THEORY OF FUZZY SETS IN DECISION-MAKING SYSTEMS OF BUILDING MANAGEMENT/NEAPIBRĖŽTŲJŲ AIBIŲ TEORIJOS TAIKYMAS PASTATŲ VALDYMO SPRENDIMŲ PRIĖMIMO SISTEMOMS
Authors: Gaučas Paulius , Zavadskas Edmundas Kazimieras 
Published: March 2019

The task of decision-making in constructing industry becomes more difficult because of rapid technical upgrowth. According to aims, circumstances and opportunity decisions are determined. Disagreement situation arises at this point. Uprising opportunities and influence of circumstances of aims, they are often contradicting each other. Constructing a building, one must look for decision of more favourable conditions for situation and minimum expenditure, but to guarantee a high reliability, so disagreement situation arises. Exacting requirements of quality logically are bound up with expensive realisation [4]. Decision must be optimum and as much as possible satisfy “goodness” indications of decision. However, “goodness” valuation is indefinite conception and disobeys black-and-white logic [Zadeh]. In this case one can understand decision like a conflict in the game theory, where the information is not always defined. To solve the problem the fuzzy sets theory can be used. Using the game theory, elements can be formulated indefinitely and a new model can be made [3]. Trying to estimate the aims of conflicts, the circumstances that influence the decision are divided into two groups. The first group—circumstances of inherent influence—defines what a decision-maker must attain (for example, to maximise quality) and describes strategy of the first player. The second group—circumstances of outward influence—defines what a decision-maker must estimate as a limitation (for example, to minimise price) and describes strategy of the second player. Dependence between inherent and outward circumstances in this step is formed.

There is no clear limit in fuzzy sets theory between dependence (circumstance 1) and independence (circumstance 0) of elements on definite set. Dependence degree of element x on A set, is described by μ A (x) function (1), (2).

The valuation in fuzzy sets theory takes place at three levels. At the first level meanings of dependence on inherent circumstances are calculated (1), (2), and matrix is determined (Fig 2). According to formula (3), dependence degree on each alternative is calculated. In the second level meanings of dependence on outward circumstances are calculated according to the formula (1), (2) and the matrix is filled in (Fig 3).

At the third level the results of first two levels are summed. Using operator of minimum general matrix of decisions-making is determined (Fig 4), According to the general matrix, the indefinite matrix of decision-making is determined (Fig 5). Minimax principle makes the decision.

The received result is optimal, because it satisfies the aim causing the conflict. In the paper, the example of a private house is selected, using the described method.

This method may be used to make decisions, when the task is of conflicting character. Competently distributing circumstances of influence or parameters of valuation by two aspects (inherent and outward) it can be explained the mean of conflicting character, and interpretation using the described method can be made.