For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value ind...

Assignment problem (AP) is a well known topic and is used very often in solving problems of engineering and management science. In this problem aij denotes the cost for assigning the jth job to the ith person. The cost is usually deterministic in nature. In this paper ãij has been considered to be trapezoidal and triangular numbers denoted by ãij which are more realistic and general in nature. ...

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to prop...

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New algorithms for calculating the proper trapezoidal approximation of fuzzy numbers with respect to the distance based on bi-symmetrical weighted functions are proposed. It is shown that the adequate approximation operator is chosen with respect both to the global spread of a fuzzy numbe...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

To face the reality of practical multiple criteria problems usually possessing characters of fuzziness, and to consider group decision making with various subjective–objective backgrounds usually participating in decision-making process. In this paper, the experts’ opinions are described by linguistic terms which can be expressed in trapezoidal (or triangular) fuzzy numbers. To make the consens...

In this paper the concept of (computational) verb number and arithmetical operations of verb numbers are presented. A verb number is a kind of special computational verb, which is derived from structures of (host) verb+(real, interval, fuzzy) number. From the linguistic point of view, a verb number is a computational verb with contexts defined by (real, interval, fuzzy) numbers. Verb numbers ca...

We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and general linear method (GLM). use trapezoidal triangular numbers as initial conditions. To demonstrate efficiency of proposed methods, exact well numerical solutions are presented graphically. In addition, a comparison is made between results from applying GLM those obtained when fif...

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper we propose a new approach of the fuzzy ranking of generalized trapezoidal fuzzy numbers based on radius of gyration point of centroids. The main advantage of the proposed approach is that the proposed approac...

this study considers an eoq inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. two fuzzy models are developed here. in the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. in the second model, the demand rate is fuzzified but the cost parameters are treated ...