Abstract: Fermatean fuzzy sets (FFSs), proposed by Senapati and Yager (2019a), can handle uncertain information more easily in the process of decision making. They defined basic operations over the Fermatean fuzzy sets. Here we shall introduce three new operations: subtraction, division, and Fermatean arithmetic mean operations over Fermatean fuzzy sets. We discuss their properties in details. Later, we develop a Fermatean fuzzy weighted product model to solve the multi-criteria decision-making problem. Finally, an illustrative example of selecting a suitable bridge construction method is given to verify the approach developed by us and to demonstrate its practicability and effectiveness.
Keywords: Fermatean fuzzy set, subtraction operation, division operation, Fermatean arithmetic mean operation, multiple criteria decision making (MCDM), weighted product model (WPM)
Citation: Informatica,
vol. 30, no. 2, pp. 391-412, 2019
Abstract: This letter reports a new type of uncertain information that is different from some well known existing uncertain information, such as probability information, fuzzy information, interval information and basic uncertain information. This type of uncertain information allows some specified compromise in interacting decision environments and gives some acceptance area when facing with uncertainties. We firstly introduce the cognitive interval information and then naturally propose the cognitive uncertain information as an extension. The featured acceptance area provides more flexibility in uncertain information handling and it can be regarded as some specified uncertain range (versus the certainty degree in basic uncertain information).…The new proposals have advantages in some uncertain decision making scenarios where intersubjectivity and interaction of decision makers play important roles. Besides, some basic structural properties are briefly discussed. Moreover, some motivational examples are presented to show its usage in group decision making to help automatically obtain consistency or consensus in aggregating the different individual evaluations.
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Keywords: Cognitive interval information, cognitive uncertain information, decision making, group decision making, information fusion, uncertain information
Abstract: The evaluation for online shopping platform is the basis for further decision and policy taking. The collected individual opinion and evaluation information are often represented by some linguistic/preference vectors. Further aggregating those vector needs to simultaneously consider two contradictory factors: the original weights assigned and the inconsistencies involved which requires some new weights assigned. Around those weights allocation factors, to mitigate the negative effect of inconsistency in the collected information, we propose an integrated evaluation model. The model uses the scatter degree as a main indicator, and extends some weights allocation methods such as regular increasing monotone (RIM) quantifier based…weights allocation in a new environment, and applies the three sets expression based paradigm and formulation. The proposed model is able to simultaneously give emphasis on those input data with high consistency and to consider the preferences of decision makers. Some detailed evaluation processes and numerical examples are also provided for practitioners to refer to.
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Keywords: Aggregation operators, evaluation for online shopping platform, information fusion, multi-criteria decision making, weights adjustment and allocation
Abstract: In many multi criteria group decision making problems, the individual evaluation values offered by experts are with uncertainties. Therefore, when assigning weights to those experts using preferences induced weights allocation, we can have two types of bi-polar preferences. The first one is the optimism-pessimism preference over evaluation values; the second one is the uncertainty aversion preference over the attached numerical certainty/uncertainty degrees. When performing preferences induced weights allocation, the certainty/uncertainty degrees will affect the optimism-pessimism preference induced weights allocation because the magnitudes of those evaluation values might not be the exact ones. Moreover, the importance of those experts in multi…criteria group decision making can also have influence over the two types of preference induced weights allocation processes, and the importance can also be with uncertainties and can be expressed using basic uncertain information. Therefore, to handle this situation with multiple inducing variables and uncertainties, we simultaneously consider the influence of the uncertainties attached to evaluation values and the influence of uncertain importance of experts, and thus we at the same time adopt the method of confidence threshold and the method of uncertain importance level function to propose some synthesized method to adjust the induced weights allocation processes. We also propose a complete multi criteria group decision making problems to show the feasibility and reasonability of the proposed decision model for the complex situation where both evaluation values and expert importance are expressed by basic uncertain information.
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Keywords: Aggregation operators, basic uncertain information, induced ordered weighted averaging operators, information fusion, multi criteria group decision making, uncertain decision making
Abstract: Uncertainty exists in numerous evaluation and decision making problems and therefore it also provides space for the subjective preferences of decision makers to affect the aggregation and evaluation results. Recently, relative basic uncertain information is proposed to further generalize basic uncertain information, but currently there is no research on how to apply this type of uncertainty in both theory and practices. There is also a paucity of decision methodology about how to build systematic preference involved decision model considering this new type of uncertainty. The relative basic uncertain information can serve as a general frame to enable the possibility for…simultaneously handling heterogeneous uncertain information including interval information, basic uncertain information, and relative basic uncertain information. Different types of bipolar subjective preferences commonly should be taken into consideration in practical decision making. With the individual heterogeneous uncertain information and the involved two types of subjective preferences, namely bipolar preferences for uncertainties and bipolar optimism-pessimism preferences, the evaluation and decision making become more complex. This work proposes a systematic intersubjective decision model which can effectively and reasonably deal with the decision scenario with such complex uncertainty, in which Yager preference induced weights allocation is applied. Some novel preference conversion and transformation functions, specified techniques, and the related decision making procedures and sub-modules are proposed and analyzed. An application is also presented to showthe practicality of the proposed decision models and related conversion and transformation functions.
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Abstract: We study the Yager OWS aggregation and the Irregular normalized Yager OWA aggregation under infinite environment. Two evaluation problems are proposed to motivate their applications. Few distinguishing properties are discussed. We show that such aggregations use the same type of weights, infinite weights (sequence), to embody the involved preferences. Their respective applications in the fields of Scientometrics and Gradual Confidence Aggregation are proposed and analyzed.
Abstract: Motivated by a specific decision-making situation, this work proposes the concept and definition of unsymmetrical basic uncertain information which is a further generalization of basic uncertain information and can model uncertainties in some new decision-making situations. We show that unsymmetrical basic uncertain information in some sense can model linguistic hedges such as “at least” and “at most”. Formative weighted arithmetic means and induced aggregations are defined for the proposed concept. Rules-based decision making and semi-copula based integral for this concept with some numerical examples are also presented.
Keywords: Aggregation operators, basic uncertain information, evaluation, information fusion, integral, uncertainty, unsymmetrical basic uncertain information
Abstract: Basic Uncertain Information (BUI) as a newly introduced concept generalized a wide range of uncertain information. The well-known Ordered Weighted Averaging (OWA) operators can flexibly and effectively model bipolar preferences of decision makers over given real valued input vector. However, there are no extant methods for OWA operators to be carried out over given BUI vectors. Against this background, this study firstly discusses the interval transformation for BUI and elaborately explains the reasonability within it. Then, we propose the corresponding preference aggregations for BUI in two different decisional scenarios, the aggregation for BUI vector without original information influencing and the…aggregation for BUI vector with original information influencing after interval transformation. For each decisional scenario, we also discuss two different orderings of preference aggregation, namely, interval-vector and vector-interval orderings, respectively. Hence, we will propose four different aggregation procedures of preference aggregation for BUI vector. Some illustrative examples are provided immediately after the corresponding aggregation procedures.
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Abstract: In this work, we propose some two-layer preference models that can be appropriately applied in management problems such as the group decision making about predicting the future market share of certain product. By introducing the convex IOWA operator paradigm and some related properties and definitions, we list some detailed preference and inducing preference models to demonstrate and exemplify the proposed conceptual frame of two-layer preference model. The convex IOWA operator paradigm facilitates the modeling process and, from mathematical view, makes it stricter. When relevant inducing information and aggregation selection change, the proposed models can be easily adapted to accommodate more…different applications in decision making and evaluation.
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Abstract: This work firstly proposes some weight adjusting and preference interfering methods to generate more suitable weight vector in two-tier multi-criteria decision making. The proposed models simultaneously consider the original weight information and subjective preferences of decision makers under interval numbers based evaluation environments. A recently proposed weights allocation method based on convex poset is applied to determine the weight vectors from subjective preferences. With well adjusted and melted weight information, some fuzzy comprehensive evaluations are realized by applying Shilkret Integrals with melted preferences. A numerical example with corresponding decision rules for online shop evaluation problem is also presented for practitioners…to refer to.
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