Научная статья на тему 'Nitrogen-phosphate fertilizers based on ammonium nitrate melt and nodule phosphorite from Kara-Kalpakistan'

Nitrogen-phosphate fertilizers based on ammonium nitrate melt and nodule phosphorite from Kara-Kalpakistan Текст научной статьи по специальности «Биологические науки»

CC BY
198
53
i Надоели баннеры? Вы всегда можете отключить рекламу.
Ключевые слова
AMMONIUM NITRATE / PHOSPHORITE / MELT / NITROGEN-PHOSPHATE FERTILIZER / COMPOSITION / GRANULE DISSOLUTION RATE / RHEOLOGICAL PROPERTIES / THERMOSTABILITY. INTRODUCTION

Аннотация научной статьи по биологическим наукам, автор научной работы — Madenov Berdimurat Dauletmuratovich, Namazov Shafoat Sattarovich, Seytnazarov Atanazar Reypnazarovich, Reymov Ahmed Mambetkarimovich, Beglov Boris Mihaylovich

The investigations on obtaining of the thermostable nitrogen-phosphate fertilizers based on ammonium nitrate melt and Kara-Kalpakistan’s phosphorite at weight ratios of ammonium nitrate: phosphorite flour from 100: 3 to 100: 35 and at temperature of 180 оC have been carried in this study. The composition and the properties (strength, solubility and granule thermostability, pH of product) of phosphate containing ammonium nitrate have been determined. The rheological properties (density and viscosity) of nitrophosphate melt in the range of temperature of 160-185 оС and weight ratios of ammonium nitrate to phosphorite 100: (3-35) have been studied.

i Надоели баннеры? Вы всегда можете отключить рекламу.
iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.
i Надоели баннеры? Вы всегда можете отключить рекламу.

Текст научной работы на тему «Nitrogen-phosphate fertilizers based on ammonium nitrate melt and nodule phosphorite from Kara-Kalpakistan»

References:

1. NRA. 2011. Readings of Environmental Radiation Level by emergency monitoring (March 2011). http://radioactivity.nsr.go.jp/en/list/207/list-201103.html [Accessed 19.11.15.].

2. Fuchs N. A. The Mechanics of Aerosols, Dover Publications, 1989. - P. 421.

3. Greenfield S. M. Rain scavenging of radioactive particulate matter from the atmosphere. Journal ofMeteorology. -1957. - № 14, - P. 115-123, doi:10.1175/1520-0469 (1957)014.

4. Slinn W. G. N. Precipitation scavenging, in: Atmospheric Science and Power Production, edited by: Randerson, D., Doc. D0E/TIC-27601, Tech. Inf. Cent., Off. Of Sci. and Tech. Inf U. S. Dep. Of Energy, Washington, D. C. 1984. - P. 466-532.

5. Kashparov V. A., Lundin S. M., Khomutinin Yu. V. Soil contamination with 90Sr in the near zone of the Chernobyl accident. J. Environ. Radioactiv. - 2001. - № 56. P. 285-298. doi:10.1016/S0265-931X (00)00207-1.

6. Kim Y.-H., Yiacoumi S., Tsouris C. Surface charge accumulation of particles containing radionuclides in open air, J. Environ. Radioactiv. - 2015. - № 143. P. 91-99, doi:10.1016/j.jenvrad.2015.02.017.

7. Pauthenier M., Cochet R. Evolution d'une gouttelette d'ean chargée dans un nuage à température positive, Rev. gén. élec., 1953. - № 62. P. 255-262.

8. Levin L. M. Research in physics coarse aerosols. Moscow, Academy of Sciences of the USSR, 1961. - P. 266. (in Russian).

Madenov Berdimurat Dauletmuratovich, Institute of General and Inorganic Chemistry Academy of Sciences of the Republic of Uzbekistan, junior scientific researcher, the Laboratory of Phosphate fertilizers E-mail: [email protected] Namazov Shafoat Sattarovich, Institute of General and Inorganic Chemistry Academy of Sciences of the Republic of Uzbekistan, Doctor of Sciences, Professor, head of the Laboratory of Phosphate fertilizers E-mail: [email protected] Seytnazarov Atanazar Reypnazarovich, Institute of General and Inorganic Chemistry Academy of Sciences of the Republic of Uzbekistan, Doctor of Science, leading specialist of the Laboratory of Phosphate fertilizers E-mail: [email protected] Reymov Ahmed Mambetkarimovich, Institute of General and Inorganic Chemistry Academy of Sciences of the Republic of Uzbekistan, Doctor of Science, Deputy of scientific study of the Institute of General and Inorganic Chemistry of AS RUz

E-mail: [email protected] Beglov Boris Mihaylovich,

Institute of General and Inorganic Chemistry Academy of Sciences of the Republic of Uzbekistan, academician of AS RUz, Doctor of Sciences, Professor, leading specialist of the Laboratory of Phosphate fertilizers

E-mail: [email protected]

Nitrogen-phosphate fertilizers based on ammonium nitrate melt and nodule phosphorite from Kara-Kalpakistan

Abstract: The investigations on obtaining of the thermostable nitrogen-phosphate fertilizers based on ammonium nitrate melt and Kara-Kalpakistan's phosphorite at weight ratios of ammonium nitrate: phosphorite flour from 100:

3 to 100: 35 and at temperature of 180 0C have been carried in this study. The composition and the properties (strength, solubility and granule thermostability, pH of product) of phosphate containing ammonium nitrate have been determined. The rheological properties (density and viscosity) of nitrophosphate melt in the range of temperature of 160-185 0C and weight ratios of ammonium nitrate to phosphorite 100: (3-35) have been studied.

Keywords: ammonium nitrate, phosphorite, melt, nitrogen-phosphate fertilizer, composition, granule dissolution rate, rheological properties, thermostability.

Introduction

Since 2009 in Uzbekistan join stock company (JSC) "Navoiazot" has developed the manufacture of ammonium nitrate containing phosphate fertilizer (APF) by introduction either Kyzyl kum's phosphate or am-mophos into ammonium's melt. Composition of the phosphorite was (wt.%): 17-18 Р2 О5, 47-48 СаО, 1718 СО2, Р2 О5 : Р2 О5 б х100 = 17-18) [1-4, 28-302 2 5усв. 2 5 общ. ' L '

35-361-368]. In this case the melt of ammonium nitrate was mixed by phosphate containing component in the mixer directly before granulation process. The phosphate additive escapes the neutralization stage, evaporation and after evaporation of ammonium nitrate solution where salt precipitation and heat-exchange apparatus skulling are not took place. Therefore, when we performance installation building to obtain nitrogen-phosphate fertilizer based on ammonium nitrate's melt and phosphorite flour we will increase gross production of phosphate containing fertilizers from low-grade phosphate raw material. According to the technical compliance (TC) 6.1-00203849-111:2007 APF has 22-28% of nitrogen, 1-6% of Р2 О5 as well as grain-size composition the following: 1-4 mm — not less 95%, less 1 mm — not over 3%. The granule strength of APF exceeds the ammonium nitrate strength upon 4-5 times.

Should be noted, that in Uzbekistan, besides the phosphorite of Central Kyzyl kum there are phosphorites from Surkhondaryo, Jizzakh, Bukhara, and KaraKalpakistan. In order to expand phosphate production to produce APF on technology of JSC "Navoiazot" we decided to use nodule phosphorite from Kara-Kalpaki-stan instead of granular Central Kyzyl kum's phosphorite. There are ten deposits of nodule phosphorites on area

Kara-Kalpakistan. These are Khodjakul, Sultan-Uizdag, Khodjeli, Nazarhan, Chukay-Tukay and others. They are differenced on their location, chemical composition and properties, as well as reserves. However, this type of phosphorite has not developed yet. Difference of nodule phosphorite of Kara-Kalpakistan from Kyzyl kum phosphorite included the following: the first there is a lot of silica in it, the second there is francoplite one. It is known that, 20-25% phosphorus exchanged by carbon in apatite structure.

In prevailing mass of ore phosphorus is in such mineral form which assimilated badly by plant. Therefore, there are few studies about nodule phosphorites in the literatures. In agrochemistry part of P2 05 leached by 2% solution of citric acid from compound is criteria ofphosphorus assimilation. The solution of citric acid on dissolution ability is

approximate to humic acid of soil. The relative content

of citric acid dissolution of P2 05 in nodule phosphorite makes 40% that is more than Karatau (Kazakhstan) and Kyzyl kum, as well as apatite ore [5, 28-32].

This fact it can be explained by crystal structure imperfection of cutsite minerale that allows to use nodule phosphorite for direct application in soil in form of phosphorite flour. However, application it on neutral or chalk soil is ineffective. Possible way of this phosphorite for crop farming in Republic concludes using them in the composition ammonium nitrate.

Experimental procedure

In this study we have investigated the APF obtaining process based on ammonium's melt (AN) and phosphorite (PR) from Khodjakul and Khodjeli, KaraKalpakistan. The chemical composition and power of the phosphorites are shown in Table 1 and 2.

Table 1. - Chemical composition of the phosphate raw

The type of phosphate raw material Components content, weight%

Р2 05tot. Р2 05acce. СаО tot. SiO2 FeÛ3 ^3 MgO СО2

Khodjakul 19,05 7,41 39,19 30,88 2,01 3,18 0,69 3,92

Khodjeli 16,48 6,59 33,39 28,04 3,26 5,09 0,49 3,84

The experiments were conducted in the following way. The sample of AN (34.5% N and 0.3% MgO), product from JSC "Maxam-Chirchik" was melt by electric heating. The phosphate raw was introduced into the

melt when weight ratios of AN: PR from 100: 3 to 100: 35, at 180 °C.

Nitrogen-phosphate melt was stirred up for 20 min. at constant 180 °C.

Table 2. - Disperse composition of the phosphate raw

The type of phosphate raw material Fractional yield, weight%

Size grade

+0,315 mm -0,315 +0,25 mm -0,25 +0,16 mm -0,16 +0,1 mm -0,1+ 0,063 mm -0,063+ 0,05 mm -0,05 mm Initial mass, %

Khodjakul 3,9 3,1 17,35 12,8 20,05 10,1 32,7 100

Khodjeli 3,82 3,60 18,05 13,1 19,95 9,90 31,58 100

Subsequently the melt was poured into the granulator, which made of metallic glass with perforated bottom; the diameter of hole was 1.2 mm.The pressure was created by air-pump the top of glass. And the melt was sprayed on polyfilm, lying on the soil, at a height of 35 mm. At that APF granules were obtained as a standard AN granules. Then measuring of granule strength was studied. Further the granules were ground and analyzed to contain of various components according to known technique [6, 218]. The decarbonization degree was calculated by C02 content changing in phosphate raw. Moreover, the dissolution rate of APF granules was determined. For that the fertilizer granule put into the glass with 100 ml distiller water where the dissolution process was tested visually and fixed completely its dissolution. The procedure was carried out at room temperature, and test was fivefold.

We studied rheological properties (density, viscosity) of nitrogen-phosphate melt having large value when technology implementation. The density and viscosity were defined noted above of ratio AN: PR in the range of 160185 °C. The density was studied picnometric method, but the viscosity with viscometer VPJ-2. The product obtained was ground in order to tested rheological properties. The result powder formed and it fed into the picnometer and 12

£ io

the viscometer, and then placed in the thermostat, filled with glycerine. While the temperature in the thermostat raised until indicated value the powder melt. The melt was hold at indicated temperature for 5-7 min. then the mea-surings were conducted. However, heat stability of granule multiply was replicated on cycle heating-cool in the ranges of 20^60 °C according to [7, 47-49]. 100 granules with the same size were placed in the special weighting battle and hold in the oven drying for 15 min. that was heated to 75°C, and then they were hold at room temperature (20 °C) and heated again.

After each cycle of heating-cool determined the numbers of destroyed granules which were removed off battle. The relative error was not over ±5%.

Results and Discussion

The results of granules strength tests are shown in fig.1. As shown that additive phosphorite from Khod-jakul in the ammonium nitrate melt in the ranges from 100: 5 to 100: 35 (in amount from 0,90 to 4,96% P2 05) increases the granule strength with diameter 2-3 mm from 3,24 to 10,26 MPa. Even 0,56% additive of P2 05 in form of phosphorite flour increases the strength of standard ammonium nitrate granule (1,6 MPa) in two times (3,24 MPa). The product obtained contents 33,45% N.

2 , ►

\ 1

100:5 100:10 100:15 100:20 100:25 100:30 100:35

Weight ratio of AN :PR

Fig. 1. Granule strength of APF samples obtained by introduction Khodjakul (1) and Khodjeli (2) phosphorite flour into ammonium nitrate melt

6 4 2

Introduction of the phosphorite from Khodjakul into the ammonium nitrate melt in the ranges from 100: 3 to 100: 35 leads to raise the granule strength from 3,2 to 9,72 MPa. The increase of granule strength argues about reduction its porosity and inside specific surface that leads to decrease amount of diesel fuel into granule. So, explosion ability of ammonium nitrate is reduced.

Table 3 presents the melt of ammonium nitrate makes an activation the phosphate raw, i. e. destroys its structure and changes unassimilable form of P2 05 into assimilable for plant form. So, the product in the range of AN: PR with use of Khodjakul phosphorite flour containing 28,46% N and assimilable form of P2 05 by relation to overall 90%. However, the product from Khodjeli phosphorite has 28,74% and 84,31%, respectively. It can be seen that the Khodjakul phosphorite in the ammonium nitrate melt more efficiently subjects to activation process than Khodjeli. This fact can be explained presence of hard decomposition phosphates in Khodjeli phosphorite, which subject badly activation process with ammonium nitrate melt. The activation process correlates well with decarbonization degree of phosphate raw. The large of phosphate raw put into the ammonium nitrate melt the reducing assimilable form of P2 05 in the product and decarbonization degree of phosphate raw.

Presence of water form of CaO and C02 waste into gas phase argues that at 180 0C occur reaction between

ammonium nitrate and calcium carbonate with formation calcium nitrate as below.

2NHNO, + CaCQ3 ■ Ca (NO.). + 2NH + CO.

+ H2o

pH of Khodjakul phosphorite was prepared by its 10% water solution that is in the ranges from 6,42 to 6,79 рН, but pH of product from Khodjeli phosphorite is from 6,37 to 7,16 (Table 3).

As these value of pH are more significant than ammonium nitrate (рН = 5,5). In connection with additive of phosphorite at 180 оС and the oxidation process does not occur, i. e. free nitric acid is neutralized rapidly by phosphorite.

It is can make a conclusion that phosphate additives influence on pH of melt and reduce acid during the heating of ammonium nitrate. Therefore, phosphate additive promotes increase ammonium thermostability.

Fig.2. presents rheological properties of nitrogen-phosphate melt in weight ratios ofAN: PR=100: (3-35) and in the temperature ranges 160-185 оС.

As it is seen from the draws that introduction of Khodjakul and Khodjeli phosphorites into ammonium nitrate melt affects appreciable on the density and the viscosity. So, at 160 оС standard ammonium nitrate does not melt and flows naturally. Additive either the same phosphorite or another one leads to reduce crystallization temperature of ammonium nitrate. Although it has large viscosity and melt at 160 оС, but flow readily.

Table 3. - Chemical composition nitrogen-phosphate fertilizers obtained by introduction of Kara-Kalpakistan phosphorite into ammonium nitrate melt

Weight ratio of AN: PRC рН of 10% solution of product Component content, weight. % СаО : wat. СаО .% tot . Decarbonization degree

N Р 0Stat СаО. t tot.

1 2 3 4 5 6 7

Based on Khodjakul phosphorite

100: 3 6,42 33,45 0,56 1,12 26,79 21,25

100: 5 6,49 32,78 0,90 1,87 25,13 19,80

100: 8 6,54 31,69 1,42 2,88 24,65 17,96

100:12 6,58 30,34 2,07 4,20 23,57 15,51

100:15 6,60 29,85 2,49 5,12 22,85 14,32

100:18 6,62 29,20 2,90 5,95 22,02 13,04

100:20 6,64 28,46 3,21 6,53 21,44 12,04

100:25 6,69 27,56 3,79 7,84 19,90 9,44

100:30 6,74 26,40 4,42 9,01 17,98 8,67

100:35 6,79 25,44 4,96 10,14 16,77 6,87

Based on Khodjeli phosphorite

100: 3 6,37 32,82 0,49 0,96 26,04 12,41

100: 5 6,45 32,71 0,77 1,57 24,20 12,00

100: 8 6,56 31,94 1,22 2,45 22,44 11,58

100:12 6,61 30,64 1,78 3,57 21,29 10,26

1 2 3 4 5 6 7

100:15 6,78 29,87 2,16 4,35 20,00 9,17

100:18 6,85 29,01 2,53 5,07 18,15 8,69

100:20 6,92 28,74 2,74 5,57 16,70 7,89

100: 25 7,01 27,42 3,32 6,66 14,86 5,56

100:30 7,11 26,48 3,81 7,70 13,25 4,30

100:35 7,16 25,45 4,29 8,65 12,14 3,00

The change the density and the viscosity of ammonium nitrate melt depending on the weight ratio of AN: PR and temperature increase of Khodjakul phosphorite additive (fig. 2-a, curve -1) from 3 to 35 weight parties to 100 weight parties of ammonium nitrate will lead to raise the density of nitrogen-phosphate.

Increase of the temperature leads to reduce the density and the viscosity of nitrogen-phosphate melt independently of AN: PR. So, temperature increase from 160 to 185 0C promotes decrease the density and the viscosity of nitrogen-phosphate melt from 1,610 to 1,592; from 1,655 to 1,629 g/cm3 and from 7,90 to 6,03; from 8,55 to 6,89 cps, respectively for weight ratios ofAN: PR = 100: 20 and 100: 30.

Fig. 2. The density (a) and the viscosity (b) temperature and amount of Khodjakul

Analogous dependence of rheological properties changing can be observed when other AN: PR. When the studied AN: PR = (100: 3-35) with use Khodjeli phosphorite raise of temperature from 160 to 185 0C makes for reduce the density and the viscosity of nitrogen-phosphate melt from 1,691 to 1,54g/cm 3 and from 9,48 to 5,21 cps, respectively (Fig. 2-a and 2-b, curve - 2).

Thus, the results of experiments on determining the density and the viscosity of nitrogen-phosphate melt say to the effect that obtained melt has significant high fluidity that creates facility to pump over them from one device to another one and to granulate existing granulation tower without techniques difficulty.

of nitrogen-phosphate melt depending on the (1) and Khodjeli (2) phosphorites additive

As it is shown data (Table 4) presence of phosphate raw in the ammonium nitrate composition effect on granule dissolution rate of the latter. When increase of the phosphorite weight portion from 3 to 35 in the APF obtained, the time of granule full dissolution increases from 49,5 to 80,8 sec., i. e. raises in 1,7 times.

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

In case of Khodjeli phosphorite and increase its weight portion from 3 to 35 leads to raise full dissolution time from 48,2 to 76 sec. Then APF granules dissolve slowly than ammonium nitrate. Slow solubility of APF granules in determined degree renders positive influence on assimilation nutritious components of fertilizers by plant root system.

Data on destructible granules of ammonium nitrate 20^60 °C are shown in Table 5. after determined amount of heat-cool cycles in the ranges

Table 5. - Thermostability of the nitrogen-phosphate granules depending on the weight ratio of ammonium nitrate: phosphorite flour and thermo cycles amount

Table 4. - Duration of APF granules dissolution in the water

The type of phosphate raw Full dissolution time of granules, sec. (Middle value)

Weight ratio of AN: PR

lOO: 3 lOO: 5 lOO: S lOO:l2 lOO:l5 100:1S 100:20 100:2, 100:30 100:3,

Khodjakul 49¿ 62,0 ,4,2 б1,2 бб,0 6S,S 71,0 7,,б 7S,4 S0,S

Khodjeli 4S,2 ,3,б ,4,4 ,7,б 61,S б7,2 б9,0 71,4 73,0 7б,0

Weight ratio of AN: PR Amount of the destructible granules on cycles transitions of form IV^III,

lO 3O 5O SO 9O lOO

Аммиачная селитра с магнезиальной добавкой 0 31 70 S, 100

Based on Khodjakul phosphorite

100: 3 0 0 0 2,

100: 20 0 0 0 2 7 12

100:30 0 0 0 1 4 7

Based on Khodjeli phosphorite

100: 3 0 0 0 б 12 23

100: 20 0 0 0 3 7 11

100:30 0 0 0 1 4 б

From it seen that ammonium nitrate granules with magnesia additive even after 30 cycles destroyed by 15%, after 50 cycles by 31%, after 80 cycles by 70%, after 100 cycles they destroyed fully. APF granules with both types of phosphate raw additives from Kara-Kalpakistan keep continuity after 60-70 cycles. Disintegration of granules starts after 80 cycles. And even after 100 thermo cycles APF granules based on Khodjakul phosphorite when ratios AN: PR = 100:3 destroyed by 25%; at 100:20 by 12%, but 100:30 by 7% only.

Similar draw is observed when use of Khodjeli phosphorite in the composition of ammonium nitrate. The heights thermostability of APF conditions that it has lower explosion hazard. Therefore, phosphate additive to ammonium nitrate melt inhibits thermo decomposition process and reduces detonating properties ofAPF in comparison with standard ammonium nitrate.

Conclusion

Low grade nodule phosphorite has used to ammonium nitrate as phosphate additive when weight ratios of AN: PR = 100: (3-35). In this case the ammonium nitrate melt is stirred with phosphorus containing component in the mixer before granulation process at 180 0C. The phosphate component escapes neutralization, evaporation, after evaporation process of am-

monium nitrate solution. Where falling out salts and heat-exchange apparatus skulling do not occurred. It was shown that nitrogen-phosphate melt obtained in the wide AN: PR and temperature 160-185 0C possesses sufficient fluidity that creates opportunity to pump over them one device into another one and to granulate existing granulation tower without techniques difficulties.

The results of granule strength determining ofsamples showed that even 0,56% additive of P2O5 in form ofphos-phorite flour (AC: OC = 100: 3) increases the strength of standard ammonium nitrate granule (1,6 MPa) in two times (3,24 MPa). It was shown that ammonium nitrate melt makes an activation phosphate raw too, i. e. destroys its structure and changes unassimilable form of P2 O5 into assimilable for plant form.

The nitrogen-phosphate fertilizer granules obtained are dissolved slower than ammonium nitrate. Ammonium nitrate granules with magnesia additive even after 30 cycles destroyed by 15%, after 50 cycles by 31%, after 80 cycles by 70%, and 100 ones destroyed fully. APF granules with phosphate raw additives from KaraKalpakistan keep wholeness after 60-70 thermo cycles. The heights thermostability ofAPF conditions that it has lower explosion hazard.

References:

1. Patent № IAP 04527 RUz. cl. C 05 G 1/00, C 05 B 7/00, C 05 C 1/00. Method of nitrogen-phosphate fertilizer/Sh. S. Namazov, B. B. Botirov, V. V. Pak, Sh. I. Salihov, A. M. Reymov, R. Yakubov, B. M. Beglov, R. K. Kurbaniyazov, N. N. Pirmanov, B. S. Zakirov. - 2012. № 7.

2. Kurabaniyazov R. K. Technology of nitrogen-phosphate fertilizer based on ammonium nitrate melt and phosphorite from Central Kyzyl kum, PhD thesis in technique, Tashkent, 2011. P. 28.

3. Reymov A., Namazov Sh. Nitrogen- phosphorous fertilizers on the base of concentrated ammonium nitrate solution and Central Kyzylkum phosphate raw material//Polish journal of Chemical Technology. - Szczecin, 2014. - vol. 16, N3. - P. 30-35.

4. Pak V. V., Ten A. V., Pirmanov N. N., Namazov Sh. S., Beglov B. M., Investigation of the phosphate containing of ammonium nitrate with ammophos additive, Chemical industry, 2011, v 88. 7. P. 361-368.

5. Veyderma M. A. Comparative physicochemical and technological behaviour of natural phosphates, Proceedings of the Estonia Republic series "Chemistry geology", № 1, v. 26, 1977. P. 28-32.

6. Vinnik M. M., Erbanova L. N., Zaysev P. M. Methods of analyses of phosphate raw, phosphoric and complex fertilizers, feed phosphates, Moscow, Publishing House 'Chemistry", 1975. P. 218.

7. Cherniy V. A., Strelsov O. A. Application of air force to modify nitrogen containing mineral fertilizer, Chemical industry, 1988. 2. P. 47-49.

Osipov Gennady Sergeevich, Sakhalin State University, Doctor of technical sciences, E-mail: [email protected]

Multi-criteria analysis of systems at fuzzy criteria

Abstract: The aim of the work is to develop a unified method of comparison of different complex technical, socio-economic, security and other systems under a set of criteria. The task of ranking the systems at fuzzy original information is solved. An algorithm of the synthesis of rank and cluster ratings of the systems in the case when the values of criteria and their significance are presented in the form of triangle or trapezoid fuzzy numbers is proposed. This allows formalizing the processing of non-structured, inaccurate, fuzzy information from experts evaluating the systems. An example of synthesis of the integral assessment in a multi-criteria task is given.

Keywords: decision-making problem, multiple alternatives, fuzzy original information.

Introduction Thus, there is a problem of formalization of the

This work is the continuation of the researches dedi- processing of inaccurate linguistic information about

cated to multi-criteria analysis of the systems based on the fuzzy models. The tasks of such class arise in the systems of support of managerial decision-making in different spheres of economic, production, social and other areas of the man's activity. In practice, the original information is, as a rule, inaccurate and presented incompletely. In this case, standard computational algorithms cannot produce a really practice-wise significant decision. Obtaining of a decision is not a guarantee of its correctness.

Original information is usually presented by experts (in the form of figures). However, it is quite difficult for an expert to formalize their assessment. It is easier for them to give a verbal assessment, which, from their point of view, reflects the real situation quite well.

the values of the criteria under which the systems are compared (alternatives, objects, subjects) and about levels of significance (weights) attributed to them.

The method of analysis and comparison of the systems under a set of criteria, which is based on the ensuring of a possibility to process fuzzy linguistic information with the help of fuzzy numbers, is proposed.

An algorithm of the synthesis of a generalized indicator of activity, analysis, comparison and rating of systems based on triangle and trapezoid fuzzy numbers is developed.

Fuzzy arithmetic for triangle and trapezoid numbers is known quite well [1; 2; 3]. However, all these researches consider operations separately, for only triangle numbers or only trapezoid numbers. There are publica-

i Надоели баннеры? Вы всегда можете отключить рекламу.