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

Sirbiladze, Gia

doi:10.3390/math9182337

Cited by 16 publications

(16 citation statements)

References 83 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the Shapley entropy maximum principle, a two-order additive fuzzy measure was created in the environment of a pair of interaction indexes and importance values of attributes of a MAGDM model. Approximately similar results were obtained in [28] under q-rung picture linguistic sets information. Associated intuitionistic fuzzy Choquet averaging (As-IFCA) and geometric (As-IFCG) aggregation operators were constructed in [23].…”

Section: Introductionsupporting

confidence: 83%

“…where ν(A n+1 ) ≡ 0. The Choquet integral has been studied well in the CBR [17,18] under different fuzzy environments [20,22,24,[26][27][28]:…”

Section: Sufficiency: Suppose For the Arbitrary Pair Of Probability M...mentioning

confidence: 99%

“…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%

“…It should be noted that the use of the CBR for practical purposes was presented to a higher degree than the MSR. This is related to the more "flexible" structure of the CBR and the ability to easily embed its APC in problems such as fuzzy measure identification [13][14][15][16] and MAGDM modeling of the Shapley values and interaction indices of interacting attributes of the environment [9,22,[26][27][28]. The main motivation for this study was to establish links between these two probabilistic representations and to obtain evidence for representations of the Choquet integral in the MSR environment as the Choquet integral is the main aggregation tool in MAGDM modeling, which considers the interactions between attributes.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Sirbiladze

Manjafarashvili

2022

Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionsupporting

confidence: 83%

“…where ν(A n+1 ) ≡ 0. The Choquet integral has been studied well in the CBR [17,18] under different fuzzy environments [20,22,24,[26][27][28]:…”

Section: Sufficiency: Suppose For the Arbitrary Pair Of Probability M...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Sirbiladze

Manjafarashvili

2022

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Existing approaches to measuring the degrees of compatibility precision of studying objects are no longer satisfactory to today's researchers. This is why the two sides of imprecision-the levels of object compatibility and incompatibility -are becoming more and more independent in new research [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. This independence is due to the dual representation of evaluation.…”

Section: Introductionmentioning

confidence: 99%

Representation of a Crisp Set as a Pair of Dual Fuzzy Sets

Sirbiladze¹,

Manjafarashvili²,

Midodashvili³

et al. 2022

AAIML

View full text Add to dashboard Cite

Expert knowledge representations often fail to determine compatibility levels on all objects, and these levels are represented for a certain sampling of universe. The samplings for the fuzzy terms of the linguistic variable, whose compatibility functions are aggregated according to a certain problem, may also be different. In such a case, neither L.A. Zadeh’s analysis of fuzzy sets and even the dual forms of developing today R.R. Yager’s q-rung orthopair fuzzy sets cannot provide the necessary aggregations. This fact, as a given, can be considered as a source of new types of information, in order to obtain different levels of compatibility according to Zadeh, presented throughout the universe. This source of information can be represented as a pair ⟨A, fA⟩, where there is some crisp subset of the universe A that determines the sampling of objects from the universe, and a function fA determines the compatibility levels of the elements of that sampling. It is a notion of split fuzzy set, constructed in this article, that allows for the semantic representation and aggregation of such information. This notion is again and again based on the notion of Zadeh fuzzy set. In particular, the operation of splitting a crisp subset into dual fuzzy sets is introduced. Definitions of set operations on split dual fuzzy-sets are presented in the paper. The proofs are also presented that follow naturally from definitions and previous results. An example of MADM is presented for illustration of the application of splitting operation.

show abstract

Uncertainty modeling in multi-objective vehicle routing problem under extreme environment

et al. 2022

View full text Add to dashboard Cite

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

Cited by 16 publications

References 83 publications

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

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

Representation of a Crisp Set as a Pair of Dual Fuzzy Sets

Uncertainty modeling in multi-objective vehicle routing problem under extreme environment

Contact Info

Product

Resources

About