Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.

New Methods to Solve Fuzzy Shortest Path Problems

This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.

K-THEORETICALLY COMPLETE VON NEUMANN REGULAR RINGS

The authors introduce the concept of Ko-complete ring and study the properties of Ko-complete unit-regular rings.

Feature Selection Based on Difference and Similitude in Data Mining

Feature selection is the pretreatment of data mining. Heuristic search algorithms are often used for this subject. Many heuristic search algorithms are based on discernibility matrices, which only consider the difference in information system. Because the similar characteristics are not revealed in discernibility matrix, the result may not be the simplest rules. Although differencesimilitude（DS） methods take both of the difference and the similitude into account, the existing search strategy will cause some important features to be ignored. An improved DS based algorithm is proposed to solve this problem in this paper. An attribute rank function, which considers both of the difference and similitude in feature selection, is defined in the improved algorithm. Experiments show that it is an effective algorithm, especially for large-scale databases. The time complexity of the algorithm is O（｜ C ｜^2｜U ｜^2）.

GENERATING EXACT NONLINEAR RANKING FUNCTIONS BY SYMBOLIC-NUMERIC HYBRID METHOD

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.

Global Rank Axioms for Poset Matroids

An excellent introduction to the topic of poset matroids is due to Barnabei, Nicoletti and Pezzoli. In this paper, we investigate the rank axioms for poset matroids; thereby we can characterize poset matroids in a “global” version and a “pseudo-global” version. Some corresponding properties of combinatorial schemes are also obtained.

Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy parameters.Intuitionistic fuzzy num-ber is considered in many real-life situations,so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy numbers.In this paper,intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number.A defuzzification method is introduced based on the pro-portional probability density function associated with the corresponding membership function,as well as the complement of non-membership function.Using the proposed ranking technique,a methodology is presented for solving bi-level programming for Stackelberg game.An application example is provided to demonstrate the applica-bility of the proposed methodology,and the achieved results are compared with the existing methods.

Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of differ- ent proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable prop- erties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Lim- itations of existing ranking methods have been studied. Fur- ther for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.

A Note on Submodularity Preserved Involving the Rank Functions

In many kinds of games with economic significance,it is very important to study the submodularity of functions.In this paper,wemainly study the problem of maximizing a concave function over an intersection of two matroids.We obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some conditions.Moreover,we also present examples showing that these conditions can be satisfied.

New Results on Global Rank Axioms of Poset Matroids

An excellent introduction to the topic of poset matroids is due to M.Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.

Rank functions and state spaces of K_0

While the formulations of localization rank and stably free rank are given, the characterizations of elements are obtained for a class of VN regular ring. For a ring R, the characters of some properties of K0R are also given in terms of the state space of K0.

Simulating Temporally and Spatially Correlated Wind Speed Time Series by Spectral Representation Method

In this paper,it aims to model wind speed time series at multiple sites.The five-parameter Johnson mdistribution is deployed to relate the wind speed at each site to a Gaussian time series,and the resultant-Z(t)dimensional Gaussian stochastic vector process is employed to model the temporal-spatial correlation of mwind speeds at different sites.In general,it is computationally tedious to obtain the autocorrelation functions Z(t)(ACFs)and cross-correlation functions(CCFs)of Z(t),which are different to those of wind speed times series.In order to circumvent this correlation distortion problem,the rank ACF and rank CCF are introduced to Z(t)characterize the temporal-spatial correlation of wind speeds,whereby the ACFs and CCFs of can be analytically obtained.Then,Fourier transformation is implemented to establish the cross-spectral density matrix Z(t)mof,and an analytical approach is proposed to generate samples of wind speeds at different sites.Finally,simulation experiments are performed to check the proposed methods,and the results verify that the five-parameter Johnson distribution can accurately match distribution functions of wind speeds,and the spectral representation method can well reproduce the temporal-spatial correlation of wind speeds.

Multi-Objective Vendor Selection Problem of Supply Chain Management Under Fuzzy Environment

Survival of a company in today's competitive business environment depends mainly on its supply chain.An adequate supply chain gives a competitive edge to a com-pany.Sourcing,which is the initial stage of a supply chain,can be made efficient by making an appropriate selection of vendors.Appropriate vendor selection results not only in reduced purchasing costs,decreased production lead time,increased customer satisfaction but also in improved corporate competitiveness.In general,the vendor selection problem is a multi-objective decision-making problem that involves some quantitative and qualitative factors.So,we have considered a multi-objective ven-dor selection problem(MOV SP)with three multiple objective goals:minimization of net ordering price,minimization of rejected units and minimization of late delivered units.In most of the cases,information about the price of a unit,percentage of rejected units,percentage of late delivered units,vendor rating value and vendor quota flexibil-ity may not be known precisely due to some reasons.In this paper,imprecision in input information is handled by the concept of a simulation technique,where the parameter follows the uniform distribution.Deterministic,stochastic,a-cut and ranking function approaches are used to get the crisp value of the simulated data sets.The four differ-ent algorithms,namely-fuzzy programming,goal programming,lexicographic goal programming and D1-distance algorithm,have been used for solving the MOVSP.In last,three different types of simulated data sets have been used to illustrate the work.