Jing-Shing Yao

Ranking fuzzy numbers based on decomposition principle and signed distance

By using the decomposition principle and the crisp ranking system on R, we construct a new ranking system for fuzzy numbers which is very realistic and also matching our intuition as in R.

Economic production quantity for fuzzy demand quantity, and fuzzy production quantity

Abstract In the fundamental production inventory model, in order to solve the economic production quantity (EPQ) per cycle we always fix both the demand quantity and the production quantity per day. But, in the real situation, both of them probably will have little disturbances every day. Therefore, we should fuzzify both of them to solve the ecoomic production quantity ( q ∗ ) per cycle. The purpose of this paper is to investigate a computing schema for the EPQ in the fuzzy sense. We find that, after defuzzification, the total cost is although slightly higher than in the crisp model; however, it permits better use of the EPQ in the crisp arising with little disturbances in the production, and demand.

Economic reorder point for fuzzy backorder quantity

Abstract In this paper we consider the backorder inventory problem with fuzzy backorder such that the backorder quantity is a triangular fuzzy number S = (s 1 , s 0 , s 2 ) . Suppose s ∗ and q ∗ denote the crisp economic backorder and order quantities respectively in the classical inventory with backorder model. According to four order relations of s ∗ and s 1 , s 0 , s 2 ( s 1 s 0 s 2 ) we find the membership function μ G q ( S ) (Z) of the fuzzy cost function G q ( S ) and their centroid. We also obtain the economic order quantity q ∗∗ and the economic backorder quantity s ∗∗ in the fuzzy sense. We conclude that, after solving the model in the fuzzy sense, the total cost is slightly higher than that in the crisp model; however, it permits better use of the economic fuzzy quantities arising with changes in orders, deliveries, and sales.

Economic order quantity in fuzzy sense for inventory without backorder model

Abstract This paper investigates a group of computing schemas for economic order quantity as fuzzy values of the inventory without backorder. We express the fuzzy order quantity as the normal triangular fuzzy number ( q 1 , q 0 , q 2 ), and then solve the aforementioned optimization problem. We find that, after defuzzification, the total cost is slightly higher than in the crisp model; however, it permits better use of the economic fuzzy quantities arising with changes in orders, deliveries, and sales.

Fuzzy inventory without backorder for fuzzy order quantity and fuzzy total demand quantity

Abstract In this paper, we consider the inventory problem without backorder such that both order and the total demand quantities are triangular fuzzy numbers Q =(q 1 , q 0 , q 2 ) , and R =(r 1 , r 0 , r 2 ) , respectively, where q 1 =q 0 − Δ 1 , q 2 =q 0 + Δ 2 , r 1 =r 0 − Δ 3 , r 2 =r 0 + Δ 4 such that 0 Δ 1 0 , 0 Δ 2 , 0 Δ 3 0 , 0 Δ 4 , and r0 is a known positive number. Under conditions 0⩽q1 μ G( Q , R ) (z) of the total fuzzy cost function G( Q , R ) and their centroid, then obtain order quantity q ∗∗ in the fuzzy sense and the estimate of the total demand quantity. Scope and purpose This paper deals with the inventory problem without backorder with total cost function F(q)=cTq/2+ar/q, q>0 . In the classical inventory (without backorder) model, both the total demand over the planning time period [0, T] and the period from ordering to arriving are fixed. In the real situation, the total demand r and order quantity q probably will be different from the values used in the total cost function. Also, r influences the values of T. In view of this circumstances, we consider the inventory problem in which both order and total demand quantities are triangular fuzzy numbers Q =(q 1 , q 0 , q 2 ) , and R =(r 1 , r 0 , r 2 ) , respectively, where q 1 =q 0 − Δ 1 , q 2 =q 0 + Δ 2 , r 1 =r 0 − Δ 3 , r 2 =r 0 + Δ 4 such that 0 G( Q , R )=cT Q /2+a R / Q , we use the extension principle to find the membership function μ G( Q , R ) of the fuzzy total cost function G( Q , R ) and their centroid (see Proposition 3). Therefore, given the value of q 1 , q 0 , q 2 , r 1 and r2, we can find an estimate of the total cost in the fuzzy sense. Finally, we make a comparison between the crisp sense and fuzzy sense by some numerical result.

Fuzzy inventory with backorder for fuzzy order quantity

This paper investigates a group of computing schemas for economic order quantity as fuzzy values, and the corresponding optimal stock quantity of the invenyory with backorder. We express the fuzzy order quantity as the normal triangular fuzzy number (q1, q0, q2), and then we solve the aforementioned optimization problem under the constraints 0 < s ⩽ q1 < q0 < q2, where s denotes the optimizing stock quantity. We find that, after defuzzification, the total cost is slightly higher than in the crisp model; however, it permits better use of the economic fuzzy quantities arising with changes in orders, deliveries, and sales.

Fuzzy economic production for production inventory

Abstract A production cycle is defined using both production and sale, for which to a certain point the production stops until all inventories are sold out. For the planning period of T days, the function of total cost is F(q) where q represents the production quantity of each cycle. The best production quantity in the Crisp sense is q ∗ . Fuzzification of q changes to fuzzy number Q ; then, how to determine the best production quantity in the light of Q is the subject of this paper. Suppose the membership function of Q is a trapezoidal fuzzy number set (q 1 ,q 2 ,q 3 ,q 4 ) satisfying the condition of 0 1 2 3 4 , the membership function of fuzzy cost F( Q ) is μ F( Q ) (z) , and its centroid, which is thought to be the estimated total cost and minimum for the condition of 0 1 ∗ 2 ∗ 3 ∗ 4 ∗ . From trapezoidal fuzzy number set (q 1 ∗,q 2 ∗,q 3 ∗,q 4 ∗) , find out its centroid as the best production quantity.

Fuzzy inventory with or without backorder for fuzzy order quantity with trapezoid fuzzy number

Abstract The purpose of this paper is to investigate a group of computing schemas for the economic order quantity as fuzzy values of the inventory with/without backorder. We express the fuzzy order quantity as the normal trapezoid fuzzy number (q1,q2,q3,q4), and then we solve the aforementioned optimization problem. We find that, after defuzzification the total cost is slightly higher than in the crisp model; however, it permits better use of the economic fuzzy quantities arising with changes in orders, and deliveries.

Fuzzy decision making for medical diagnosis based on fuzzy number and compositional rule of inference

Abstract Klir and Yuan [2] mentioned the medical decision making problem in chapter 17. In this paper we use interval estimation to get fuzzy number r ij and from point estimation we get r ij . Set R =(r ij ) and R ∗ =( r ij ) . Let fuzzy relation of the set P of the patients and the set S of the symptoms be Q =(a ij ) and fuzzy relation of the set S of the symptoms and the set~ D of the diseases be R . From the compositional rule of inference, we have T = Q ∘ R . Therefore, we can have a fuzzy decision making for medical diagnosis. This paper changes R to R ∗ and use T ∗ = Q ∘ R ∗ to do a fuzzy decision making for medical diagnosis.

Fuzzy inventory with backorder for fuzzy total demand based on interval-valued fuzzy set

Abstract It is difficult to determine the fixed total demand r 0 in an inventory problem with backorder in a whole plan period. We will fuzzify it as R=⌈ near r 0 ⌋ . In this article, we will classify R into three kinds: (1) fuzzy total demand with triangular fuzzy number ( Section 2 ), (2) fuzzy total demand with interval-valued fuzzy set based on two triangular fuzzy numbers ( Section 3 ), (3) fuzzy total demand with interval-valued fuzzy set based on two trapezoidal fuzzy numbers ( Section 4 ). We will find the corresponding order quantities and the shortage inventories, respectively.