Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM

Sirbiladze, Gia; Sikharulidze, Anna

doi:10.1142/s0219622018500037

Cited by 20 publications

(20 citation statements)

References 70 publications

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“…. , x i(h−1) , g x i(0 In [51] an overview of CA's extensions the for intuitionistic fuzzy environment is given. Based on the negation function in [49] R. Yager developed the CA operator under q-ROF information [8].…”

Section: Discussionmentioning

confidence: 99%

“…However, when the interactions between the attributes are exposed to a high degree there arise a significant problem with the reliability of the use of these aggregation operators. The CA operator does not reflect the overall interactions among all of attributes [51]. When the interaction between the attributes is revealed to be of high degree, then this defect becomes essential in the decision-making process.…”

Section: Motivation Of Research and Problem's Decision Methodologymentioning

confidence: 99%

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Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Sirbiladze

2021

Mathematics

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In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

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Section: Discussionmentioning

confidence: 99%

Section: Motivation Of Research and Problem's Decision Methodologymentioning

confidence: 99%

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Sirbiladze

2021

Mathematics

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“…We especially highlight the probabilistic representations of a fuzzy measure [8,[17][18][19] as the main object of our research. Therefore, the authors of this work have continued to study probabilistic representations of fuzzy measures [20][21][22][23][24][25][26][27][28][29][30], which have received new perspectives for their use.…”

Section: Introductionmentioning

confidence: 99%

“…The new aggregates are based on an associated probabilistic class of a fuzzy measure. In [26], new aggregation operators reflecting the interactions between all attribute combinations in fuzzy MAGDM models were built. In [27], the authors created a Choquet integral-based new aggregation operators' family under q-rung orthopair fuzzy sets information.…”

Section: Introductionmentioning

confidence: 99%

Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure

Sirbiladze

Manjafarashvili

2022

Mathematics

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Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is important to study the representations of fuzzy measures, including, in particular, additive, probabilistic representations. In this paper, we discuss a couple of probability representations of a fuzzy measure: the Campos-Bolanos representation (CBR) and the Murofushi–Sugeno representation (MSR). The CBR is mainly represented by the Associated Probability Class (APC). The APC is well studied and the aspects of its use can be found in many interesting studies. This is especially true for the environment of interactive attributes in their identification and multi-attribute group decision-making (MAGDM) models, related to the attributes’ Shapley values and interaction indexes. The MSR is a less-used tool in practice today. The main motivation of the research presented here was to explore the connections between these two representations, which will help increase the usability of the MSR in practice in the future. In the MSR, we constructed the nonequivalent representation class (NERC) of a fuzzy measure. This probabilistic new representation is somewhat similar to the APC in the CBR environment. The proposition on the existence of the MSR induced by the CBR was proven. The presented formula of the APC by the NERC was obtained. The duality property of fuzzy measures for the CBR is well studied with respect to fuzzy measures—Choquet second-order dual capacities. Significant properties were proven for the representation of a monotone expectation (ME) under the NERC conditions: as is known, the necessary and sufficient conditions for the existence of the second-order Choquet dual capacities are proven in the terms of the APC of a CBR and ME. After establishing the links between the APC of a CBR and the NERC of a MSR, we proved the same in the case of the MSR. A recursive connection formula between the interaction indexes, Shapley values, and the probability distribution of the NERC of a two-order additive fuzzy measure was obtained in the environment of a general MAGDM. A new distance concept was introduced for all fuzzy measures’ classes defined in finite sets in terms of the NERC. The distance between two fuzzy measures was defined as the distance between their NERCs. This distance is equivalent to the distance defined on the same class under the conditions of the APC of a CBR. The correctness proposition on the extension of the distance between fuzzy measures for the NERC was preserved: distances between any two fuzzy measures and between their dual fuzzy measures also coincided in the CBR as the MSR. After parameterization, the calculation formula of the new distance was obtained. An illustrative example was considered in order to easily present the obtained results. The connection schemes between the CBR and MSR and the sequential scheme of key facts and results obtained are presented at the end of this work.

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“…Presently, information aggregation operators are attracting an increasing amount of attention for dealing with MADM. Many aggregation operators have been developed in intuitionistic fuzzy MADM [29][30][31]. Wang and Li [32,33] and Wang et al [34] developed some intuitionistic normal aggregation operators and proposed some MADM methods based on these operators, while Wang et al [5] developed some aggregation operators for NIFN.…”

Section: Introductionmentioning

confidence: 99%

Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

Huang

2018

Information

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For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle. Moreover, the proposed operators do not take into account the correlation between any aggregation arguments. In order to overcome the deficiencies of the existing ranking method, based on the nonnegative normal neutrosophic number, this paper redefines the score function, the accuracy function, and partial operational laws. Considering the correlation between any aggregation arguments, the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator were investigated, and their properties are presented. Here, these two operators are applied to deal with a multiple attribute decision making problem. Example results show that the proposed method is effective and superior.

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Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM

Cited by 20 publications

References 70 publications

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure

Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

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