Abstract
The introduction of soft set theory by Molodstov has gained attention by many as it is useful in dealing with uncertain data. It is advantageous to use due to its parameterization form of data. This concept has been used in solving many decision making problems and has been generalized in various aspects in particular to fuzzy soft set (FSS) theory. In decision making using FSS, the objective is to select an object from a set of objects with respect to a set of choice parameter using fuzzy values. Although FSS theory has been extensively used in many applications, the importance of weight of parameters has not been highlighted and thus is not incorporated in the calculation. As it depends on one’s perception or opinion, the importance of the parameters may differ from one decision maker to another. Besides, existing methods in FSS only consider one or two decision makers to select the alternatives. In reality, group decision making normally involves more than two decision makers. In this paper we present a method for solving group decision making problems that involves more than two decision makers based on fuzzy soft set by taking into consideration the weight of parameters. The method of lambda – max which frequently utilize in fuzzy analytic hierarchy process (FAHP) has been applied to determine the weight of parameters and an algorithm for solving decision making problems is presented. Finally we illustrate the effectiveness of our method with a numerical example.
Highlights
Soft set theory was first introduced by a Russian researcher Molodstov [1] with the intention to solve some complicated problems such as in economics, engineering and environment that are usually not successfully solved by classical methods due to the presence of uncertainties of various types
We present Fuzzy soft max – min decision making (FSMmDM) incorporating the weight of criteria using Lambda – max method, an approach of criteria weight determination in Fuzzy Analytic Hierarchy Process (FAHP)
R11 r12 r1n where [rij ] is a fuzzy soft matrix of decision maker k, m refers to the number of alternatives involved in problems and n refers to the parameters/criteria
Summary
Soft set theory was first introduced by a Russian researcher Molodstov [1] with the intention to solve some complicated problems such as in economics, engineering and environment that are usually not successfully solved by classical methods due to the presence of uncertainties of various types. As a generalization of the standard concept of soft sets, Maji et al [8] introduced the theory of fuzzy soft and applied it to decision making problems. In 2011, Yang and Ji [14], defined fuzzy soft matrix (FSM) which is very useful in representing and computing the data involving fuzzy soft sets. They showed that the SMmDM method of [13], unable to solve decision making problems that involve more than two. Even though many approaches have been applied using soft set and fuzzy soft set theories, these methods are limited to one decision maker.
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