A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

2022

Self Cite

To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices.

Section: Discussionmentioning

confidence: 99%

Regular Partial Residuated Lattices and Their Filters

Sheng

2022

Self Cite

“…In addition, considering non-commutative fuzzy logic, the non-commutative generalization of weak IBL-algebras is also worth studying, which is what we are doing. Moreover, as an interesting research topic, we can consider a new model of fuzzy rough sets (see [26][27][28]) based on inflationary (pseudo-) general residuated lattices.…”

Section: Discussionmentioning

confidence: 99%

Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

Liang²,

Bedregal³

2022

Self Cite

After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every inflationary general overlap function can induce an inflationary BL-algebra by a counterexample and thus propose the new concept of weak inflationary BL-algebras. We prove that each inflationary general overlap function corresponds to a weak inflationary BL-algebra; therefore, two mistaken results in the previous paper are revised. In addition, some properties satisfied by weak inflationary BL-algebras are discussed, and the relationships among some non-classical logic algebras are analyzed. Finally, we establish the theory of filters and quotient algebras of inflationary general residuated lattice (IGRL) and inflationary pseudo-general residuated lattice (IPGRL), and characterize the properties of some kinds of IGRLs and IPGRLs by naBL-filters, (weak) inflationary BL-filters, and weak inflationary pseudo-BL-filters.

“…Huang et al used interval numbers to represent the attribute information in the group decision matrix, and then proposed a distributed interval weighted average operator to integrate qualitative data and quantitative judgments; then, they defined relevant operation rules, and finally ranked and selected the best green suppliers [34]. To solve the problem that different approximation methods for rough sets affect the results, Wang et al first proposed an attribute metric method based on fuzzy sets, and then constructed Choquet integral operators based on the attribute metric and matching degree, and finally used the operators to rank and select the alternatives [47].…”

Section: Multi-attribute Decision Making Methodsmentioning

confidence: 99%

A New Multi-Attribute Decision Making Method for Overvalued Star Ratings Adjustment and Its Application in New Energy Vehicle Selection

Chen

2023

Under the global consensus of carbon peaking and carbon neutrality, new energy vehicles have gradually become mainstream, driven by the dual crises regarding the atmospheric environment and energy security. When choosing new energy vehicles, consumers prefer to browse the post-purchase reviews and star ratings of various new energy vehicles on platforms such as DCar.com. However, it is easy for consumers to become lost in the high-star text reviews and mismatched reviews. To solve the above two issues, this study selected nine new energy vehicles and used a multi-attribute decision making method to rank the vehicles. We first designed adjustment rules based on star ratings and text reviews to cope with the issue of high star ratings but negative text reviews. Secondly, we classified consumers and recommended the optimal alternative for each type of consumer to deal with the issue of mismatched demands between review writers and viewers. Finally, this study compared the ranking results with the sales charts of the past year to verify the feasibility of the proposed method initially. The feasibility and stability of the proposed method were further verified through comparative and sensitivity analyses.