A New Method for Interval-Valued Intuitionistic Group Decision Making
Ivanosca A. da Silva1, Benjam´ın Bedregal2, Regivan H.N. Santiago2, and Adri˜ao D.
D´oria Neto3
1 Programa de P´os-Graduac¸˜ao em Engenharia El´etrica e de Computac¸˜ao – PPgEEC
2 Departamento de Inform´atica e Matem´atica Aplicada – DIMAp Grupo de L´ogica, Linguagens, Informac¸˜ao, Teoria e Aplicac¸˜oes – LoLITA
3 Departamento de Engenharia de Computac¸˜ao e Automac¸˜ao – DCA Universidade Federal do Rio Grande do Norte – UFRN
59072-970, Natal, RN
Abstract. In this paper we provide an extension of weighted average operator for interval-valued intuitionistic degrees and apply it as part of adaptation of weighted voting strategy in order to develop a new method for interval-valued intuitionistic fuzzy group decision making. In order to rank alternatives we use total order introduced by Xu and Yager for interval-valued intuitionistic degrees.
A characteristic of this proposed method is that it works with interval-valued intuitionistic fuzzy values in all moments and therefore considers the uncertainty on the membership and non-membership in all steps of decision making. The method provide good results and compared with other approaches it is very simple.
Keywords: Interval-valued intuitionistic fuzzy sets; Group decision making; Voting method; Weighted average operators, Xu-Yager total order.
1 Introduction
From introduction of Fuzzy Set Theory by Zadeh [48] several extended theories were also proposed. Among them we remark interval-valued fuzzy sets theory (IVFST) [49, 18, 12] and Atanassov intuitionistic fuzzy sets theory (AIFST) [2, 5, 17]. IVFST is suitable when difficulty or impossibility of an expert to determine an exact value of membership degrees rise. In this case, an interval captures the degree’s imprecision. AIFST adds an extra degree to the usual fuzzy sets in order to model the hesitation of membership.
This hesitation degree (or non-membership degree) is by default the complement of the membership degree, i.e. 1−µA(x). Atanassov and Gargov provide in [3] what they called Interval-Valued Intuitionistic Fuzzy Sets Theory (IVIFST). This extension mixes imprecision and hesitation. Several applications of IVFST had been made, see for example [4, 10, 11, 43, 38, 37, 44].
Group Decision Making consists in the choice of one or more alternatives by a group of decision makers (experts) which express their own preferences among alternatives [15]. Fuzzy logic has played an important role in this field. So it is not surprising that some fuzzy methods used in Group Decision Making be extended, e.g. [21, 32, 13].
