The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms

We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomial-size fuzzy circuits composed of fuzzy gates. We also introduce fuzzy proof verification systems to model the fuzzification of nondeterminism. Those models help us identify four complexity classes: Fuzzy-FPA of fuzzy functions, Fuzzy-PA and Fuzzy-NPA of fuzzy decision problems, and Fuzzy-NPAO of fuzzy optimization problems. Based on a relative approximation scheme targeting fuzzy membership degree, we formulate two notions of "reducibility" in order to compare the computational complexity of two fuzzy problems. These reducibility notions make it possible to locate the most difficult fuzzy problems in Fuzzy-NPA and in Fuzzy-NPAO.Comment: A4, 10pt, 10 pages. This extended abstract already appeared in the Proceedings of the Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS 2014) and 15th International Symposium on Advanced Intelligent Systems (ISIS 2014), December 3-6, 2014, Institute of Electrical and Electronics Engineers (IEEE), pp. 29-35, 201

PENENTUAN BILANGAN KROMATIK FUZZY PADA GRAF FUZZY GF(V,EF) MELALUI BILANGAN KROMATIK PADA CUT Gα(V,Eα)

Bilangan kromatik pada graf klasik G adalah bilangan asli terkecil k sedemikian hingga titik‐titik di G dapat diwarnai dengan k warna. Konsep graf telah digeneralisasi menjadi graf fuzzy. Terdapat beberapa tipe graf fuzzy, diantaranya graf fuzzy GF(V,EF) dengan himpunan sisi fuzzy EF dan fungsi keanggotaan μ: V x V → I. Konsep‐konsep dasar pada graf klasik juga telah digeneralisasi untuk graf fuzzy, diantaranya konsep pewarnaan dan bilangan kromatik. Pada makalah ini akan dibahas penentuan bilangan kromatik fuzzy pada graf fuzzy GF(V,EF). Penentuan bilangan kromatik ini dimulai dengan konstruksi cut‐α dari graf GF, yaitu graf klasik Gα=(V,Eα) α∈I, dengan Eα cut pada himpunan sisi EF. Langkah berikutnya penentuan bilangan kromatik χα pada Gα. Bilangan kromatik pada GF(V,EF) adalah bilangan fuzzy χ(GF) = {(x,v(x)) | x∈X}, dimana: X={1,2,…, |V|}, v(x) = maks {α∈I | x∈ Aα } untuk setiap x∈X, dan Aα = {1,2,…, χα} untuk setiap α∈I. Kata kunci: Bilangan kromatik, Graf Fuzzy GF(V,EF), cut‐Gα(V,Eα), Bilangan Kromatik Fuzz

MENENTUKAN LINTASAN DENGAN WAKTU TEMPUH TERCEPAT UNTUK RUTE PENGIRIMAN IKAN ARWANA (Studi Kasus: CV. Argo Mega Arwana)

Penentuan rute dengan waktu tempuh tercepat terhadap pengiriman ikan arwana oleh CV. Argo Mega Arwana merupakan implementasi dalam kasus lintasan pada graf. Pemilihan rute pengiriman tercepat direkomendasikan agar dapat menghindari risiko ikan kelelahan dan mati. Permasalahan tersebut direpresentasikan ke dalam graf dengan simpul awal pada graf merepresentasikan titik keberangkatan yaitu CV. Argo Mega Arwana, simpul akhir merepresentasikan titik tujuan yaitu Bandara Supadio Pontianak dan simpul-simpul lainnya merepresentasikan persimpangan antar ruas jalan. Sementara busur pada graf yang menghubungkan antar simpul merepresentasikan ruas-ruas jalan. Bobot pada sisi merupakan waktu tempuh suatu jalan yang diperoleh dari penelitian dilapangan. Waktu tempuh pada suatu jalan dapat berbeda-beda atau tidak dapat dipastikan dengan jelas karena dipengaruhi oleh padatnya kendaraan. Hari kerja dan sekolah di Pontianak mempengaruhi padatnya kendaraan. Ketidakjelasan dalam waktu tempuh ini yang masuk kedalam konsep fuzzy. Konsep fuzzy yang digunakan pada penelitian ini yaitu bilangan fuzzy segitiga. Waktu dalam bilangan fuzzy segitiga direpresentasikan kedalam kondisi cepat, sedang dan lama. Algoritma dengan konsep bilangan fuzzy segitiga yang digunakan dalam penelitian ini yaitu algoritma Chuang-Kung. Algoritma Chuang-Kung menggunakan derajat kesamaan tertinggi yang dimiliki suatu lintasan dari lintasan-lintasan yang mungkin dilalui dalam menentukan lintasan dengan waktu tempuh tercepat. Berdasarkan perhitungan menggunakan algoritma Chuang-Kung diperoleh rute dengan waktu tempuh tercepat untuk pengiriman ikan arwana dari CV. Argo Mega Arwana dengan tujuan Bandara Supadio Pontianak adalah melewati Jln. Adi Sucipto, Jln. Sungai Raya Dalam, Jln. Arteri Supadio, dan Jln. Bandara Supadio dengan waktu tempuh tercepat yaitu 9 menit 1 detik dan waktu tempuh terlama yaitu 21 menit 41 detik. Kata Kunci : Graf, Lintasan Terpendek, Bilangan Fuzzy Segitig

Coverage and invariability in fuzzy systems

This paper presents a new complex system systemic. Here, we are working in a fuzzy environment, so we have to adapt all the previous concepts and results that were obtained in a non-fuzzy environment, for this fuzzy case. The direct and indirect influences between variables will provide the basis for obtaining fuzzy and/or non-fuzzy relationships, so that the concepts of coverage and invariability between sets of variables will appear naturally. These two concepts and their interconnections will be analyzed from the viewpoint of algebraic properties of inclusion, union and intersection (fuzzy and non-fuzzy), and also for the loop concept, which, as we shall see, will be of special importance

Invariability, orbits and fuzzy attractors

In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality

Application of Fuzzy Expert Systems to Manage the Projects Time in Iranian Gas Refineries

The National Iranian Gas Company (NIGC) is one of the top ten gas companies in the gas industry in the Middle East and is comprised of 7 gas refineries. So this company needs to apply the most optimum time management methods to achieve its goals. Custom scheduling calculation of project planning uses the Critical Path Method (CPM) as a tool for Planning Projects activities. CPM is now widely used in planning and managing projects but in spite of its wide application, this method has a critical weak point of not taking into account the uncertainties in scheduling calculation. This article aims to present a precise method based on the application of Fuzzy Expert Systems in order to improve the Time Estimation Method in construction projects and in this regard, reviews the results of the implementation of this method in construction projects of Iranian Gas Refineries. The results show that the proposed method increases the accuracy of time estimation about 7 to 22 percent

Proposing an Optimum Model for Time Estimation of Construction Projects in Iranian Gas Refineries

Time management can be effective in a project when the project schedule is based on comprehensive time scheduling. In the industries with complicated processes, many uncertainties and risks affect the timing of projects. Considering the very low reliability of the project planning in certainty-based approach, using more secure models for control and interact with uncertainty should be placed on the agenda. Iranian Gas Company has been using risk management to manage probable uncertainties in construction projects but in the field of possible uncertainties, actions are very scarce. This article aims to propose an optimum model based on the integrated risk management and fuzzy expert systems in order to provide comprehensive project time estimation and in this regard, reviews the results of the implementation of this model in construction projects of Iranian gas refineries. The results show that the proposed model increases the accuracy of time estimation about 8 to 24 percent.Time management can be effective in a project when the project schedule is based on comprehensive time scheduling. In the industries with complicated processes, many uncertainties and risks affect the timing of projects. Considering the very low reliability of the project planning in certainty-based approach, using more secure models for control and interact with uncertainty should be placed on the agenda. Iranian Gas Company has been using risk management to manage probable uncertainties in construction projects but in the field of possible uncertainties, actions are very scarce. This article aims to propose an optimum model based on the integrated risk management and fuzzy expert systems in order to provide comprehensive project time estimation and in this regard, reviews the results of the implementation of this model in construction projects of Iranian gas refineries. The results show that the proposed model increases the accuracy of time estimation about 8 to 24 percent

A review on taxonomy of fuzzy graph

Fuzzy graph is a graph that incorporates fuzziness. Fuzzy graph originated from the concept of Fuzzy Set and Graph. In this paper, taxonomy of fuzzy graph is reviewed. Several results on fuzzy graph are presented together with some examples. The fuzzy graph introduced by Yeh and Bang is proven to be a special case of Rosenfeld’s fuzzy graph. Two descriptions of isomorphic crisp graph are proven to be equivalent and every crisp isomorphism of two graphs is proven to be a fuzzy isomorphism. This paper provides an underlying knowledge on fuzzy graph which is an important foundation for further development and application of fuzzy graph

Chemometrics fuzzy autocatalytic set method for halal authentication of gelatin

Fourier transform infrared (FTIR) spectroscopy is one of the established techniques in food adulteration analysis. The issue of halal authenticity of food and pharmaceutical products has become a concern among Muslims due to fraud and unknown sources of ingredients. The most common non-halal ingredient found in some food and pharmaceuticals products is porcine gelatin. In addition, there are other sources of gelatin such as bovine and fish. Fuzzy autocatalytic set (FACS) is a concept that incorporates fuzziness and autocatalytic set. The study related to the characteristics and uses of FACS method is progressing significantly, especially in the area of chemical engineering and also signal and network analysis. However, in this research, FACS is implemented on FTIR spectra of bovine, porcine, and fish gelatins since their spectra exhibit very similar patterns and thus further analysis is required to differentiate them. The spectra of the gelatin are analyzed using a new developed chemometrics technique, namely chemometrics FACS (c-FACS). Several definitions and theorems are introduced to furnish the c-FACS technique. A coded algorithm called Multisystem Dynamic Identification of Gelatin Sources is built for the technique. The algorithm is executed on the gelatins’ spectra. The results showed that each gelatin has a unique range signature of wavenumbers and porcine gelatin particularly showed distinct pattern compared to others. The efficiency and the rigorousness of the c-FACS are established when compared to the principal component analysis (PCA) method

Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory

Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical structures of FACS and its properties were explored based on the suitable concept of fuzzy and non-fuzzy metric structure and fuzzy and non-fuzzy normed structure with the structure of its graph. In other words, the possible new structures of FACS have been explored via two new insights of its metric fuzziness and its normed fuzziness. Firstly, a fuzzy detour FT3-distance between vertices in FACS was investigated whereby a quasi-pseudo-FT3-metric fuzziness on FACS which depends on this distance was established, followed by an introduction to the concept FT3-cycle space of FACS as a vector space which is then proven as a normed space. These concepts have led to the visualization of the structure of FACS in a fuzzy norm, hence some propositions and theorems were established. In addition, the study on these structures of FACS was exploited, in particular the connection with functional analysis features and the application of these structures to the clinical incineration process