Some results on information measures for complex intuitionistic fuzzy sets

Garg, Harish; Rani, Dimple

doi:10.1002/int.22127

Cited by 100 publications

(49 citation statements)

References 60 publications

(148 reference statements)

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“…The comparative study of existing and proposed operators is also developed with the help of an example. In future research, it would be interesting to develop some immediate probability geometric and power aggregation operators for the diverse fuzzy environment [43][44][45][46][47].…”

Section: Resultsmentioning

confidence: 99%

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

et al. 2019

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The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches.

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Section: Resultsmentioning

confidence: 99%

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

et al. 2019

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“…In future research work, we can expand the explored operators to neutrosophic set [42][43][44], q-rung orthopair fuzzy set [45][46][47] and other uncertain environments [48][49][50][51][52][53][54][55][56].…”

Section: Resultsmentioning

confidence: 99%

Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

Garg

Wang

2019

Mathematics

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A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method.Mathematics 2019, 7, 1150 2 of 25 that 0.4 + 0.8 > 1, so IFS cannot solve this issue, but since 0.4 2 + 0.8 2 < 1, then the PFS can easily deal with it. Therefore, in some cases, the PFS can settle a large number of problems, while the IFS cannot. Since PFS appeared, it has become a useful technique for modeling vagueness and indeterminacy of the MADM issues or multiple attribute group decision making (MAGDM) issues [5][6][7][8][9][10][11][12]. Some evaluation methods in the light of PFS are given to solve Pythagorean fuzzy MADM problems. For instance, Rani et al. [13] extended traditional TOPSIS (technique for an order of preference by similarity to ideal solution) approach to Pythagorean fuzzy numbers (PFNs) and studied the selection of a sustainable recycling partner. Considering DM's psychological characteristics, in the light of the prospect and regret theories, Peng and Dai [14] explored a stochastic decision approach under Pythagorean fuzzy setting. Ren et al. [15] extended traditional TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) approach to PFNs. Chen [16] introduced a Pythagorean fuzzy VIKOR (vlseKriterijumska optimizacija I Kompromisno Resenje in Serbian) approach for MADM. Zhang [17] expanded the hierarchical QUALIFLEX (qualitative flexible multiple criteria method) algorithm to the interval-valued PFSs, and employed it to investigate the industries' risk evaluation.The way of evaluation methods in Pythagorean fuzzy decision-making problems is only one aspect, the other ...

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“…To check the consistency of the method with some existing studies [42,44,45,52] under the CIFS environment, an analysis is conducted by their method and the corresponding results are discussed as below: (iii) By applying the Garg and Rani [45] method based on correlation coefficient 'C', we obtain the indices values as C(A 1 , A * ) = 0.9407, C(A 2 , A * ) = 0.9571, C(A 3 , A * ) = 0.7547 and C(A 4 , A * ) = 0.8926. Clearly, seen that the best alternative is A 2 .…”

Section: Comparative Analysis With Cifs Studiesmentioning

confidence: 99%

“…Recently, Garg and Rani [51] presented exponential, logarithm and compensative AOs for aggregating the different CIFSs. However, Garg and Rani [52] presented the study on the various information measures of CIFSs.…”

Section: Introductionmentioning

confidence: 99%

Novel Exponential divergence measure of complex intuitionistic fuzzy sets with an application to decision-making process

Garg

Rani

2019

Scientia Iranica

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As a generalization of the intuitionistic fuzzy sets (IFSs), complex IFSs (CIFSs) is a powerful and worthy tool to realize the imprecise information by using complex-valued membership degrees with an extra term, named as phase term. Divergence measure is a valuable tool to determine the degree of discrimination between the two sets. Driven by these fundamental characteristics, it is fascinating to manifest some divergence measures to the CIFSs. In this paper, we explain a method to solve the multi-criteria decision-making (MCDM) problem under CIFS environment. For it, firstly, the divergence measures are introduced between two CIFSs and examined their several properties and relations. Secondly, a novel algorithm is given based on the proposed measures to solve the problems in which weights corresponding to criteria are resolved using maximizing deviation method. Thirdly, a reasonable example is provided to verify the developed approach and to exhibit its practicality and utility with a comparative analysis to show its more manageable and adaptable nature.

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Some results on information measures for complex intuitionistic fuzzy sets

Cited by 100 publications

References 60 publications

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

Novel Exponential divergence measure of complex intuitionistic fuzzy sets with an application to decision-making process

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