Fuzzy Translations of a Fuzzy Set in UP-Algebras

In this paper, we apply the concept of fuzzy translations of a fuzzy set to UP-algebras.For any fuzzy set $\mu$ in a UP-algebra,the concepts of fuzzy $\alpha$-translations of $\mu$ of type \textrm{I} and of fuzzy $\beta$-translations of $\mu$ of type \textrm{II} are introduced, their basic properties are investigated and some useful examples are discussed.The concepts of prime fuzzy sets and of weakly prime fuzzy sets in UP-algebras are also studied.Moreover, we discuss the concepts of extensions and of intensions of a fuzzy set in UP-algebras

Another look on tense and related operators

Motivated by the classical work of Halmos on functional monadic Boolean algebras we derive three basic sup-semilattice constructions, among other things the so-called powersets and powerset operators. Such constructions are extremely useful and can be found in almost all branches of modern mathematics, including algebra, logic and topology. Our three constructions give rise to four covariant and two contravariant functors and constitute three adjoint situations we illustrate in simple examples

Decomposition theorems and extension principles for hesitant fuzzy sets

We prove a decomposition theorem for hesitant fuzzy sets, which states that every typical hesitant fuzzy set on a set can be represented by a well-structured family of fuzzy sets on that set. This decomposition is expressed by the novel concept of hesitant fuzzy set associated with a family of hesitant fuzzy sets, in terms of newly defined families of their cuts. Our result supposes the first representation theorem of hesitant fuzzy sets in the literature. Other related representation results are proven. We also define two novel extension principles that extend crisp functions to functions that map hesitant fuzzy sets into hesitant fuzzy sets

Neke nove mrežno vrednosne algebarske strukture sa komparativnom analizom različitih pristupa

In this work a comparative analysis of several approaches to fuzzy algebraic structures and comparison of previous approaches to the recent one developed at University of  Novi Sad has been done. Special attention is paid to reducts and expansions of algebraic structures in fuzzy settings. Besides mentioning all the relevant algebras and properties developed in this setting, particular new algebras and properties are developed and investigated. Some new structures, in particular Omega Boolean algebras, Omega Boolean lattices and Omega Boolean rings are developed in the framework of omega structures. Equivalences among these structures are elaborated in details. Transfers from Omega groupoids to Omega groups and back are demonstrated. Moreover, normal subgroups are introduced in a particular way. Their connections to congruences are elaborated in this settings. Subgroups, congruences and normal subgroups are investigated for Ω-groups. These are latticevalued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal Ω-subgroup is defined as a particular class in an Ω-congruence. Our main result is that the quotient groups over cuts of a normal Ω- subgroup of an Ω-group G, are classical normal subgroups of the corresponding quotient groups over G. We also describe the minimal normal Ω-subgroup of an Ω-group, and some other constructions related to Ω-valued congruences.Further results that are obtained are theorems that connect various approaches of fuzzy algebraic structures. A special notion of a generalized lattice valued Boolean algebra is introduced. The universe of this structure is an algebra with two binary, an unary and two nullary operations (as usual), but which is not a crisp Boolean algebra in general. A main element in our approach is a fuzzy  quivalence relation such that the Boolean algebras identities are approximately satisfied related to the considered fuzzy equivalence. Main properties of the new introduced notions are proved, and a connection with the notion of a structure of a generalized fuzzy lattice is provided.Ovaj rad bavi se komparativnom analizom različitih pristupa rasplinutim (fazi) algebarskim strukturama i odnosom tih struktura sa odgovarajućim klasičnim   algebrama. Posebna pažnja posvećena je poredenju postojećih pristupa ovom   problemu sa novim tehnikama i pojmovima nedavno razvijenim na Univerzitetu u Novom Sadu. U okviru ove analize, proučavana su i proširenja kao i redukti algebarskih struktura u kontekstu rasplinutih algebri. Brojne važne konkretne algebarske strukture istraživane su u ovom kontekstu, a neke nove uvedene su i ispitane. Bavili smo se detaljnim istrazivanjima Ω-grupa, sa stanovista kongruencija, normalnih podgrupa i veze sa klasicnim grupama. Nove strukture koje su u radu uvedene u posebnom delu, istrazene su sa aspekta svojstava i medusobne ekvivalentnosti. To su Ω-Bulove algebre, kao i odgo-varajuce mreže i Bulovi prsteni. Uspostavljena je uzajamna ekvivalentnost tih struktura analogno odnosima u klasičnoj algebri. U osnovi naše konstrukcije su mrežno vrednosne algebarske strukture denisane na klasičnim algebrama koje ne zadovoljavaju nužno identitete ispunjene na odgovarajucim klasičnim strukturama (Bulove algebre, prsteni, grupe itd.), već su to samo algebre istog tipa. Klasična jednakost zamenjena je posebnom kompatibilnom rasplinutom (mrežno-vrednosnom) relacijom ekvivalencije. Na navedeni nacin i u cilju koji je u osnovi teze (poredenja sa postojecim pristupima u ovoj naucnoj oblasti) proucavane su (vec denisane)  Ω-grupe. U nasim istraživanju uvedene su odgovarajuće normalne podgrupe. Uspostavljena je i istražena njihova veza sa Ω-kongruencijama. Normalna podgrupa  Ω-grupe definisana je kao posebna  klasa Ω-kongruencije. Jedan od rezultata u ovom delu je da su količničke grupe definisane pomocu nivoa Ω-jednakosti klasične normalne podgrupe odgovarajućih količničkih podgrupa polazne  -grupe. I u ovom slučaju osnovna  struktura na kojoj je denisana Ω-grupa je grupoid, ne nužno grupa. Opisane su osobine najmanje normalne podgrupe u terminima Ω-kongruencija, a date su i neke konstrukcije  Ω-kongruencija. Rezultati koji su izloženi u nastavku povezuju različite pristupe nekim mrežno- vrednosnim strukturama. Ω-Bulova algebra je uvedena na strukturi sa dve binarne, unarnom i dve nularne operacije, ali za koju se ne zahteva ispunjenost klasičnih aksioma. Identiteti za Bulove algebre važe kao mrežno-teoretske formule u odnosu na mrežno-vrednosnu jednakost. Klasicne Bulove algebre ih zadovoljavaju, ali obratno ne vazi: iz tih formula ne slede standardne aksiome za Bulove algebre. Na analogan nacin uveden je i  Ω-Bulov prsten. Glavna svojstva ovih struktura su opisana. Osnovna osobina je da se klasične Bulove algebre odnosno Bulovi prsteni javljaju kao količničke strukture na nivoima Ω -jednakosti. Veza ove strukture sa Ω-Bulovom mrežom je pokazana. Kao ilustracija ovih istraživanja, u radu je navedeno više primera

Ω-Algebarski sistemi

The research work carried out in this thesis is aimed   at fuzzifying algebraic and relational structures in the framework of Ω-sets, where Ω is a complete lattice. Therefore we attempt to synthesis universal algebra and fuzzy set theory. Our  investigations of Ω-algebraic structures are based on Ω-valued equality, satisability of identities and cut techniques. We introduce Ω-algebras, Ω-valued congruences,  corresponding quotient  Ω-valued-algebras and  Ω-valued homomorphisms and we investigate connections among these notions. We prove that there is an Ω-valued homomorphism from an Ω-algebra to the corresponding quotient Ω-algebra. The kernel of an Ω-valued homomorphism is an Ω-valued congruence. When dealing with cut structures, we prove that an Ω-valued homomorphism determines classical homomorphisms among the corresponding quotient structures over cut  subalgebras. In addition, an  Ω-valued congruence determines a closure system of classical congruences on cut subalgebras. In addition, identities are preserved under Ω-valued homomorphisms. Therefore in the framework of Ω-sets we were able to introduce Ω-attice both as an ordered and algebraic structures. By this Ω-poset is defined as an Ω-set equipped with  Ω-valued order which is  antisymmetric with respect to the corresponding Ω-valued equality. Thus defining the notion of pseudo-infimum and pseudo-supremum we obtained the definition of Ω-lattice as an ordered structure. It is also defined that the an Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality fulfilling some particular lattice Ω-theoretical formulas. Thus using axiom of choice we proved that the two approaches are equivalent. Then we also introduced the notion of complete Ω-lattice based on Ω-lattice. It was defined as a generalization of the classical complete lattice. We proved results that characterizes Ω-structures and many other interesting results. Also the connection between Ω-algebra and the notion of weak congruences is presented. We conclude with what we feel are most interesting areas for future work.Tema ovog rada je fazifikovanje algebarskih i relacijskih struktura u okviru omega- skupova, gdeje Ω kompletna mreza. U radu se bavimo sintezom oblasti univerzalne algebre i teorije rasplinutih (fazi) skupova. Naša istraživanja omega-algebarskih struktura bazirana su na omega-vrednosnoj jednakosti,zadovoljivosti identiteta i tehnici rada sa nivoima. U radu uvodimo omega-algebre,omega-vrednosne kongruencije, odgovarajuće omega-strukture, i omega-vrednosne homomorfizme i istražujemo veze izmedju ovih pojmova. Dokazujemo da postoji Ω -vrednosni homomorfizam iz Ω -algebre na odgovarajuću količničku Ω -algebru. Jezgro Ω -vrednosnog homomorfizma je Ω- vrednosna kongruencija. U vezi sa nivoima struktura, dokazujemo da Ω -vrednosni homomorfizam odredjuje klasične homomorfizme na odgovarajućim količničkim strukturama preko nivoa podalgebri. Osim toga, Ω-vrednosna kongruencija odredjuje sistem zatvaranja klasične kongruencije na nivo podalgebrama. Dalje, identiteti su očuvani u Ω- vrednosnim homomorfnim slikama.U nastavku smo u okviru Ω-skupova uveli Ω-mreže kao uredjene skupove i kao algebre i dokazali ekvivalenciju ovih pojmova. Ω-poset je definisan kao Ω -relacija koja je antisimetrična i tranzitivna u odnosu na odgovarajuću Ω-vrednosnu jednakost. Definisani su pojmovi pseudo-infimuma i pseudo-supremuma i tako smo dobili definiciju Ω-mreže kao uredjene strukture. Takodje je definisana Ω-mreža kao algebra, u ovim kontekstu nosač te strukture je bi-grupoid koji je saglasan sa Ω-vrednosnom jednakošću i ispunjava neke mrežno-teorijske formule. Koristeći aksiom izbora dokazali smo da su dva pristupa ekvivalentna. Dalje smo uveli i pojam potpune Ω-mreže kao uopštenje klasične potpune mreže. Dokazali smo još neke rezultate koji karakterišu Ω-strukture.Data je i veza izmedju Ω-algebre i pojma slabih kongruencija.Na kraju je dat prikaz pravaca daljih istrazivanja

NEGOTIATION-BASED RISK MANAGEMENT FOR PPP-BOT INFRASTRUCTURE PROJECTS

Ph.DDOCTOR OF PHILOSOPH

Exploring Locational Criteria to Optimise Biofuel Production Potential in Nigeria

Energy is one of the important building blocks of any economy and the sustainability of its supply is crucial. Renewable energy sources are being explored with the objective of harnessing their potential to address demand shortages and provide sustainable clean energy. Biofuels, as one of these renewables, continue to expand and their share in global energy consumption continues to increase. Apart from lower net carbon emissions compared to fossil fuels and their role as transitional fuel sources in global shift towards renewable energy, biofuels offer other benefits such as increasing the volume of liquid fuels, improving air quality, expanding trade, import substitution and energy diversification. Therefore, there are strong environmental and economic arguments for the Nigerian Government to embark on deployment of renewable energy, including biofuels. Despite abundant biomass resources, biofuel programmes have not been fully operationalised in the country, partly because biofuels vary in their favourability profiles which depend on local conditions and practices, as well as spatial conflicts between land designed for energy production and other land uses such as agriculture or nature reserves. Consequently, there is a need for robust and detailed approaches to this location-related problem. Although Spatial Multi-criteria Analysis (SMCA) as a support tool has been applied to biofuel production analysis, accounting for multiple stakeholder opinions has been one of the major challenges. In Nigeria, there have been few attempts to apply spatial analysis to locational problems related to biofuel production. In addition, these studies are limited in terms of scope, were based on feedstock other than energy crops, and provided superficial analysis of suitability of the identified sites. The goal of this thesis was to show how to improve the robustness and transparency of spatial analysis in Nigeria through answering some spatial questions about biofuel production, which extends our knowledge of GIS and is relevant to practice. Robustness implies detailed exploration of the required environmental criteria and incorporation of the expert decisions on the criteria preferences. This work transparently demonstrates detailed application of the combined geospatial and multi-criteria methods to make the academic contribution transferable. The technical goal of the work was to conduct spatial optimisation for biofuel production in the country through detailed assessment of environmental criteria, modelling land suitability for cultivating sweet sorghum, sugarcane, cassava, oil palm and jatropha as biofuel crops in Nigeria and modelling optimal sites for biofuel processing and/or blending. This will provide support for spatial decisions regarding establishing biofuel processing plants or expanding the existing ones. Analytical Hierarchy Process (pairwise comparison) was adopted as the multi-criteria analysis method due to its robustness regarding stakeholder inclusion. Weighted overlay was adopted as method of land suitability modelling and supply area modelling was adopted as the method of site optimisation. The analysis showed that northcentral geo-political zone of Nigeria has the largest areas of land that is very suitable for cultivating sugarcane, cassava, oil palm and jatropha, while northeast has the largest areas of land that is very suitable for cultivating sweet sorghum. Based on these, three sizes of service area were considered assuming worst, average and highest crop yields scenarios to optimise processing/blending sites. Existing petroleum depots were considered as the candidate sites. Ilorin petroleum depot was found to be the most optimal location for processing/blending biofuel in Nigeria based on all the crop yields scenarios, within 300 km service area. However, assuming worst case yields scenario within 100 km service area, Maiduguri depot was found to be the best location for sweet sorghum and sugarcane biofuel processing/blending, but Yola depot was suggested as replacement for sugarcane. Ibadan was found to be the best for oil palm and jatropha, but Ikot Abasi depot was suggested as replacement for oil palm. Aba was found to be the best for cassava, but Makurdi was suggested as replacement. This work had demonstrated how robust integration of GIS tools with MCDM techniques could improve the effectiveness of spatial decision-making process regarding positioning biofuel production in developing countries like Nigeria. It is therefore concluded that this work will serve as a point of reference for state-of-the-art application of spatial multi-criteria evaluation analysis, not only for the biofuel industry, but also for other sectors of environmental management such as river basin management, land use or settlement planning. The tendency of a biofuel programme in Nigeria to succeed would greatly be enhanced by adopting sustainability strategies along its value chain through climate smart agriculture, designing and/or adopting a suitable feedstock supply model, effective land use management, realigning policy objectives, enforcing policy directives and balancing between strong and weak sustainability strategies. This will create a conducive environment for stimulating biofuel programme, delivering energy source diversification, economic growth and sustainable development for Nigeria

Exploring Locational Criteria to Optimise Biofuel Production Potential in Nigeria

Energy is one of the important building blocks of any economy and the sustainability of its supply is crucial. Renewable energy sources are being explored with the objective of harnessing their potential to address demand shortages and provide sustainable clean energy. Biofuels, as one of these renewables, continue to expand and their share in global energy consumption continues to increase. Apart from lower net carbon emissions compared to fossil fuels and their role as transitional fuel sources in global shift towards renewable energy, biofuels offer other benefits such as increasing the volume of liquid fuels, improving air quality, expanding trade, import substitution and energy diversification. Therefore, there are strong environmental and economic arguments for the Nigerian Government to embark on deployment of renewable energy, including biofuels. Despite abundant biomass resources, biofuel programmes have not been fully operationalised in the country, partly because biofuels vary in their favourability profiles which depend on local conditions and practices, as well as spatial conflicts between land designed for energy production and other land uses such as agriculture or nature reserves. Consequently, there is a need for robust and detailed approaches to this location-related problem. Although Spatial Multi-criteria Analysis (SMCA) as a support tool has been applied to biofuel production analysis, accounting for multiple stakeholder opinions has been one of the major challenges. In Nigeria, there have been few attempts to apply spatial analysis to locational problems related to biofuel production. In addition, these studies are limited in terms of scope, were based on feedstock other than energy crops, and provided superficial analysis of suitability of the identified sites. The goal of this thesis was to show how to improve the robustness and transparency of spatial analysis in Nigeria through answering some spatial questions about biofuel production, which extends our knowledge of GIS and is relevant to practice. Robustness implies detailed exploration of the required environmental criteria and incorporation of the expert decisions on the criteria preferences. This work transparently demonstrates detailed application of the combined geospatial and multi-criteria methods to make the academic contribution transferable. The technical goal of the work was to conduct spatial optimisation for biofuel production in the country through detailed assessment of environmental criteria, modelling land suitability for cultivating sweet sorghum, sugarcane, cassava, oil palm and jatropha as biofuel crops in Nigeria and modelling optimal sites for biofuel processing and/or blending. This will provide support for spatial decisions regarding establishing biofuel processing plants or expanding the existing ones. Analytical Hierarchy Process (pairwise comparison) was adopted as the multi-criteria analysis method due to its robustness regarding stakeholder inclusion. Weighted overlay was adopted as method of land suitability modelling and supply area modelling was adopted as the method of site optimisation. The analysis showed that northcentral geo-political zone of Nigeria has the largest areas of land that is very suitable for cultivating sugarcane, cassava, oil palm and jatropha, while northeast has the largest areas of land that is very suitable for cultivating sweet sorghum. Based on these, three sizes of service area were considered assuming worst, average and highest crop yields scenarios to optimise processing/blending sites. Existing petroleum depots were considered as the candidate sites. Ilorin petroleum depot was found to be the most optimal location for processing/blending biofuel in Nigeria based on all the crop yields scenarios, within 300 km service area. However, assuming worst case yields scenario within 100 km service area, Maiduguri depot was found to be the best location for sweet sorghum and sugarcane biofuel processing/blending, but Yola depot was suggested as replacement for sugarcane. Ibadan was found to be the best for oil palm and jatropha, but Ikot Abasi depot was suggested as replacement for oil palm. Aba was found to be the best for cassava, but Makurdi was suggested as replacement. This work had demonstrated how robust integration of GIS tools with MCDM techniques could improve the effectiveness of spatial decision-making process regarding positioning biofuel production in developing countries like Nigeria. It is therefore concluded that this work will serve as a point of reference for state-of-the-art application of spatial multi-criteria evaluation analysis, not only for the biofuel industry, but also for other sectors of environmental management such as river basin management, land use or settlement planning. The tendency of a biofuel programme in Nigeria to succeed would greatly be enhanced by adopting sustainability strategies along its value chain through climate smart agriculture, designing and/or adopting a suitable feedstock supply model, effective land use management, realigning policy objectives, enforcing policy directives and balancing between strong and weak sustainability strategies. This will create a conducive environment for stimulating biofuel programme, delivering energy source diversification, economic growth and sustainable development for Nigeria

Extension principles for fuzzy set theory

JOURNAL OF INFORMATION SCIENCE