A mathematical programming model for the fuzzy analytic network process—applications of international investment

Abstract

Currently, the analytic network process (ANP) method is widely employed to consider the multiple criteria analysis problems with dependence and feedback effects. However, in order to extend the ANP to resolve the problem of uncertainty or human subjective judgment, the concepts of fuzzy numbers should be incorporated into the ANP to represent the subjective uncertain pairwise judgments. In this paper, therefore, we propose a novel fuzzy analytic network process (FANP) model by solving a mathematical programming problem. Unlike other FANPs, the proposed method does not require the reciprocity assumption of the weight ratios between criteria, and it can derive local and global weights simultaneously in a single model. Two numerical examples of international investment problems are used to demonstrate the proposed method.

Deriving Fuzzy Weights of the Fuzzy Analytic Network Process via Fuzzy Inverse Matrix

“…Later, [15] proposed another concise mathematical model to derive the FANP as follows. Let Π be a supermatrix of the ANP and Π (κ) as the ever entry positive (i.e., Π is regular), there is a unique column matrix π satisfying Ππ = π, and the entries of π are positive and sum to 1, where π is the global weight vector of the ANP.…”

“…That is, the fuzzy global weights of the FANP can be given as the last column of C and [α] is the α-cut operation. However, [15] only derived the fuzzy weights based on the Zadeh's extension principle without further considering the minimum spread of fuzzy weights. Though the final result of the model might still provide rational interval weights, we can provide a new model to obtain fuzzy weights with less spread.…”

“…Huang (2012) gave the following mathematical programming to calculate the interval number of C−1 with respect to a specific α-cut by consider the constraint C C −I as: s.t. c 11 c 11 + c 12 c 21 + • • • + c 1n c n1 = 1,…”

A hybrid multi-criteria decision making technique to improve the quality of hotel industry services in Mashhad City

“…The values of verbal variables are words or sentences found in natural language, but they are not numbers (Gottwald, 2015). Verbal variables can be quantified by use of fuzzy set theory and used in calculations (Huang, 2012;Karwowski and Mital 2014). In classical set theory, an existence may be or may not be the member of a set Since, an existence is uncertainty in a fuzzy set, we should define the membership function, that is the fundamental of the fuzzy sets, for each existence in the set.…”

Efficiency Measurement for Hierarchical Network Systems Using Network DEA and Intuitionistic Fuzzy ANP

“…For this purpose, in the most solving methods of AHP, fuzzy numbers have been used to do the paired comparison and the membership function is the basis of the determining of the weight of the criteria and subcriteria. Huang [6] proposed a novel fuzzy ANP (FANP) model by solving a mathematical programming problem. Li et al [7] used a generalized fuzzy number, which represents a different fuzzy number when the parameter changes.…”