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And-like-uninorm based consistency analysis and optimized fuzzy weight closed-form solution of triangular fuzzy additive preference relations.
- Source :
-
Information Sciences . Apr2020, Vol. 516, p429-452. 24p. - Publication Year :
- 2020
-
Abstract
- • Introduce indices to measure different kinds of vagueness in a triangular fuzzy additive preference relation (TFAPR). • Propose an and-like-uninorm based method to generate consistent TFAPRs from]0, 1[-valued triangular fuzzy weights. • Present two novel multiplicative normalization frameworks for]0, 1[-valued triangular fuzzy weights. • Obtain crucial properties of multiplicatively consistent TFAPRs. • Develop some optimization models to derive a closed-form solution of optimized triangular fuzzy weights. This paper focuses on multiplicative consistency of triangular fuzzy additive preference relations (TFAPRs) and deriving a closed-form solution of optimized triangular fuzzy weights (TFWs) from TFAPRs. And-like-uninorm based indices are introduced to measure increasing part vagueness, decreasing part vagueness and overall vagueness for ]0,1[-valued triangular fuzzy preferences and TFAPRs. An index is then defined to measure row vagueness proportionality of TFAPRs. An and-like-uninorm based method is further proposed to generate multiplicatively consistent TFAPRs from ]0,1[-valued TFWs. By discussing equivalency of ]0,1[-valued TFW vectors, the paper presents two frameworks of normalized TFWs called multiplicatively modal-value-normalized TFWs and multiplicatively support-interval-normalized TFWs. Based on crucial properties of consistent TFAPRs, a logarithmic least square (LLS) model is established to seek multiplicatively support-interval-normalized TFWs from TFAPRs. By decomposing its goals and constraints, the LLS model is transformed into two least square models whose closed-form solutions are found by the Lagrange multiplier method. On basis of the obtained closed-form solution of TFWs, an algorithm including acceptable consistency checking is developed for decision making with TFAPRs. The rationality and advantages of the presented models are illustrated by a numerical example with five TFAPRs and a comparative analysis. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00200255
- Volume :
- 516
- Database :
- Academic Search Index
- Journal :
- Information Sciences
- Publication Type :
- Periodical
- Accession number :
- 141778057
- Full Text :
- https://doi.org/10.1016/j.ins.2019.12.055