Unbalanced OWA Operators for Atanassov Intuitionistic Fuzzy Sets
In this work we introduce a new class of OWA operators for Atanassov intuitionistic fuzzy sets which distinguishes between the weights for the membership degree and the weights for the nonmembership degree; we call these operators Unbalanced Atanassov Int
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Departamento de Automatica y Computacion, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain {laura.demiguel,edurne.barrenechea,miguel.pagola,aranzazu.jurio, joseantonio.sanz,mikel.elkano,bustince}@unavarra.es Institute of Smart Cities, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain
Abstract. In this work we introduce a new class of OWA operators for Atanassov intuitionistic fuzzy sets which distinguishes between the weights for the membership degree and the weights for the nonmembership degree; we call these operators Unbalanced Atanassov Intuitionistic OWA operators. We also study under which conditions these operators are aggregation functions with respect to the Atanassov intuitionistic admissible linear orders. Finally, we apply these aggregation functions in an illustrative example of a decision making problem.
Keywords: Atanassov Intuitionistic Fuzzy Set Unbalanced OWA operators
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OWA operators
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Introduction
Aggregation functions have shown to be a useful tool in problems where information should be fused. Although a partial order is used in some generalizations of aggregation function on other sets (see, for example [1]), some particular classes of these functions such as OWA operators and Choquet or Sugeno integrals require all the elements being comparable. Consequently a linear order is needed. However, these orders are not trivially generated in the extensions of fuzzy sets where more than one value is used to define the membership degree. This is the case, for instance of Interval-Valued Fuzzy Sets (IVFSs) [2] or Atanassov Intuitionistic Fuzzy Sets (AIFSs) [3]. Although some constructions of linear orders on AIFSs have already been studied [4], more works generalizing different notions using linear orders are indispensable for its use in applications. In particular, we aim to define on AIFSs a new class of OWA operators which may apply different weight vectors for the membership and nonmembership degree. We denote these operators Unbalanced Atanassov Intuitionistic OWA operators (UAIOWAs). Taking into account that OWA operators are a particular class of aggregation functions frequently used c Springer International Publishing Switzerland 2016 J.P. Carvalho et al. (Eds.): IPMU 2016, Part II, CCIS 611, pp. 435–444, 2016. DOI: 10.1007/978-3-319-40581-0 35
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in applications, our final goal is to study when U AIOW As satisfy the properties demanded to the aggregation functions. Finally, we introduce an illustrative example on a decision making problem where the Unbalanced Atanassov intuitionistic OWA operators are a suitable option to solve the problem. The structure of the work is as follows: In Sect. 2 we introduce some wellknown concepts which are necessary for the development of this work. The notion of Unbalanced Atanassov intuitionistic OWA operators is introduced in Sect. 3 where we study when these operators are aggregation functions. Section 4 shows an example where Unbalanced Atanassov intuitionistic OWA ope
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