) s h s m m h M m (, H) fs f h (4) s the smarty measures of Vague sets betwee s ad h of the metrcs. Theorem 4 If the eemet weght (,,, ) s b [0,], ad ote m 0,,,. the the codtos Theorem 3, the formua ( m) ( m) ( m) ( m) ( ) ( ) s h s m m h M m (, H) b fs f h (5) s the weghted smarty measures betwee Vague sets ad H. b, ad

5 6 Vague Optmzato The comprehesve decso-makg rues of Vague sets Referece [6] are reorgazed to Vague optmzato method ft for the research o the assessmet of ew varetes of wheat. Ther specfc appcato steps are as foows: the set-up of characters to determe the evauato; the estabshmet of a coecto of ew varetes of wheat to be optmzed; 3 the extract of the dea set of ew wheat varetes ; 4 the costructo of Vague evromet to coect a varetes of Vague sets; 5 the Vague optmzato: to cacuate smarty measures betwee Vague sets to obta the ew wheat varetes based o umerca smarty measures. If Vague sets of patter recogto s for the purpose of optmzato, the the patter recogto method of Vague sets ca be caed the Vague optmzato method. o Vague set optmzato method s a speca case of the patter recogto. It has oe stadard mode ad severa to be recogzed over the Vague sets of patter recogto methods. 7 Optma assessmet of ew varetes of wheat Fuzzy Comprehesve Evauato Referece [7] s used to study the assessmet of ew varetes of wheat. I ths paper, Vague optmzato method s apped to reexame the ssue. 7. To estabsh the evauato set of trats Take as the "yed (kg/667m)"; as "stra rate (%)"; 3 as the" drought dex "; 4 as a" vad spke umber (mo / 667m) "; 5 as" gras per spke ( tabets) "; as" gra weght (g) ", the the evauato of the set of characters s 6 L {,,, }. 6 Fac tor Tabe. The characterstcs of ew varetes of wheat, the average data The characterstcs of ew varetes of wheat, the average d ata H

6 To set up the optma set of ew varetes of wheat Take as the "Lao 97 Kam 30", as "Zhema 0", 3 as "Kyrgyzsta prg 9806", 4 as the "Lao Chu 9 (ck)". They are composed of a coecto of trats evauated o a set of L {,,, 6}. They cosst of a coecto of ew varetes of wheat to be optmzed. The specfc data are from Referece [7], as show Tabe. 7.3 To extract the dea project Referece [7] tes that f the ew varetes of wheat are expected to be a "optma" a trats, the the bgger the s, the better shoud be; the smaer the s, the better; the bgger the s, the better; the more the s, the better; the more the s the better; the heaver 6 s, the better. Extractg the best data of varous trats avaabe to evauate the set of characters composed of a coecto of L {,,, 6}. o the H, whch s caed the dea of ew wheat varetes. The data for each trat are show Tabe. 7.4 Eter the Vague Evromet Formua () ca be apped to Characters,,, ad ; Formua () s apped to. Tabe ca be tured to Tabe. Tabe The characterstcs of ew varetes of wheat Vague data Factor The characterstcs of ew varetes of wheat Vague data 3 4 [.000,.000] [0.947,0.986] [0.90,0.974] [0.806,0.948] [.000,.000] [0.,0.64] [0.434,0.898] [0.000,0.000] [0.7,0.438] [0.434,0.898] 3 [0.74,0.9] [.000,.000] [0.540,0.857] [0.607,0.880] [.000,.000] 4 [0.90,0.979] [.000,.000] [0.78,0.94] [0.774,0.938] [.000,.000] 5 [.000,.000] [0.953,0.988] [0.958,0.989] [0978,0.994] [.000,.000] 6 [0.945,0.986] [0.70,0.95] [.000,.000] [0.99,0.98] [.000,.000] Tabe shows the seecto of the ew wheat varetes of,, 3, 4,ad H ew varetes of wheat dea Vague coecto. H

7 7.5 Vague Optmzato New varetes of wheat are sorted out through cacuatg the smarty measures betwee Vague sets, accordg to the sze of umerca smarty measure. The formua (4) s as foows: take m, cacuate the smarty measures betwee Vague sets (,,3, 4) ad H. The resuts are: M(, H) 0.843, M(, H) 0.956, M( 3, H) 0.79, M( 4, H) Thus, accordg to the sze of smarty measures, the order s: M(, H) M(, H) M( 4, H) M( 3, H). The smarty of Vague sets s that the arger the umber s, the more smar these two Vague sets are; the smaer the vaue s, the more dssmar the two Vague sets are. o the cocuso of Vague optmzato decso: amog whch the best varety s : Zhema 0. The secod s : Lao 97 Kam 30. ad poorer oe s 4 : Lao Chu 9 (ck) ad 3 : J Chu 9806, 4 : Lao Chu 9 (ck). 8 Cocuso The Fuzzy comprehesve evauato method used apped Referece [7], athough t s abe to "make up for the ack of aayss of varace," s reatvey more compcated, partcuar t eeds to cacuate fuzzy matrx, whose speed s rather sow. The optmzato method, by meas of wheat Vague eecto of ew varetes, s feasbe. It s more reasoabe ad easer to use tha the exstg oe, ad t provdes a more practca approach optmzg the ew wheat varetes. ted to provde. From the exampe metoed-above, Vague optmzato method s a ateratve to the fuzzy comprehesve evauato. As we a kow, the appcato of fuzzy comprehesve evauato process s more cumbersome, ad wth a arge umber of cacuato. Vague optmzato method ot oy provdes a ew method for dscussg the smar probems, ad ts appcato the feds such as speces optmzato s of a great poteta area. Ad the formua (), (), (3), (4) ad (5) put forward ths paper provde the techca support for t. Refereces. Gau We-Lug, Buehrer D J. Vague ets [J].IEEE Trasactos o ystems, Ma ad Cyberetcs. 993; 3(): Zadeh L A.Fuzzy ets [J].Iformato ad Cotro, 965; (8): Wag Hog-xu. Defto ad trasformg formuas from the sge vaued data to the vague vaued data [J].Computer Egeerg ad Appcatos, 00; 46(4): Lu Hua-we, Wag Feg-yg. Trasformatos ad marty Measures of Vague ets [J].Computer Egeerg ad Appcatos, 004, 40(3):79-8, Wag Hog-xu. marty measure betwee vague sets ad ther appcato [J]. Computer Egeerg ad Appcatos, 00;46(6): Wag Hog-xu. ythess decso rue of vague sets ad ts appcato scheme optmum seekg [J]. Computer Egeerg ad Appcatos, 00 ; 46 (7): 45-47

8 7. Modeeto, Erduga, Bayatu,etc.The fuzzy comprehesve evauato to the appcato of ew wheat evauato [J].Ier Mogoa Agrcutura cece ad Techoogy, 007; ():37-38