Ultra LILI-ideals in lattice implication algebras

summary:We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal

A Soft Rough-Fuzzy Preference Set-Based Evaluation Method for High-Speed Train Operation Diagrams

This paper proposes a method of high-speed railway train operation diagram evaluation based on preferences of locomotive operation, track maintenance, S & C, vehicles and other railway departments, and customer preferences. The application of rough set-based attribute reduction obtains the important relative indicators by eliminating excessive and redundant evaluation indicators. Soft fuzzy set theory is introduced for the overall evaluation of train operation diagrams. Each expert utilizes a set of indicators during evaluation based on personal preference. In addition, soft fuzzy set theory is applied to integrate the information obtained via expert evaluation in order to obtain an overall evaluation. The proposed method was validated by a case study. Results demonstrate that the proposed method flexibly expresses the subjective judgments of experts while effectively and reasonably handling the uncertainty of information, which is consistent with the judgment process of humans. The proposed method is also applicable to the evaluation of train operation schemes which consist of multiple diagrams

The ALMA-QUARKS Survey: II. the ACA 1.3 mm continuum source catalog and the assembly of dense gas in massive star-forming clumps

Leveraging the high resolution, high sensitivity, and wide frequency coverage of the Atacama Large Millimeter/submillimeter Array (ALMA), the QUARKS survey, standing for "Querying Underlying mechanisms of massive star formation with ALMA-Resolved gas Kinematics and Structures", is observing 139 massive star-forming clumps at ALMA Band 6 ($\lambda\sim$ 1.3 mm). This paper introduces the Atacama Compact Array (ACA) 7-m data. Combining multi-wavelength data, we provide the first edition of QUARKS atlas, offering insights into the multiscale and multiphase interstellar medium in high-mass star formation. The ACA 1.3 mm catalog includes 207 continuum sources that are called ACA sources. Their gas kinetic temperatures are estimated using three formaldehyde (H$_2$CO) transitions with a non-LTE radiation transfer model, and the mass and density are derived from a dust emission model. The ACA sources are massive (16-84 percentile values of 6-160 $M_{\odot}$), gravity-dominated ($M\propto R^{1.1}$) fragments within massive clumps, with supersonic turbulence ($\mathcal{M}>1$) and embedded star-forming protoclusters. We find a linear correlation between the masses of the fragments and the massive clumps, with a ratio of 6% between the two. When considering the fragments as representative of dense gas, the ratio indicates a dense gas fraction (DGF) of 6%, although with a wide scatter ranging from 1% to 10%. If we consider the QUARKS massive clumps to be what is observed at various scales, then the size-independent DGF indicates a self-similar fragmentation or collapsing mode in protocluster formation. With the ACA data over four orders of magnitude of luminosity-to-mass ratio ($L/M$), we find that the DGF increases significantly with $L/M$, which indicates clump evolutionary stage. We observed a limited fragmentation at the subclump scale, which can be explained by dynamic global collapse process.Comment: 24 pages, 7 figures. Accepted for publication in Research in Astronomy and Astrophysics. QUARKS atlas link: https://drive.google.com/file/d/1KTqXxCDduYepvLd9kIvZVSSytK48OmfL/view?usp=sharin

Incomplete Fuzzy Soft Sets and Their Application to Decision-Making

The research of incomplete fuzzy soft sets is of paramount importance in fuzzy soft sets, where the combination of incomplete fuzzy soft set and decision-making problem is of great significance. Incomplete information in fuzzy soft sets leads to more uncertainty and ambiguity in decision-making. The focus of this paper to propose an algorithm of fuzzy soft set based decision-making problems under incomplete information. On the basis of the weighted function, we introduce the notions of weighted incomplete soft sets and weighted incomplete fuzzy soft sets, and show an approach to weighted incomplete fuzzy soft sets for dealing with decision-making. Considering the missing weight function, the concept of incomplete weighted fuzzy soft sets is presented. Meanwhile, we apply the incomplete weighted fuzzy soft sets to solve the decision-making problem. As modal-style operators for fuzzy soft sets have a precise description of attributes possessed by objects, we apply modal-style operator for incomplete fuzzy soft set to deal with decision-making and propose a new algorithm to make it more accurate and simple

A Method for Fuzzy Soft Sets in Decision-Making Based on an Ideal Solution

In this paper, a decision model based on a fuzzy soft set and ideal solution approaches is proposed. This new decision-making method uses the divide-and-conquer algorithm, and it is different from the existing algorithm (the choice value based approach and the comparison score based approach). The ideal solution is generated according to each attribute (pros or cons of the attributes, with or without constraints) of the fuzzy soft sets. Finally, the weighted Hamming distance is used to compute all possible alternatives and get the final result. The core of the decision process is the design phase, the existing decision models based on soft sets mostly neglect the analysis of attributes and decision objectives. This algorithm emphasizes the correct expression of the purpose of the decision maker and the analysis of attributes, as well as the explicit decision function. Additionally, this paper shows the fact that the rank reversal phenomenon occurs in the comparison score algorithm, and an example is provided to illustrate the rank reversal phenomenon. Experiments indicate that the decision model proposed in this paper is efficient and will be useful for practical problems. In addition, as a general model, it can be extended to a wider range of fields, such as classifications, optimization problems, etc

Similarity Measure and Entropy of Fuzzy Soft Sets

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. Recently, uncertainty measures of soft sets and fuzzy soft sets have gained attentions from researchers. This paper is devoted to the study of uncertainty measures of fuzzy soft sets. The axioms for similarity measure and entropy are proposed. A new category of similarity measures and entropies is presented based on fuzzy equivalence. Our approach is general in the sense that by using different fuzzy equivalences one gets different similarity measures and entropies. The relationships among these measures and the other proposals in the literatures are analyzed