An Approach Towards Decision-Making and Shortest Path Problems Based on T-Spherical Fuzzy Information

Zedam, Lemnaouar; Jan, Naeem; Rak, Ewa; Mahmood, Tahir; Ullah, Kifayat

doi:10.1007/s40815-020-00820-1

Cited by 21 publications

(12 citation statements)

References 36 publications

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“…In Section 4, this SF shall be utilized in the problems of the shortest path. Definition 9 (see [43]).…”

Section: Definition 8 (See [43]) For Tsfnsmentioning

confidence: 99%

“…Definition 10 (see [43]). A pair H � (N * , Ę * ) is said to be T-spherical fuzzy subgraph (TSFSG) of TSFG Ɠ � (N, Ę) if…”

Section: Definition 8 (See [43]) For Tsfnsmentioning

confidence: 99%

“…Definition 11 (see [43]). e complement of a TSFG Ɠ � (N, Ę) is defined as Definition 12 (see [43]). e degree of a TSFG Ɠ � (N, Ę) is denoted and is defined by e vertices are purely TSFNs for n � 4 in Figure 12.…”

Section: Definition 8 (See [43]) For Tsfnsmentioning

confidence: 99%

“…Gani and Jabarulla [38] also studied the shortest paths in the environment of IFSs, and for details on finding out the shortest path in an IFG using Dijkstra algorithm, see [39]. Plenty of works have been carried out on the topic of shortest path problems (one may refer to [40][41][42][43]).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

Ullah

Bashir

Anjum

et al. 2021

Mathematical Problems in Engineering

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The concept of fuzzy graph (FG) and its generalized forms has been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems, and so on. This paper is based on some developments in generalization of FG theory to deal with situation where imprecision is characterized by four types of membership grades. A novel concept of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of FG, intuitionistic fuzzy graph (IFG), and picture fuzzy graph (PFG) based on the recently introduced concept of T-spherical fuzzy set (TSFS). The significance and novelty of proposed concept is elaborated with the help of some examples, graphical analysis, and results. Some graph theoretic terms are defined and their properties are studied. Specially, the famous Dijkstra algorithm is proposed in the environment of TSFGs and is applied to solve a shortest path problem. The comparative analysis of the proposed concept and existing theory is made. In addition, the advantages of the proposed work are discussed over the existing tools.

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“…In Section 4, this SF shall be utilized in the problems of the shortest path. Definition 9 (see [43]).…”

Section: Definition 8 (See [43]) For Tsfnsmentioning

confidence: 99%

“…Definition 10 (see [43]). A pair H � (N * , Ę * ) is said to be T-spherical fuzzy subgraph (TSFSG) of TSFG Ɠ � (N, Ę) if…”

Section: Definition 8 (See [43]) For Tsfnsmentioning

confidence: 99%

Section: Definition 8 (See [43]) For Tsfnsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

Ullah

Bashir

Anjum

et al. 2021

Mathematical Problems in Engineering

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“…In the future, we will extend the present work to consider (1) aggregation operators for different FSs, e.g., the linguistic neutrosophic set [44], probabilistic linguistic information [45], linguistic D number [46], interval type-2 FS [47], T-spherical FS [48,49], and others [50], and (2) MADM methods [51][52][53][54][55][56][57][58][59], which will be more flexible for future directs.…”

Section: Resultsmentioning

confidence: 99%

Generalized complex q-rung orthopair fuzzy Einstein averaging aggregation operators and their application in multi-attribute decision making

Лю

Ali

Mahmood

2020

Complex Intell. Syst.

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The recently proposed q-rung orthopair fuzzy set, which is characterized by a membership degree and a non-membership degree, is effective for handling uncertainty and vagueness. This paper proposes the concept of complex q-rung orthopair fuzzy sets (Cq-ROFS) and their operational laws. A multi-attribute decision making (MADM) method with complex q-rung orthopair fuzzy information is investigated. To aggregate complex q-rung orthopair fuzzy numbers, we extend the Einstein operations to Cq-ROFSs and propose a family of complex q-rung orthopair fuzzy Einstein averaging operators, such as the complex q-rung orthopair fuzzy Einstein weighted averaging operator, the complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator, the generalized complex q-rung orthopair fuzzy Einstein weighted averaging operator, and the generalized complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator. Desirable properties and special cases of the introduced operators are discussed. Further, we develop a novel MADM approach based on the proposed operators in a complex q-rung orthopair fuzzy context. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

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Multiple criteria choice modeling using the grounds of T‐spherical fuzzy REGIME analysis

Chen

2021

Int J of Intelligent Sys

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In an uncertain context of T‐spherical fuzzy (T‐SF) sets, the purpose of this study is to propound an efficacious multiple criteria choice model, named a T‐SF REGIME method, predicated on a dominance analysis and a prioritization analysis. The REGIME methodology is a well‐founded evaluation technique suitable for multiple criteria choice analysis owing to it has good applicability to the processing of qualitative information and to complex scenarios. Unlike the existing REGIME techniques, this paper takes advantage of a new Minkowski‐type distance measure and an evolved Gaussian preference function to propound a ground‐breaking T‐SF REGIME model. This paper first concentrates on an evolution of the Minkowski‐type distance measure and explores special cases with relevant properties for functional use. Next, this paper concerns an ascertainment of the evolved Gaussian preference function as a part of the proposed T‐SF REGIME mechanism. This paper focuses on an advancement of the REGIME structure to T‐SF uncertain contexts and unfolds an inventive T‐SF REGIME methodology by virtue of superiority identifiers/indices, guide identifiers/indices, and joint generalized indices. The usefulness and strength points of the advanced methodology are scrutinized through a realistic application in the field of solar plant to prioritize the options of photovoltaic cells. The application results and comparisons corroborate the high efficiency and strengths of the evolved methodology.

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An Approach Towards Decision-Making and Shortest Path Problems Based on T-Spherical Fuzzy Information

Cited by 21 publications

References 36 publications

Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

Generalized complex q-rung orthopair fuzzy Einstein averaging aggregation operators and their application in multi-attribute decision making

Multiple criteria choice modeling using the grounds of T‐spherical fuzzy REGIME analysis

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