Deli I., Subas Y., Smarandache F., Mumtaz Ali.
Internet-publication. — 8 p. English. (OCR-слой).[Irfan Deli. Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Turkey.
Yusuf Şubaş. Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Turkey.
Florentin Smarandache. University of New Mexico, Gallup, New Mexico, USA.
Mumtaz Ali. Department of Mathematics, Quaid-i-Azam University Islamabad, Pakistan].Abstract.
Interval valued bipolar fuzzy weighted neutrosophic set(IVBFWN-set) is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making.
Therefore, in this paper, we propose concept of IVBFWN-set and its operations. Also we give the IVBFWN-set average operator and IVBFWN-set geometric operator to aggregate the IVBFWN-sets, which can be considered as the generalizations of some existing ones under fuzzy, neutrosophic environments and so on.
Finally, a decision making algorithm under IVBFWN environment is given based on the given aggregation operators and a real example is used to demonstrate the effectiveness of the method.Introduction.
To overcome containing various kinds of uncertainty, the concept of fuzzy sets [18] has been introduced by Zadeh.
After Zadeh, many studies on mathematical modeling have been developed. For example; to model indeterminate and inconsistent information Smarandache [13] introduced the concept of neutrosophic set which is independently characterized by three functions called truth-membership function, indeterminacy-membership function and falsity membership function. Recently, studies on neutrosophic sets are made rapidly in [1,2].
Bipolar fuzzy sets, which are a generalization of Zadeh’s fuzzy sets [18], were originally proposed by Lee [9].
Bosc and Pivert [4] said that “Bipolarity refers to the propensity of the human mind to reason and make decisions on the basis of positive and negative effects. Positive information states what is possible, satisfactory, permitted, desired, or considered as being acceptable. On the other hand, negative statements express what is impossible, rejected, or forbidden.Introduction.
Preliminaries.
Definition Bipolar-Valued Fuzzy Set.
Interval Valued Bipolar Fuzzy Weighted Neutrosophic Set.
NBN-Decision Making Method.
Conclusion.
References (18 publ).
