Journal
APPLIED SOFT COMPUTING
Volume 35, Issue -, Pages 792-801Publisher
ELSEVIER
DOI: 10.1016/j.asoc.2015.03.012
Keywords
Decision making; Nondominance algorithm; Interval-valued fuzzy relation; Weak transitivity; Transitivity; Interval valued reciprocal relation
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Funding
- Center for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszow [RPPK.01.03.00-18-001/10]
- Spanish Ministry of Science [TIN2013-40765-P]
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In this paper we analyze under which conditions we must use interval-valued fuzzy relations in decision making problems. We propose an algorithm to select the best alternative from a set of solutions which have been calculated with the nondominance algorithm using intervals and different linear orders among them. Based on the study made by Orlovsky in his work about nondominance, we study a characterization of weak transitive and 0.5-transitive interval-valued fuzzy relations, as well as the conditions under which transitivity is preserved by some operators on those relations. Next, we study the case of interval-valued reciprocal relations. In particular, we describe the preservation of reciprocity by different operators and analyze the transitivity properties for these interval-valued reciprocal relations. Finally, we propose to use, in the nondominance algorithm, linear interval orders generated by means of operators which preserve transitivity. (C) 2015 Elsevier B.V. All rights reserved.
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