In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.Keywords: pentagonal intuitionistic fuzzy number, interval valued intuitionistic fuzzy number, interval valued intuitionistic fuzzy arithmetic, modified interval valued intuitionistic fuzzy arithmetic, interval valued intuitionistic fuzzy multi-objective linear programming problem.
This paper is focused on arithmetic operations on fuzzy and intuitionistic fuzzy numbers to solve the fuzzy unconstrained optimization problems with triangular and trapezoidal, fuzzy number coefficients. The optimal solution is obtained by fuzzy Newton's method, and the MATLAB outputs are also provided with illustrative examples. The method proposed in this research work has been compared with the existing Newton's method.
In evidence theory, basic probability assignment plays an important role. The basic probability assignment is usually provided by experts. The evaluation of evidence dependability is till open issue, when preliminary data is unavailable. In this paper, we propose a new method to evaluate evidence dependability on the stimulus of neutrosophic set. The dependability of evidence was evaluated based on the truth degree between Basic Probability Assignments (BPAs). First, basic probability assignments were revamp to neutrosophic set. By the similarity degree between the neutrosophic set, we can obtain the truth degree between the Basic Probability Assignments. Then dependability of evidence can be computed based on its rapport with supporting degree. Based on the new evidence dependability, we formulated a new method for combining evidence sources with different dependability degrades. Finally, the validity of the proposed method is exemplified by the real life example.
In this paper, we proposed a method for solving unconstrained optimization problems by Newton’s method with single-valued neutrosophic triangular fuzzy number coefficients. Also, some numerical examples demonstrate the effectiveness of the proposed algorithm. MATLAB programs are also developed for the proposed method.
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