Bellman–Ford algorithm for solving shortest path problem of a network under picture fuzzy environment

Extended QUALIFLEX method for electronic music acoustic quality evaluation based on the picture fuzzy multiple attribute group decision making

In the past, different useful extensions of fuzzy sets were established by the researchers to manage the vagueness and uncertainty in various practical problems. Usually, the real numbers are utilized to express the decision information, but it is noted that the description of attributes using picture fuzzy sets (PFSs) proves to be more appropriate. As a powerful decision tool, PFSs provides more decision information that requires the application of some specific situations more types of response of human ideas: yes, contain, no, reject. QUALIFLEX (qualitative flexible multiple criteria method), is one of the well-known outranking methods to solve the multiple attribute group decision making (MAGDM) problems with crisp numbers. The QUALIFLEX method can perfectly address the complex MAGDM problems where a lot of attributes are utilized to assess a limited number of alternatives. The electronic music acoustic quality evaluation is a classical MAGDM. This paper proposes and utilizes the QUALIFLEX to develop the picture fuzzy QUALIFLEX(PF-QUALIFLEX) method for MAGDM. The current study is mainly devoted to explore and extend the measurement of alternatives and ranking according to the QUALIFLEX under the background of PFSs. Furthermore, an example to evaluate the electronic music acoustic quality is handled through the proposed method to substantiate the extended approach.

Cancer Therapy Assessment Accounting for Heterogeneity Using q-Rung Picture Fuzzy Dynamic Aggregation Approach

Due to the fact that there is no symmetry in the division of cancer cells, it is important to consider this asymmetrical behavior. Because of this heterogeneity during any therapy, not every cancer cell that is killed only is abolished, which is sensitive to the particular treatment chosen. Mathematical models that describe these pathways are critical for predicting cancer cell proliferation behavior. The literature on the mathematical modeling of cancer onset, growth, and metastasis is extensive. Both deterministic and stochastic factors were used to develop mathematical models to mimic the development rate of cancer cells. We focus on the cell’s heterogeneity in our model so that the cells generally responsible for spreading cancer, which are called stem cells, can be killed. Aggregation operators (AOs) play an important role in decision making, especially when there are several competing factors. A key issue in the case of uncertain data is to develop appropriate solutions for the aggregation process. We presented two novel Einstein AOs: q-rung picture fuzzy dynamic Einstein weighted averaging (q-RPFDEWA) operator and q-rung picture fuzzy dynamic Einstein weighted geometric (q-RPFDEWG) operator. Several enticing aspects of these AOs are thoroughly discussed. Furthermore, we provide a method for dealing with multi-period decision-making (MPDM) issues by applying optimal solutions. A numerical example is presented to explain how the recommended technique can be used in cancer therapy assessment. Authenticity analysis is also presented to demonstrate the efficacy of the proposed technique. The suggested AOs and decision-making methodologies are generally applicable in real-world multi-stage and dynamic decision analysis.

Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries

In contrast to classical data envelopment analysis (DEA), network DEA has attention to the internal structure of a production system and reveals the relationship between the efficiency of system and efficiencies of the processes. However, the flexibility of weights and the need for crisp input and output data in the evaluation process are two major shortcomings of classical network DEA models. This paper presents a common weights approach for a relational network DEA model in a fuzzy environment to measure the efficiencies of the system and the component processes. The proposed approach first finds upper bounds on input and output weights for a given cut level and then it determines a common set of weights (CSW) for all decision-making units (DMUs). Hence, the fuzzy efficiencies of all processes and systems for all DMUs are obtained based on the resulting CSW. The developed fuzzy relational network DEA and the proposed common weights approach are illustrated with a numerical example. The obtained results confirm that the fuzzy data affects over the efficiency scores and complete ranking of DMUs. The applicability of the proposed network model is illustrated by performance evaluation of gas refineries in Iran.

Applying the Dijkstra Algorithm to Solve a Linear Diophantine Fuzzy Environment

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify the shortest path (SP) problem for linear Diophantine fuzzy graphs. Linear Diophantine fuzzy numbers (LDFNs) are used to represent the weights associated with arcs. The main goal of the presented work is to create a solution technique for directed network graphs by introducing linear Diophantine fuzzy (LDF) optimality constraints. The weights of distinct routes are calculated using an improved score function (SF) with the arc values represented by LDFNs. The conventional Dijkstra method is further modified to find the arc weights of the linear Diophantine fuzzy shortest path (LDFSP) and coterminal LDFSP based on these enhanced score functions and optimality requirements. A comparative analysis was carried out with the current approaches demonstrating the benefits of the new algorithm. Finally, to validate the possible use of the proposed technique, a small-sized telecommunication network is presented.