L.T. Kurmangaziyeva -PhD.

Atyrau Institute of Oil and Gas

APPROACH TO FORMALIZATION OF THE DECISION-MAKING PROBLEM ON THE BASIS OF KNOWLEDGE

Abstract:

Decision-making problems to select optimal modes of operation of refining technological facilities on the example of the Catalytic Reforming Unit ЛГ are formalized in this paper, new formulation of such problems have been obtained.

Novelty of received multicriteria decision-making problems is that they are formulated and solved in a fuzzy environment, without converting them to deterministic problems, i.e. keeping and using available information of a qualitative nature. Proposed approach is based on knowledge and experience of specialists and experts can get adequate solutions of complex industrial problems.

Quality and results of work of industrial facilities are estimated by some indicators - local criteria of economic, environmental, technological and other character. For optimal management of such facilities it is required to pay these criteria in extreme (high or low). Such problems are formalized in a form of multicriteria decision-making problems, which are decided on the basis of mathematical models of the facility managed.

Because of the large number and variety of parameters that govern the processes of catalytic reforming due to internal relations between parameters of the technological complex, mathematically non-formalized actions of a human operator, these objects and their optimization are complex. In addition, when decision-making problems on management of such facilities there are some range of problems associated with many contradictory and unclear described criteria that determine the quality of the object. In these cases during decision-making problems by main sources of information will be the human being (experts, process engineer, unit operator) that is their knowledge, experience, intuition and judgment, which are expressed by qualitative information, i.e. verbally.

Let’s consider the approach to formalization and formulation of decision-making problems in the term of discussed multicriteriality and uncertainty caused by the fuzziness of information available. We concretize the formalization and formulation problems of optimization using mathematical models on the example of the decision-making process to manage the process unit of the catalytic reforming, as described in the previous section.

Let f(x) = f₁(x),…,f_m(x) is criteria vector that evaluates quality of work, for example, economic efficiency and environmental safety of process complex of the reforming unit. For example: f₁(x), f₂(x), f₃(x) - respectively, yield of the desired product - volume of catalysate, dry gas and HCG (hydrogen containing gas); f₄(x), f₅(x),…,f₁₄(x) - qualitative indicators of output products (eg. for catalysate - gasoline: octane number, a fractional composition according to GOST - 10% and 50% distillation; saturated vapor pressure; content of the actual resin, content of water-soluble acids and alkalis, for dry gas: content of hydrogen, methane, ethane, propane, isobutane and n-butane; for HCG: hydrogen% vol.; specific gravity), f₁₅(x), f₁₆(x),…, f₂₃(x) - local criteria to evaluate environment safety, e.g. solid, liquid and gaseous wastes and emissions (spent catalysts, waste waters, air emissions - hydrocarbon gases, hydrogen sulfide, sulfur dioxide, carbon monoxide, nitrogen dioxide, carbon black), as well as environment damage caused by pollution and waste processing [1].

Each of m criteria depends on vector of n parameter (control actions, operating parameters) x = (x₁,…,x_n), such as temperature and pressure of reactors, ovens, etc., content of raw materials, specifications of the catalysts, etc. This dependence is described by the model developed in the previous section. In practice, there are always various constraints (economic, technological, environmental) that can be described by some of the features – restrictions j_q³b_q, q=. It should be noted that some of the considered local criteria and constraints are reduced to qualitative restrictions of kind no more or no less than b_q (j_qb_q). Regime, controlling also have their changes intervals made by the unit regulations: x_jÎW = [x_j^min, x_j^max], x_j^min, x_j^max - lower and upper limits of the parameter x_j. These limitations may be fuzzy ().

It is required to select the optimal solution – mode of working of the reforming unit, ensuring extreme value of the criteria vector when execution of set constraints and fuzziness of some initial data, and takes into account the preferences of decision-makers.

Formalized the problem in terms of multicriteria and fuzziness can be written as the following decision-making problem:

max f_i(x), i= (1)

xÎX

Х = { xÎW, j_q(x) b_q, q=} (2)

Solution to this problem is a vector of operating parameters x^*=(x₁^*,…,x_n^*), providing local criteria such values that satisfy the decision maker.

If part or all of the elements of problem given (criteria, limitations, importance of criteria and constraints) are not described quantitatively but qualitatively (fuzzy) then this problem is called decision-making problem under uncertainty on the basis of quality information. In the known methods for solving such problems, mainly considered one-criteria cases, there is no flexibility with the view of preferences of decision-makers [2]. Thus, as a rule, fuzzy task during setting is replaced by equivalent deterministic that will result to loss of information.

In many cases, the qualitative factors (fuzzy statements, judgments) are basic and familiar to the human being. Converting of fuzzy description to a quantitative description is not always possible or impractical. Therefore, in this paper we propose the most promising approach based to develop methods of decision-making adapted to human language, to qualitative factors of any nature, to the human decision-making procedures that are formulated and solved in a fuzzy environment, without converting them to deterministic problems, i.e., without losing of available information of fuzzy character.

Thus, we reduce the problem (1) - (2) to the multicriteria decision-making problem with qualitative nature of initial information.

Let m₀(x) = (m₀¹(x),…, (m₀^m(x)) - a normalized vector of criteria f_i(x), i= that evaluates criteria to control the catalytic reforming unit. Assume that for each fuzzy restrictions j_q(x)b_q, q= function of membership of its execution is constructed m_q(x), q=. Known or several priorities for local criteria I_k = {1,…,m} and limitations I_r = {1,…,L}, or a weight vector, which reflects the mutual significance of criteria (g = (g₁, …,g_m)) and restrictions b = (b₁,…,b_L)).

Then, for example, on the basis of the ideas of methods of the main criterion and maximin, multicriteria decision-making problem with vector restrictions with quality initial information (1) - (2) can be written in the following formulation:

max m₀¹(x), (3)

xÎX

X={x: xÎWLarg(m₀ⁱ(x)³m_rⁱ)Larg (max min (b_qm_q(x)), i=,q=} (4)

xÎW qÎL

where L - logical symbol "and", requiring all their allegations be true, m_rⁱ - limiting values for local criteria m₀ⁱ(х), i= set by decision-makers. Scope of definition of variable x and implementation of fuzzy constraints is based on the principle of maximin (guaranteed result).

Changing m_rⁱ and vector of restrictions importance b=(b₁,…,b_L), we obtain a family of solutions of (3) - (4) - x^*(m_r, b). Selection of best solutions can be carried out on the basis of dialogue with decision-makers.

Using the ideas of Pareto optimality and ideal point, modifying them in the event of qualitative nature of the initial information, multicriteria decision-making problem (1) - (2) can be rewritten as:

m₀(х), m₀(х) = g_i m₀ⁱ(x), (5)

X={x: xÎW L arg(m_q(x) ³ min ||m(x)–m^u||_D), q=}, (6)

where || × ||_D - used metric D, m(x) = (m₁(x) ,…, m_L(x)), m^u = (max m₁(x), …, max m_L(x)). Option to use as the origin of an ideal point m u units: m u = (1, ..., 1); g = (g 1, ..., g m) - weight vector, reflecting the mutual importance of local criteria.
Using the idea of the principles of absolute (relative) concessions and Pareto optimality in terms of fuzzyness, we can set following multicriteria decision-making problem PR with a few restrictions:

m₀(x), m₀(x)=g_im₀ⁱ(x)(m₀(x)= (m₀ⁱ(x))^gi или m₀(x)=g_ilogm₀ⁱ(x)) (7)

X={x: xÎW L arg b_qm_q(х)L b_q=1Lb_q³0, q=} (8)

where L - logical symbol "and", requiring all their allegations be true, g = (g₁, …,g_m) и b = (b₁,…,b_L) - respectively, weight vectors reflecting the mutual importance of criteria and constraints.

Thus, various decision-making problems to select optimal modes of operation of refining technological complex on the example of the Catalytic Reforming Unit ЛГ under uncertainty are formalized in this paper. On the basis of compromise schemes and methods of the theory of tasks possibilities are put in the form of multicriteria decision-making problems, which are novelty of this work. Specific problems of decision and selection of optimal modes of technological units of the catalytic reforming unit have been obtained based on these results. Dialogue algorithms to solve problems are being developed by the author based on the modifications of ideas if various compromise schemes of decision-making.

References:

1. Production schedules catalytic reforming LG-35-11/300-95 (up to 2008).PC « Atyrau Oil Refinery», Atyrau:2002 -130p.

2. Orlovsky, S.A. Decision making with fuzzy initial information -М.: 1981. -206 p.