Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

Fuzzy Set Operation Based on Measure Theory

Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure based operation, there are only two basic operators: operator for intersection and operator for union. These two operators are interrelated with each other, and conditional fuzzy measures(or conditional membership functions) are also included in these operators. Moreover, the operator for complement is not independently defined, and it is derived from the above two basic operators. The measure based operation brings to light some relations between Zadeh's operation and probabilistic operation. We show that both Zadeh's operation and probabilistic operation are special cases of measure based operators.We also discuss the problem of the law of excluded middle and the law of contradiction. It is shown that these laws still hold in fuzzy sets and this conclusion causes no difficulty in explaining the nature of fuzziness.

Development of a mathematical model to evaluate the rate of aggregate risk of invasive alien plant species： Fuzzy risk assessment approach

This study presents a novel approach to evaluate the rate of aggregate risk of Invasive Alien Plant Species. Using risk values and grade of importance of weights of risk factors which may reflect invasiveness of plant species are considered. We use Linguistic Ordered Weighted Averaging operator to evaluate the grade of important of weights. Since the risk values and important weights are identified from two different linguistic term sets, fuzzy set theory techniques were used to combine the two sets. The rates obtained from the model were compared with NRA risk levels and the model was validated with data from known and non-invasive species. The model is improved by weighting the risk values of risk factors. The improved model produced significant results and resulted a better tracking system for identifying potential invaders than the conventional risk assessment.