Abstract: According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.
Abstract: Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.
Abstract: Increasing number of vehicles and lack of awareness among road users may lead to road accidents. However no specific literature was found to rank vehicles involved in accidents based on fuzzy variables of road users. This paper proposes a ranking of four selected motor vehicles involved in road accidents. Human and non-human factors that normally linked with road accidents are considered for ranking. The imprecision or vagueness inherent in the subjective assessment of the experts has led the application of fuzzy sets theory to deal with ranking problems. Data in form of linguistic variables were collected from three authorised personnel of three Malaysian Government agencies. The Multi Criteria Decision Making, fuzzy TOPSIS was applied in computational procedures. From the analysis, it shows that motorcycles vehicles yielded the highest closeness coefficient at 0.6225. A ranking can be drawn using the magnitude of closeness coefficient. It was indicated that the motorcycles recorded the first rank.
Abstract: Decision making preferences to certain criteria
usually focus on positive degrees without considering the negative
degrees. However, in real life situation, evaluation becomes more
comprehensive if negative degrees are considered concurrently.
Preference is expected to be more effective when considering both
positive and negative degrees of preference to evaluate the best
selection. Therefore, the aim of this paper is to propose the
conflicting bifuzzy preference relations in group decision making by
utilization of a novel score function. The conflicting bifuzzy
preference relation is obtained by introducing some modifications on
intuitionistic fuzzy preference relations. Releasing the intuitionistic
condition by taking into account positive and negative degrees
simultaneously and utilizing the novel score function are the main
modifications to establish the proposed preference model. The
proposed model is tested with a numerical example and proved to be
simple and practical. The four-step decision model shows the
efficiency of obtaining preference in group decision making.
Abstract: Intuitionistic fuzzy sets as proposed by Atanassov,
have gained much attention from past and latter researchers for
applications in various fields. Similarity measures between
intuitionistic fuzzy sets were developed afterwards. However, it does
not cater the conflicting behavior of each element evaluated. We
therefore made some modification to the similarity measure of IFS
by considering conflicting concept to the model. In this paper, we
concentrate on Zhang and Fu-s similarity measures for IFSs and
some examples are given to validate these similarity measures. A
simple modification to Zhang and Fu-s similarity measures of IFSs
was proposed to find the best result according to the use of degree of
indeterminacy. Finally, we mark up with the application to real
decision making problems.