Spatial fuzzy consumer's decision making: A multicriteria analysis
A model of consumers' behavior in terms of fuzzy relations is presented. The main topics considered in the model are: X, a set of located goods \((X=G\times P\), where G is a set of goods and P is a set of locations), Y, a set of characteristics of the located goods and Z, a set of a priori possible consumer behaviors. The complete model includes also the following fuzzy relations between these objects: \(A\subset X\times Y\), \(B\subset Y\times Z\) and \(C\subset X\times Z\). The particular membership functions of these relations mean: \(\mu_ A(x_ i,y_ k):\) the degree in which the located good \(x_ i\) possesses the characteristic \(y_ k\) (in the consumer's opinion), \(\mu_ B(y_ k,z_ j):\) the valuation assigned to the characteristic \(y_ k\) for the state of satisfaction \(z_ j\) (a priori possible behavior) and \(\mu_ C(x_ i,z_ j):\) the valuation of the located good \(x_ i\) with respect to the consumer's possible behavior \(z_ j\). The relation A expresses the step of information treatment, relation B the step of characteristic valuation and C represents the result (revealed behavior) in the decision-making process connected with the consumer's behavior. The author analyses, in the formal part of the paper, the equation \(B\circ A=C\), where ''\(\circ ''\) indicates the operation of the max-min composition of fuzzy relations. He presents and proves some necessary and sufficient conditions for the existence of a solution B (solution A) of the equation \(B\circ A=C\) when A and C (B and C) are given.
scientific article; zbMATH DE number 3970423