Generalization and ranking of fuzzy numbers by relative preference relation

We define $$2n+1$$ 2 n + 1 and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2n fuzzy numbers. When the data is representable in terms of $$2n+1$$ 2 n + 1 fuzzy number, we generalize the FMCDM (fuzzy multi-criteria decision making) model constructed with TOPSIS and relative preference relation. Lastly, we give an example from telecommunications to present the proposed FMCDM model and validate the results obtained.

Two-stage Algorithm for solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

MULTI-OBJECTIVE TRANSPORTATION PROBLEM UNDER TYPE-2 TRAPEZOIDAL FUZZY NUMBERS WITH PARAMETERS ESTIMATION AND GOODNESS OF FIT

The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

Implementation of Modified Best Candidate Method in Fuzzy Assignment Problem

To meet the demands of every customer by supplying the products at the limited time by maximizing the profit is a dream for many companies. By choosing the best candidate among the other candidates and effectively reaching the optimal solution with a new modified approach using Best Candidate Method in Fuzzy assignment problems. In this paper the author solve Fuzzy assignment problem in which Triangular and Trapezoidal fuzzy numbers are used. Robust Ranking Technique is used for the ranking of fuzzy numbers.

A Modified TODIM Based on Compromise Distance for MAGDM with q-Rung Orthopair Trapezoidal Fuzzy Numbers

The q-rung orthopair fuzzy number (q-ROFN) has been recently developed by Yager and has been widely applied in handling real-life decision-making problems. To enhance its usefulness in dealing with complex practical issues, this paper first proposes the new concept of q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) which is a new and useful extension of q-ROFNs. Then, we investigate the operation of q-ROTrFNs and develop a new ranking method for q-ROTrFNs. We also propose a new q-rung orthopair trapezoidal fuzzy Hamming distance measure. More important, we develop a useful q-rung orthopair trapezoidal fuzzy modified TODIM group decision-making method. In this method, a new q-rung orthopair trapezoidal fuzzy weighted aggregating (q-ROTrFWA) operator is developed to integrate individual decision matrices into the collective decision matrix, and a q-rung orthopair trapezoidal fuzzy distance measure-based compromise approach is proposed to determine the relative dominance degree of alternatives. It is worth to mention that the modified TODIM method not only expands the freedom of decision makers but also allows decision makers to choose the appropriate risk preference parameter. Finally, a case study on health management of hypertensive patients is conducted to demonstrate the feasibility of the modified TODIM group decision-making method, and the developed method is further verified by comparison analysis with the existing methods and sensitive analysis of different parameters.