This paper develops a new the weakest t-norm (Tω) fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) to evaluate green supply chain management (GSCM). Traditional DEMATEL is a popular method for making decision. In order to apply a realistic environment the fuzzy DEMATEL had to be developed for analyzing expert judgments with preferences, which are often unclear and ambiguous. The fuzzy DEMATEL usually adopts α-cut arithmetic operations to calculate results. However, general fuzzy DEMATEL model has not really handled fuzzy cause and effect relationships due to the accumulating phenomenon of fuzziness of the a-cut arithmetic. In the numerical example, using novel Tωfuzzy DEMATEL find out real cause and effect relationships with fuzzy bounds among criteria of GSCM. The Tωfuzzy DEMATEL can provide more credible information/results and analysis of across quadrants to evaluate cause and effected relationships, because the decision-maker usually wants to accurately grasp uncertain influential factors in the GSCM.

The fuzzy cross entropy of intuitionistic fuzzy sets, so-called intuitionistic cross entropy, is introduced by analogy with the cross entropy of probability distributions. This paper introduces the concepts of discrimination information and cross-entropy in the intuitionistic fuzzy sets. Based on this improved entropy measure, we add information of an intuitionistic fuzzy index and reveal an intuitive and mathematical connection between the notions of entropy for intuitionistic fuzzy sets in terms of fuzziness and intuitionism. Finally, a fault diagnosis example of the turbine has been illustrated. The example demonstrates that the proposed method cannot only diagnose the main fault types of the turbine, it can also detect useful information for future trends and multi-fault analysis.

Long-term business cycle forecasting is a very important issue in economic evaluation. This study presents a novel intuitionistic fuzzy least-squares support vector regression (IFLS-SVR) model for accurately forecasting long-term index of business cycle. Traditional support vector regression (SVR) and least-squares support vector regressions (LS-SVR) have been successfully applied in forecasting problems especially complex/nonlinear system. In this paper, the prediction model adopts two least-squares support vector regressions with intuitionistic fuzzy sets to approach fuzzy upper and lower bounds respectively, and then approach the crisp predict values. Genetic algorithms (GAs) are also employed in order to select two parameters of IFLS-SVR models. In this study, IFLS-SVR, LS-SVR and SVR are employed for the Taiwan business index forecasting. Empirical results indicate that the IFLS-SVR has better performance in terms of forecasting accuracy. Therefore, the IFLS-SVR model can efficiently provide credible long-term prediction for the Taiwan business index forecasting.

This paper presents a straightforward and useful fuzzy regression approach to estimate heat tolerance of plants by chlorophyll fluorescence measurement. The chlorophyll fluorescence measurement is an indicator of functional change of photosynthesis and is sensitive to temperature. Using the fluorescence-temperature curves, the experimenter may determine the heat tolerance (Tc) of plants by intersections of two linear regression lines. However, as traditional statistical regression analysis shows, the experiment may contain uncertain factors or phenomena such as leaf nature and growth environment, which concludes that data may vary among individual plants and different species. This research presents a fuzzy bicluster regression (FBCR) analysis with genetic algorithms, which helps derive a fuzzy intersection set and fuzzy heat tolerance of plants, in addition to the traditional statistical regression analysis. A fuzzy clustering concept and simultaneously optimal determination of data clusters is also developed. Especially, when there are nonlinear inflections in data curves, due to the imperative use of linear regression models, the traditional regression analysis may become unable to sufficiently model the uncertainties exhibited. The FBCR analysis can resolve this problem effectively due to the nonlinear tolerance of the system, even in a linear model. To demonstrate the FBCR analysis, it was applied to estimate the heat tolerance of five plant species. The results derived appeared to be more suitable than that of the conventional method. The approach may provide a useful means for the experimenters to derive more credible results from their chlorophyll fluorescence-temperature data.

In this paper a novel way to construct pairwise alignment of protein sequence is proposed. Currently in protein sequence alignment the vital problem is having too many uncertain factors and causes significant data loss while using crisp data. For this important premise, fuzzy concept is introduced and fuzziness is implemented in the matrix for 250 point accepted mutations (PAMs) in sequence aligning, and integrated with the genetic algorithm (GA). The purpose for this implementation is to reduce the effects of uncertain factor, avoid making use of crisp values or weights resulting in significant data loss, and increase solution accuracy and method suitability. Experimental results of fuzzy matrix for 250 PAM can find more continuous and identical protein sequence after sequence alignment by GA.

The problems of /spl alpha/-cut fuzzy arithmetic have been shown, like in interval arithmetic, that distinct states of fuzzy parameters (or fuzzy variable values) may be chosen and produce an overestimated fuzziness. Meanwhile, local extrema of a function may exist inside the support of fuzzy parameters and cause an underestimation of fuzziness and an illegal fuzzy number's result. Previous approaches to overcoming these problems have appeared in literature. Yet, the computational burden of these approaches became even heavier. Thus, this paper is based on the vertex method in literature and extensively proposes newly devised rules observed greatly useful for simplifying the vertex method. These rules are devised through a function partitioned into subfunctions, distinguishing the types of fuzzy parameter/variable occurrences, and types of subfunctions or functions with the various observations. The improved efficiency has been found able to significantly reduce the combination (vertex) test of the vertex method for the fuzzy parameters' /spl alpha/-cut endpoints possibly to only a few fuzzy parameters' endpoint combinations. Also as related, a procedure for the fuzzy optimization of fuzzy functions with a fuzzy blurred argument (a single variable) is examined with the vertex method as well. A proper and useful preliminary algorithm is proposed. Numerical examples with results are provided.

Fuzzy weighted average (FWA), which can be applied to various fields such as engineering design, decision analysis, etc., and as function of fuzzy numbers, is suitable for the problem of multiple occurrences of fuzzy parameters. Additional fuzziness may be introduced in the$alpha$-cut arithmetic. This paper reviews and compares discrete algorithms for the FWAs in both theoretical comparison and numerical comparisons, as opposed to the linear programming algorithms that may be efficient but require the help of linear programming software. An alternative efficient algorithm is also proposed. The algorithm introduces an all-candidate (criteria ratings) weights-replaced benchmark adjusting procedure other than a binary (dichotomy) search in the existing methods. The theoretical worst-case comparison shows that the algorithms of Guu and Guh and our alternative algorithm require the same order of calculation complexity$O(n)$, where$n$is the number of FWA terms. Yet, the Guh algorithm always requires$2(n-1)$calculations to be performed. The algorithm of Guu requires the elemental comparison complexity$O(n)$, and is superior to the other algorithms, in the worst case. On the other hand, our alternative algorithm and Lee and Park algorithm have the same comparison complexity$O(nlog n)$. Yet, our alternative algorithm requires$O(n)$calculation complexity which is better than$O(nlog n)$of the Lee and Park algorithm. The numerical experiments show that the algorithm of Guu and our alternative algorithm generally perform and converge faster by requiring fewer calculations than that of Lee and Park's algorithm. The alternative algorithm requires a slightly smaller number of calculations than that of the Guu algorithm, due to the use of the convergent benchmark adjustment procedure rather than a somewhat fixed binary search. Conversely, in the number of element comparisons, Lee and Park's algorithm is shown numerically generally slightly better than the alternative algorithm due to the simple binary search scheme used. The alternative algorithm also requires fewer comparisons than that of the Guu algorithm. Furthermore, in comparison of the average CPU time requirements, the ranks of the results of these algorithms are consistent with those of the algorithms for the average numbers of calculations. In general, the alternative algorithm may provide an efficient alternative algorithm to the FWAs. In the worse-case situation, the Guu algorithm still may be considered as an efficient alternative.